Simulation

class: center, middle, title-slide

.title[
# Simulation
]
.author[
### Luke Tierney
]
.institute[
### University of Iowa
]
.date[
### 2023-05-19
]

---

layout: true

$$
\renewcommand{\Real}{\mathbb{R}}
\renewcommand{\Norm}[1]{\|{#1}\|}
\renewcommand{\Var}{\text{Var}}
\newcommand{\Cov}{\text{Cov}}
$$

## Computer Simulation
---

Computer simulations are experiments performed on the computer using
computer-generated random numbers.

Simulation is used to

* study the behavior of complex systems such as
 
    * biological systems;
    * ecosystems;
    * engineering systems;
    * computer networks;

* compute values of otherwise intractable quantities such as integrals;

* maximize or minimize the value of a complicated function;

* study the behavior of statistical procedures;

* implement novel methods of statistical inference.

---

Simulations need

* uniform random numbers;

* non-uniform random numbers;

* random vectors, stochastic processes, etc.;

* techniques to design good simulations;

* methods to analyze simulation results.

---
layout: true
## Uniform Random Numbers
---

The most basic distribution is the uniform distribution on `$[0,1]$`.

Ideally we would like to be able to obtain a sequence of
independent draws from the uniform distribution on `$[0,1]$`.

Since we can only use finitely many digits, we can also work with:

* A sequence of independent discrete uniform random numbers on
  `$\{0, 1, \dots, M-1\}$` or `$\{1, 2, \dots, M\}$` for some large `$M$`.

* A sequence of independent random bits with equal probability for 0
  and 1.

Some methods are based on physical processes such as:

* [Nuclear decay](https://www.fourmilab.ch/hotbits/).

* [Atmospheric noise](https://www.random.org/); the R package
  [`random`](https://cran.r-project.org/package=random)
  provides an interface.

* Air turbulence over disk drives or thermal noise in a
  semiconductor (Toshiba Random Master PCI device)

* Event timings in a computer (Linux `/dev/random`).

---

.pull-left[
### Using `/dev/random` from R

```r
devRand <- file("/dev/random", open = "rb")
U <- function() {
    d <- readBin(devRand, "integer")
    (as.double(d) + 2^31) / 2^32
}

x <- numeric(1000)
for (i in seq_along(x)) x[i] <- U()
hist(x)

y <- numeric(1000)
for (i in seq_along(x)) y[i] <- U()
plot(x, y)

close(devRand)
```
]

.pull-right[
<img src="img/devrand1.png" width="50%" style="display: block; margin: auto;" /><img src="img/devrand2.png" width="50%" style="display: block; margin: auto;" />
]

---

### Issues with Physical Generators

They can be very slow.

Not reproducible except by storing all values.

The distribution is usually not exactly uniform; can be off by enough
to matter.

Departures from independence may be large enough to matter.

Mechanisms, defects,  are hard to study.

They can be improved by combining with other methods.

---
layout: true
## Pseudo-Random Numbers
---

Pseudo-random number generators produce a sequence of numbers that is

* not random;

* easily reproducible;

* "unpredictable;" "looks random";

* behaves in many respects like a sequence of independent draws
  from a (discretized) uniform `$[0,1]$` distribution;

* fast to produce.

---

Pseudo-random generators come in various qualities

.pull-left[
* Simple generators

* easy to implement;
    * run very fast;
    * easy to study theoretically;
    * usually have known, well understood flaws.
{{content}}
]
--

* More complex

* often based on combining simpler ones;
    * somewhat slower but still very fast;
    * sometimes possible to study theoretically, often not;
    * guaranteed to have flaws; flaws may not be well understood (yet).

.pull-right[
* [Cryptographic strength](https://www.schneier.com/academic/fortuna/)

* often much slower, more complex;
    * thought to be of higher quality;
    * may have legal complications;
    * weak generators can enable exploits; this was an [issue in iOS
      7](https://threatpost.com/weak-random-number-generator-threatens-ios-7-kernel-exploit-mitigations/104757/).
{{content}}
]
--

We use mostly generators in the first two categories.
{{content}}
--

Some argue we should move to cryptographic strength ones.

---

### General Properties

.pull-left[
Most pseudo-random number generators produce a sequence of integers
`$x_1, x_2, \dots$` in the range `$\{0, 1, \dots, M-1\}$` for some `$M$`
using a recursion of the form

`\begin{equation*}
  x_n = f(x_{n-1}, x_{n-2}, \dots, x_{n-k})
\end{equation*}`
{{content}}
]
--

Values `$u_1, u_2, \dots$` are then produced by

`\begin{equation*}
  u_i = g(x_{di}, x_{di-1}, \dots, x_{di - d + 1})
\end{equation*}`
{{content}}
--

Common choices of `$M$` are

* `$M = 2^{31}$` or `$M = 2^{32}$`
* `$M = 2^{31} - 1$`, a _Mersenne prime_
* `$M = 2$` for bit generators

.pull-right[
The value `$k$` is the _order_ of the generator
{{content}}
]
--

The set of the most recent `$k$` values is the _state_ of the
generator.
{{content}}
--

The initial state `$x_1, \dots, x_k$` is called the _seed_.
{{content}}
--

Since there are only finitely many possible states, eventually these
generators will repeat.
{{content}}
--

The length of a cycle is called the _period_ of a generator.
{{content}}
--

The maximal possible period is on the order of `$M^k$`

---

Needs change:

* As computers get faster, larger, more complex simulations are run.

* A generator with period `$2^{32}$` used to be good enough.

* A current computer can run through `$2^{32}$` pseudo-random numbers in
  under one minute.

* Most generators in current use have periods `$2^{64}$` or more.

* Parallel computation also raises new issues.

---

### Linear Congruential Generators

.pull-left[
A linear congruential generator is of the form

`\begin{equation*}
  x_i = (a x_{i-1} +c) \mod M
\end{equation*}`

with `$0 \le x_i < M$`.
{{content}}
]
--

* `$a$` is the _multiplier_
* `$c$` is the _increment_
* `$M$` is the _modulus_
{{content}}
--

A multiplicative generator is of the form

`\begin{equation*}
  x_i = a x_{i-1} \mod M
\end{equation*}`

with `$0 < x_i < M$`.

.pull-right[
A linear congruential generator has full period `$M$` if and only if
three conditions hold:

* `$\gcd(c,M) = 1$`
* `$a \equiv 1 \mod p$` for each prime factor `$p$` of `$M$`
* `$a \equiv 1 \mod 4$` if 4 divides `$M$`
{{content}}
]
--

A multiplicative generator has period at most `$M-1.$`
{{content}}
--

Full period is achieved if and only if `$M$` is prime and `$a$` is a
_primitive root modulo `$M$`_, i.e. `$a \neq 0$` and

`$$a^{(M-1)/p} \not \equiv 1 \mod M$$`

for each prime factor `$p$` of `$M-1$`.

---

#### Examples

.pull-left[
Lewis, Goodman, and Miller ("minimal standard" of Park and Miller):
{{content}}
]
--

`\begin{align*}
  x_i &= 16807 x_{i-1} \mod (2^{31}-1)\\
      &= 7^5 x_{i-1} \mod (2^{31}-1)
\end{align*}`
{{content}}
--

This has reasonable properties.
{{content}}
--

Period `$2^{31}-2 \approx 2.15 * 10^9$` is very
short for modern computers.

.pull-right[
RANDU:
{{content}}
]
--

`\begin{equation*}
  x_i = 65538 x_{i-1} \mod 2^{31}
\end{equation*}`
{{content}}
--

Period is only `$2^{29}$` but that is the least of its problems:
{{content}}
--

`\begin{equation*}
  u_{i+2} - 6 u_{i+1} + 9 u_{i} = \text{an integer}
\end{equation*}`
{{content}}
--

So `$(u_{i}, u_{i+1}, u_{i+2})$` fall on 15 parallel planes.

---

<!--
In `xlispstat`:

(load-data "randu")
(load-example "addhandrotate")
(spin-plot randu)
-->

.pull-left[
Using the `randu` data set and the `rgl` package:

```r
library(rgl)
points3d(randu)
par3d(FOV = 1)  ## removes perspective distortion
```
]

.pull-right[

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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz/vNormal.w), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i])\n        lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - 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vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true}},"evals":[],"jsHooks":[]}</script>
]

---

.pull-left[
With a larger number of points:

```r
seed <- as.double(1)
RANDU <- function() {
    seed <<- ((2^16 + 3) * seed) %% (2^31)
    seed / (2^31)
}

U <- matrix(replicate(10000 * 3, RANDU()),
            ncol = 3,
            byrow = TRUE)
clear3d()
points3d(U)
par3d(FOV = 1)
```
]

.pull-right[
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+OQPqsHPT8BLWI/BMknPwshez8itXw/L6vAPTIi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\nYD5PRsA+7h6QPsp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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz/vNormal.w), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i])\n        lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, textureColor.a);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*textureColor.a);\n#endif\n \n#endif\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true}},"evals":[],"jsHooks":[]}</script>
]

This generator used to be the default generator on IBM 360/370 and DEC
PDP11 machines.

Some examples are available
[on line](../examples/sim.Rmd).

---

#### Lattice Structure

All linear congruential sequences have a _lattice structure_.

Methods are available for computing characteristics, such as maximal
distance between adjacent parallel planes.

Values of `$M$` and `$a$` can be chosen to achieve good lattice structure
for `$c = 0$` or `$c = 1$`; other values of `$c$` are not particularly
useful.

---

### Shift-Register Generators

Shift-register generators (also called Tauseworth or feedback-shift
generators) take the form

`\begin{equation*}
  x_i = a_1 x_{i-1} + a_2 x_{i-2} + \dots + a_p x_{i-p} \mod 2
\end{equation*}`

for binary constants `$a_1, \dots, a_p$`.

Values in `$[0,1]$` are often constructed as

`\begin{equation*}
  u_i = \sum_{s=1}^L 2^{-s}x_{ti + s}
  = 0.x_{it+1}x_{it+2}\dots x_{it+L}
\end{equation*}`

for some `$t$` and `$L \le t$`.  `$t$` is the _decimation_.

The maximal possible period is `$2^p-1$` since all zeros must be
excluded.

---

The maximal period is achieved if and only if the polynomial

`\begin{equation*}
  z^p + a_1 z^{p-1} + \dots + a_{p-1} z + a_p
\end{equation*}`

is irreducible over the finite field of size 2.

Theoretical analysis is based on `$k$`-distribution:

A sequence of `$M$` bit integers with period `$2^p-1$` is
`$k$`-_distributed_ if every `$k$`-tuple of integers appears `$2^{p-kM}$`
times, except for the zero tuple, which appears one time fewer.

Generators are available that have high periods and good
`$k$`-distribution properties.

---

### Lagged Fibonacci Generators

Lagged Fibonacci generators are of the form

`\begin{equation*}
  x_i = (x_{i - k} \circ x_{i - j}) \mod M
\end{equation*}`

for some binary operator `$\circ$`.

Knuth recommends

`\begin{equation*}
  x_i = (x_{i - 100} - x_{i-37}) \mod 2^{30}
\end{equation*}`

There are some regularities if the full sequence is used.

One recommendation is to generate in batches of 1009 and use only the
first 100 in each batch.

Initialization requires some care.

---

### Combined Generators

Combining several generators may produce a new generator with better
properties.

Combining generators can also fail miserably.

Theoretical properties are often hard to develop.

---

#### Examples

**Wichmann-Hill** generator:

`\begin{align*}
  x_i &= 171 x_{i-1} \mod 30269\\
  y_i &= 172 y_{i-1} \mod 30307\\
  z_i &= 170 z_{i-1} \mod 30323
\end{align*}`

and

`\begin{equation*}
  u_i = \left(\frac{x_i}{30269} + \frac{y_i}{30307} + \frac{z_i}{30232}\right)
  \mod 1
\end{equation*}`

The period is around `$10^{12}$`.

This turns out to be equivalent to a multiplicative generator with
modulus `$M = 27,817,185,604,309$`.

Marsaglia's **Super-Duper**, used in S-PLUS and others, combines a linear
congruential and a feedback-shift generator.

---

### Other Generators

Mersenne twister (currently the default in R);

Marsaglia multicarry;

Parallel generators:

* [SPRNG](http://www.sprng.org/).

* [L'Ecuyer, Simard, Chen, and Kelton](http://www.iro.umontreal.ca/~lecuyer/myftp/streams00/)

---

### Pseudo-Random Number Generators in R

R provides a number of different basic generators:

* **Wichmann-Hill:** Period around `$10^{12}$`

* **Marsaglia-Multicarry:** Period at least `$10^{18}$`

* **Super-Duper:** Period around `$10^{18}$` for most seeds; similar to
  S-PLUS

* **Mersenne-Twister:** Period `$2^{19937} - 1 \approx 10^{6000}$`;
  equidistributed in 623 dimensions; current default in R.

* **Knuth-TAOCP:** Version from second edition of _The Art of
    Computer Programming, Vol. 2_; period around `$10^{38}$`.

* **Knuth-TAOCP-2002:** From third edition; differs in
  initialization.

* **L'Ecuyer-CMRG:** A _combined multiple-recursive generator_ from
  L'Ecuyer (1999). The period is around `$2^{191}$`. This provides the
  basis for the multiple streams used in package `parallel`.

---

* **user-supplied:** Provides a mechanism for installing your own
  generator; used for parallel generation by

* `rsprng` package interface to SPRNG
    * `rlecuyer` package interface to L'Ecuyer, Simard, Chen,
      and Kelton system
    * `rstreams` package, another interface to L'Ecuyer et al.

---

### Testing Generators

All generators have flaws; some are known, some are not (yet).

Tests need to look for flaws that are likely to be important in
realistic statistical applications.

Theoretical tests look for

* bad lattice structure
--

* lack of `$k$`-distribution
--

* other tractable properties

Statistical tests look for simple simulations where pseudo-random
number streams produce results unreasonably far from known answers.

Some batteries of tests:

* [DIEHARD](https://web.archive.org/web/19971024144607/http://stat.fsu.edu/pub/diehard/)
* [DIEHARDER](https://www.phy.duke.edu/~rgb/General/dieharder.php)
* [NIST Test Suite](https://csrc.nist.gov/groups/ST/toolkit/rng/)
* [TestU01](http://www-labs.iro.umontreal.ca/~lecuyer/)

---

### Issues and Recommendations

Good choices of generators change with time and technology:

* Faster computers need longer periods.

* Parallel computers need different methods.

All generators are flawed

* Bad simulation results due to poor random number generators are very
  rare; coding errors in simulations are not.

* Testing a generator on a similar problem with known answers is a
  good idea (and may be useful to make results more accurate).

* Using multiple generators is a good idea; R makes this easy to do.

* Be aware that some generators can produce uniforms equal to 0 or 1
  (I believe R's will not).

---

It is a good idea to avoid methods that are sensitive to low order bits.

In probability theory, if `$U$` is uniformly distributed on `$[0, 1]$`
and `$X_1, X_2, \dots$` is the (infinite) sequence of binary digits
in the binary expansion of `$U$`, then `$X_1, X_2, \dots$` are IID
Bernoulli with success probability 1/2.

* This is not true for computer-generated uniform "random" variables.

* It may be a reasonable approximation for the first 27-31 bits
  (depending on the generator).

* The best any uniform generator returning floating point values could
  possibly do is produce 53 good bits of randomness; most do not.

Again some examples are available
[on line](../examples/sim.Rmd).

---

### Reproducible Random Numbers in R

For many reasons, including debugging, it is important to be able to
_exactly_ reproduce the results of a simulation.

R provides three levels of control:

* `set.seed` resets the seed of the current generator.

* `RNGkind` can be used so set the uniform generator, the generation
  strategy for normals, and the generation strategy used by `sample`.
  More possible adjustments might be added in the future.

* `RNGversion` can be used to request the `RNGkind` settings in effect
  for a particular R version.

---

You can use this code to ensure that subsequent code run in your
session will produce identical random numbers in current and future R
releases:

```r
RNGversion("4.1.0")
set.seed(54321)
```

Keep in mind:

* This may not be sufficient if parallel computations can
  non-deterministically vary the order in which the random number
  stream is accessed.

* Numerical changes in updated code that operates on random numbers
  can change results.

---
layout: true
## Non-Uniform Random Variate Generation
---

Starting point: Assume we can generate a sequence of independent
uniform `$[0,1]$` random variables.

Develop methods that generate general random variables from uniform
ones.

.pull-left[
Considerations:
{{content}}
]
--

* Simplicity, correctness;
{{content}}
--

* Accuracy, numerical issues;
{{content}}
--

* Speed:

* Setup;
    * Generation.

.pull-right[
General approaches:
{{content}}
]
--

* Univariate transformations;
{{content}}
--

* Multivariate transformations;
{{content}}
--

* Mixtures;
{{content}}
--

* Accept/Reject methods.

---

.pull-left[
### Inverse CDF Method
{{content}}
]
--

Suppose `$F$` is a cumulative distribution function (CDF).
{{content}}
--

Define the inverse CDF as

`\begin{equation*}
  F^{-}(u) = \min \{x: F(x) \ge u\}
\end{equation*}`
{{content}}
--

If `$U \sim \text{U}[0,1]$` then `$X = F^{-}(U)$` has CDF `$F$`.

.pull-right[
<img src="img/invcdf.png" width="90%" style="display: block; margin: auto;" />
]

---

#### Proof

Since `$F$` is right continuous, the minimum is attained.

Therefore
`$F(F^{-}(u)) \ge u$` and

`\begin{equation*}
F^{-}(F(x)) = \min\{y:F(y) \ge F(x)\}.
\end{equation*}`

`\begin{equation*}
  \{(u,x): F^{-}(u) \le x\} =     \{(u,x): u \le F(x)\}
\end{equation*}`

and thus

`\begin{equation*}
  P(X \le x) = P(F^{-}(U) \le x) = P(U \le F(x)) = F(x).
\end{equation*}`

---

#### Example: Unit Exponential Distribution

The unit exponential CDF is

`\begin{equation*}
  F(x) = 
  \begin{cases}
    1-e^{-x} & x > 0\\
    0 & \text{otherwise}
  \end{cases}
\end{equation*}`

with inverse CDF

`\begin{equation*}
  F^{-}(u) = -\log(1-u)
\end{equation*}`

So `$X = -\log(1-U)$` has an exponential distribution.

Since `$1-U \sim \text{U}[0,1]$`, `$-\log U$` also has a unit exponential
distribution.

If the uniform generator can produce 0, then these should be rejected.

---

#### Example: Standard Cauchy Distribution

The CDF of the standard Cauchy distribution is

`\begin{equation*}
  F(x) = \frac{1}{2} + \frac{1}{\pi}\arctan(x)
\end{equation*}`

with inverse CDF

`\begin{equation*}
  F^{-}(u) = \tan(\pi(u-1/2))
\end{equation*}`

So `$X = \tan(\pi(U-1/2))$` has a standard Cauchy distribution.

---

An alternative form is: Let `$U_1, U_2$` be independent `$\text{U}[0,1]$`
random variables and set

`\begin{equation*}
  X =  
  \begin{cases}
     \tan(\pi(U_2/2) & U_1 \ge 1/2\\
     -\tan(\pi(U_2/2) & U_1 < 1/2\\
  \end{cases}
\end{equation*}`

* `$U_1$` produces a random sign

* `$U_2$` produces the magnitude

* This will preserve fine structure of `$U_2$` near zero, if there is any.

---

#### Example: Standard Normal Distribution

The CDF of the standard normal distribution is

`\begin{equation*}
  \Phi(x) = \int_{-\infty}^x \frac{1}{\sqrt{2\pi}} e^{-z^2/2} dz
\end{equation*}`

and the inverse CDF is `$\Phi^{-1}$`.

Neither `$\Phi$` nor `$\Phi^{-1}$` are available in closed form.

Excellent numerical routines are available for both.

---

Inversion is currently the default method for generating standard
normals in R.

The inversion approach uses two uniforms to generate one
higher-precision uniform via the code

```c
    case INVERSION:
#define BIG 134217728 /* 2^27 */
        /* unif_rand() alone is not of high enough precision */
        u1 = unif_rand();
        u1 = (int)(BIG*u1) + unif_rand();
        return qnorm5(u1/BIG, 0.0, 1.0, 1, 0);
```

---

#### Example: Geometric Distribution

The geometric distribution with PMF
`$f(x) = p(1-p)^x$` for `$x = 0, 1, \dots$`, has CDF

`\begin{equation*}
  F(x) = 
  \begin{cases}
    1 - (1 - p)^{\lfloor x + 1\rfloor} & x \ge 0\\
    0 & x < 0
  \end{cases}
\end{equation*}`

where `$\lfloor y \rfloor$` is the integer part of `$y$`.

The inverse CDF is

`\begin{align*}
  F^{-}(u) &= \lceil \log(1-u)/ \log(1-p) \rceil - 1\\
  &= \lfloor \log(1-u)/ \log(1-p) \rfloor & \text{except at the jumps}
\end{align*}`

for `$0 < u < 1$`.

So `$X = \lfloor \log(1-U)/ \log(1-p) \rfloor$` has a
geometric distribution with success probability `$p$`.

---

Other possibilities:

`\begin{equation*}
  X = \lfloor \log(U)/ \log(1-p) \rfloor
\end{equation*}`

`\begin{equation*}
  X = \lfloor -Y / \log(1-p) \rfloor
\end{equation*}`

where `$Y$` is a unit exponential random variable.

---

#### Example: Truncated Normal Distribution

Suppose `$X \sim \text{N}(\mu, 1)$` and

`\begin{equation*}
  Y \sim X | X > 0.
\end{equation*}`

The CDF of `$Y$` is

`\begin{equation*}
  F_Y(y) =
  \begin{cases}
    \frac{P(0 < X \le y)}{P(0 < X)} & y \ge 0\\
    0 & y < 0
  \end{cases} =
  \begin{cases}
    \frac{F_X(y) - F_X(0)}{1 - F_X(0)} & y \ge 0\\
    0 & y < 0
  \end{cases}.
\end{equation*}`

The inverse CDF is

`\begin{equation*}
  F_Y^{-1}(u) = F_X^{-1}(u(1-F_X(0)) + F_X(0)) = F_X^{-1}(u + (1-u)F_X(0)).
\end{equation*}`

---

An R function corresponding to this definition is

```r
Q1 <- function(p, m) qnorm(p + (1 - p) * pnorm(0, m), m)
```
--

This seems to work well for positive `$\mu$` but not for negative values
far from zero:

```r
Q1(0.5, c(1, 3, 5, 10, -10))
## [1]  1.200174  3.001692  5.000000 10.000000       Inf
```
--

The reason is that `pnorm(0, -10)` is rounded to one.

---

A mathematically equivalent formulation of the inverse CDF is

`\begin{equation*}
  F_Y^{-1}(u) = F_X^{-1}(1 - (1 - u)(1 - F_X(0)))
\end{equation*}`

which leads to

```r
Q2 <- function(p, m)
    qnorm((1 - p) * pnorm(0, m, lower.tail = FALSE),
          m, lower.tail = FALSE)
```

and

```r
Q2(0.5, c(1, 3, 5, 10, -10))
## [1]  1.20017369  3.00169185  5.00000036 10.00000000
## [5]  0.06841184
```

---

#### Issues

In principle, inversion can be used for any distribution.

Sometimes routines are available for `$F^{-}$` but are quite expensive:

```r
system.time(rbeta(1000000, 2.5, 3.5))
##    user  system elapsed 
##   0.083   0.000   0.082
system.time(qbeta(runif(1000000), 2.5, 3.5))
##    user  system elapsed 
##   1.234   0.004   1.238
```

`rbeta` is about 20 times faster than inversion.

---

If `$F^{-}$` is not available but `$F$` is, then one can solve the
equation `$u=F(x)$` numerically for `$x$`.

Accuracy of `$F$` or `$F^{-}$` may be an issue, especially when writing
code for a parametric family that is to work well over a wide
parameter range.

Even when inversion is costly,

* the cost of random variate generation may be a small fraction of
  the total cost of a simulation;

* using inversion creates a simple relation between the variables
  and the underlying uniforms that may be useful.

---

### Multivariate Transformations

Many distributions can be expressed as the marginal distribution of a
function of several variables.

#### Box-Muller Method for the Standard Normal Distribution

Suppose `$X_1$` and `$X_2$` are independent standard normals.

The polar coordinates `$\theta$` and `$R$` are independent,

* `$\theta$` is uniform on `$[0,2\pi)$`;
--

* `$R^2$` is `$\chi_2^2$`, which is exponential with mean 2.

So if `$U_1$` and `$U_2$` are independent and uniform on `$[0,1]$`, then

`\begin{align*}
  X_1 &= \sqrt{-2\log U_1} \cos(2 \pi U_2)\\
  X_2 &= \sqrt{-2\log U_1} \sin(2 \pi U_2)
\end{align*}`

are independent standard normals.

This is the _Box-Muller method_.

---

#### Polar Method for the Standard Normal Distribution

The trigonometric functions can be somewhat slow to compute.

Suppose `$(V_1,V_2)$` is uniform on the unit disk

`\begin{equation*}
  \{(v_1,v_2): v_1^2 + v_2^2 \le 1\}
\end{equation*}`

Let `$R^2 = V_1^2 + V_2^2$` and

`\begin{align*}
  X_1 &= V_1 \sqrt{-(2\log{R^2})/R^2}\\
  X_2 &= V_2 \sqrt{-(2\log{R^2})/R^2}
\end{align*}`

Then `$X_1, X_2$` are independent standard normals.

This is the _polar method_ of Marsaglia and Bray.

---

Generating points uniformly on the unit disk can be done using
_rejection sampling_, or _accept/reject sampling:_

&nbsp;&nbsp;**repeat**<BR>
&nbsp;&nbsp;&nbsp;&nbsp;generate independent `$V_1, V_2 \sim \text{U}(-1,1)$`<BR>
&nbsp;&nbsp;**until** `$V_1^2 + V_2^2 \le 1$`<BR>
&nbsp;&nbsp;**return** `$(V_1, V_2)$`

This independently generates pairs `$(V_1, V_2)$` uniformly on the
square `$(-1,1) \times (-1,1)$` until the result is inside the unit
disk.

* The resulting pair is uniformly distributed on the unit disk.

* The number of pairs that need to be generated is a geometric
  variable with success probability
  `$$p = \frac{\text{area of disk}}{\text{area of square}} = \frac{\pi}{4}$$`

* The expected number of generations needed is `$1/p = 4/\pi = 1.2732$`.

* The number of generations needed is independent of the final
  pair.

---

#### Polar Method for the Standard Cauchy Distribution

The ratio of two independent standard normals has a Cauchy distribution.

Suppose two standard normals are generated by the polar method,

`\begin{align*}
  X_1 &= V_1 \sqrt{-(2\log{R^2})/R^2}\\
  X_2 &= V_2 \sqrt{-(2\log{R^2})/R^2}
\end{align*}`

with `$R^2 = V_1^2 + V_2^2$` and `$(V_1,V_2)$` uniform on the unit disk.

Then

`\begin{equation*}
  Y = \frac{X_1}{X_2} = \frac{V_1}{V_2}
\end{equation*}`

is the ratio of the two coordinates of the pair that is uniformly
distributed on the unit disk.

This idea leads to a general method, the _Ratio-of-Uniforms method_.

---

#### Student's t Distribution

.pull-left[
Suppose

* `$Z$` has a standard normal distribution,
* `$Y$` has a `$\chi_\nu^2$` distribution,
* `$Z$` and `$Y$` are independent.
{{content}}
]
--

Then

`\begin{equation*}
  X = \frac{Z}{\sqrt{Y/\nu}}
\end{equation*}`

has a `$t$` distribution with `$\nu$` degrees of freedom.

.pull-right[
To use this representation we will need to be able to generate from a
`$\chi_\nu^2$` distribution, which is a `$\text{Gamma}(\nu/2,2)$`
distribution.
]

---

#### Beta Distribution

.pull-left[
Suppose `$\alpha > 0$`, `$\beta > 0$`, and

* `$U \sim \text{Gamma}(\alpha, 1)$`
* `$V \sim \text{Gamma}(\beta, 1)$`
* `$U, V$` are independent
{{content}}
]
--

Then

`\begin{equation*}
  X = \frac{U}{U+V}
\end{equation*}`

has a `$\text{Beta}(\alpha, \beta)$` distribution.

---

#### F Distribution

.pull-left[
Suppose `$a > 0$`, `$b > 0$`, and

* `$U \sim \chi_a^2$`
* `$V \sim \chi_b^2$`
* `$U, V$` are independent
{{content}}
]
--

Then

`\begin{equation*}
  X = \frac{U/a}{V/b}
\end{equation*}`

has an F distribution with `$a$` and `$b$` degrees of freedom.

.pull-right[
Alternatively, if `$Y \sim \text{Beta}(a/2, b/2)$`, then

`\begin{equation*}
  X = \frac{b}{a}\frac{Y}{1-Y}
\end{equation*}`

has an F distribution with `$a$` and `$b$` degrees of freedom.
]

---

#### Non-Central t Distribution

.pull-left[
Suppose

* `$Z \sim \text{N}(\mu, 1)$`,
* `$Y \sim \chi_\nu^2$`,
* `$Z$` and `$Y$` are independent.
{{content}}
]
--

Then

`\begin{equation*}
  X = \frac{Z}{\sqrt{Y/\nu}}
\end{equation*}`

has non-central `$t$` distribution with `$\nu$` degrees of freedom and
non-centrality parameter `$\mu$`.

---

#### Non-Central Chi-Square Distribution

.pull-left[
Suppose

* `$Z_1, \dots, Z_k$` are independent
* `$Z_i \sim \text{N}(\mu_i,1)$`
{{content}}
]
--

Then

`\begin{equation*}
  Y = Z_1^2 + \dots + Z_k^2
\end{equation*}`

has a non-central chi-square distribution with `$k$` degrees of freedom
and non-centrality parameter

`\begin{equation*}
  \delta = \mu_1^2 + \dots + \mu_k^2
\end{equation*}`

.pull-right[
An alternative characterization:
{{content}}
]
--

If `$\widetilde{Z}_1, \dots, \widetilde{Z}_k$` are independent standard
normals then

`\begin{align*}
  Y &= (\widetilde{Z}_1 + \sqrt{\delta})^2 + \widetilde{Z}_2^2
  \dots + \widetilde{Z}_k^2\\
  &= (\widetilde{Z}_1 + \sqrt{\delta})^2 + \sum_{i=2}^k \widetilde{Z}_i^2
\end{align*}`

has a non-central chi-square distribution with `$k$` degrees of freedom
and non-centrality parameter `$\delta$`.

---

#### Non-Central F Distribution

.pull-left[
The non-central F is of the form

`\begin{equation*}
  X = \frac{U/a}{V/b}
\end{equation*}`

where `$U$`, `$V$` are independent, `$U$` is a non-central `$\chi_a^2$` and
`$V$` is a central `$\chi_b^2$` random variable.
]

---

#### Bernoulli and Binomial Distributions

.pull-left[
Suppose `$p \in [0,1]$`, `$U \sim \text{U}[0,1]$`, and

`\begin{equation*}
  X = 
  \begin{cases}
    1 & U \le p\\
    0 & \text{otherwise}
  \end{cases}
\end{equation*}`
{{content}}
]
--

Then `$X$` bas a `$\text{Bernoulli}(p)$` distribution.
{{content}}
--

If `$Y_1, \dots, Y_n$` are independent `$\text{Bernoulli}(p)$` random
variables, then

`\begin{equation*}
  X = Y_1 + \dots + Y_n
\end{equation*}`

has a  `$\text{Binomial}(n,p)$` distribution.

.pull-right[
For small `$n$` this is an effective way to generate binomials.
]

---

.pull-left[
### Mixtures and Conditioning
{{content}}
]
--

Many distributions can be expressed using a hierarchical structure:

`\begin{align*}
  X|Y &\sim f_{X|Y}(x|y)\\
  Y &\sim f_Y(y)
\end{align*}`
{{content}}
--

The marginal distribution of `$X$` is called a _mixture
  distribution_.
{{content}}
--
  
We can generate `$X$` by

&nbsp;&nbsp;**Generate** `$Y$` from `$f_Y(y)$`.<BR>
&nbsp;&nbsp;**Generate** `$X|Y=y$` from `$f_{X|Y}(x|y)$`.

.pull-right[
#### Student's t Distribution
{{content}}
]
--

Another way to think of the `$t_\nu$` distribution is:

`\begin{align*}
  X|Y &\sim \text{N}(0, \nu/Y)\\
  Y &\sim \chi_\nu^2
\end{align*}`
{{content}}
--

The `$t$` distribution is a _scale mixture of normals_.
{{content}}
--

Other choices of the distribution of `$Y$` lead to other distributions
for `$X$`.

---

#### Negative Binomial Distribution

.pull-left[
The negative binomial distribution with PMF

`\begin{equation*}
  f(x) = \binom{x+r-1}{r-1}p^r(1-p)^x
\end{equation*}`

for `$x=0, 1, 2, \dots,$` can be written as a gamma mixture of Poissons:
{{content}}
]
--

`\begin{align*}
  X|Y &\sim \text{Poisson}(Y)\\
  Y &\sim \text{Gamma}(r, (1-p)/p)
\end{align*}`

then `$X \sim \text{Negative Binomial}(r, p)$`.

.pull-right[
[The notation `$\text{Gamma}(\alpha,\beta)$` means that `$\beta$` is the
scale parameter.]
{{content}}
]
--

This representation makes sense even when `$r$` is not an integer.

---

#### Non-Central Chi-Square

.pull-left[
The density of the non-central `$\chi_\nu^2$` distribution with
non-centrality parameter `$\delta$` is

`\begin{equation*}
  f(x) = 
  e^{-\delta/2} \sum_{i=0}^\infty \frac{(\delta/2)^i}{i!}
  f_{\nu+2i}(x)
% I think Monahan's formula is wrong and this is right:
% f(x) = exp(-lambda/2) SUM_{r=0}^infty (lambda^r / 2^r r!) pchisq(x, df + 2r)
\end{equation*}`

where `$f_k(x)$` central `$\chi^2_k$` density.
{{content}}
]
--

This is a Poisson-weighted average of `$\chi^2$` densities.

.pull-right[
So if

`\begin{align*}
  X|Y &\sim \chi_{\nu+2Y}^2\\
  Y &\sim \text{Poisson}(\delta/2)
\end{align*}`

then `$X$` has a non-central `$\chi_\nu^2$` distribution with
non-centrality parameter `$\delta$`.
]

---

#### Composition Method

.pull-left[
Suppose we want to sample from the density

`\begin{equation*}
  f(x) = 
  \begin{cases}
    x/2 & 0 \le x < 1\\
    1/2 & 1 \le x < 2\\
    3/2 - x/2 & 2 \le x \le 3\\
    0 & \text{otherwise}
  \end{cases}
\end{equation*}`
]
--

.pull-right[
We can write `$f$` as the mixture

`\begin{equation*}
  f(x) = \frac{1}{4} f_1(x) + \frac{1}{2} f_2(x) + \frac{1}{4} f_3(x)
\end{equation*}`

with

`\begin{align*}
  f_1(x) &= 2x & 0 \le x < 1\\
  f_2(x) &= 1 & 1 \le x < 2\\
  f_3(x) &= 6-2x & 2 \le x \le 3
\end{align*}`

and `$f_i(x) = 0$` for other values of `$x$`.
]

---

.pull-left.width-50[
Generating from the `$f_i$` is straight forward.
{{content}}
]
--

So we can sample from `$f$` using:

&nbsp;&nbsp;**Generate** `$I$` from `$\{1, 2, 3\}$` with probabilities
`$\frac{1}{4}, \frac{1}{2}, \frac{1}{4}$`
.<br>
&nbsp;&nbsp;**Generate** `$X$` from `$f_I(x)$` by inversion.
{{content}}
--

This approach can be used in conjunction with other methods.

.pull-right[
#### Example
{{content}}
]
--

The polar method requires sampling uniformly from the
unit disk.
{{content}}
--

This can be done by
{{content}}
--

* encloseing the unit disk in a regular hexagon;
{{content}}
--

* using composition to sample uniformly from the hexagon until the
  result is in the unit disk.

---

#### Alias Method

.pull-left[
Suppose `$f(x)$` is a probability mass function on `$\{1, 2, \dots, k\}$`.
{{content}}
]
--

Then `$f(x)$` can be written as

`\begin{equation*}
  f(x) = \sum_{i=1}^k \frac{1}{k} f_i(x)
\end{equation*}`
{{content}}
--

where

`\begin{equation*}
  f_i(x) = 
  \begin{cases}
    q_i & x = i\\
    1-q_i & x = a_i\\
    0 & \text{otherwise}
  \end{cases}
\end{equation*}`

for some `$q_i \in [0,1]$` and some `$a_i \in \{1, 2, \dots, k\}$`.

.pull-right[
Once values for `$q_i$` and `$a_i$` have been found, generation is easy:
{{content}}
]
--

&nbsp;&nbsp;**Generate** `$I$` uniform on `$\{1, \dots ,k\}$`<BR>
&nbsp;&nbsp;**Generate** `$U$` uniform on `$[0,1]$`<BR>
&nbsp;&nbsp;**if** `$U \le q_I$`<BR>
&nbsp;&nbsp;&nbsp;&nbsp;**return** `$I$`<BR>
&nbsp;&nbsp;**else**<BR>
&nbsp;&nbsp;&nbsp;&nbsp;**return** `$a_I$`
{{content}}
--

This is _Walker's alias method_.

---

The setup process used to compute the `$q_i$` and `$a_i$` is called
_leveling the histogram_:

A complete description is in Ripley (1987, Alg 3.13B).

The alias method is an example of trading off a setup cost for fast
generation.

The alias method is used by the `sample` function for unequal
probability sampling with replacement when there are enough reasonably
probable values ([source code in
svn](https://svn.r-project.org/R/trunk/src/main/random.c)).

---

### Accept/Reject Methods

#### Sampling Uniformly from the Area Under a Density

.pull-left[
Suppose `$h$` is a function such that

* `$h(x) \ge 0$` for all `$x$`
* `$\int h(x) dx < \infty$`.
{{content}}
]
--

Let

`\begin{equation*}
  \mathcal{G}_h = \{(x,y): 0 < y \le h(x)\}
\end{equation*}`
{{content}}
--

The area of `$\mathcal{G}_h$` is

`\begin{equation*}
  |\mathcal{G}_h| = \int h(x) dx < \infty  
\end{equation*}`

.pull-right[
<img src="sim_files/figure-html/unnamed-chunk-13-1.png" style="display: block; margin: auto;" />
]

---

Suppose `$(X,Y)$` is uniformly distributed on `$\mathcal{G}_h$`.

Then

* The conditional distribution of `$Y|X=x$` is uniform on `$(0,h(x))$`.

* The marginal distribution of `$X$` has density
  `$f_X(x) = h(x)/\int h(y) dy$`:
--

`\begin{equation*}
f_X(x) = \int_0^{h(x)}\frac{1}{|\mathcal{G}_h|} dy
       = \frac{h(x)}{\int h(y) dy}
\end{equation*}`

---

#### Rejection Sampling Using an Envelope Density

.pull-left[
Suppose `$g$` is a density and `$M > 0$` is a real number such that

`\begin{equation*}
  h(x) \le M g(x)
\end{equation*}`
for all `$x$`.
{{content}}
]
--

or, equivalently,

`\begin{equation*}
  \sup \frac{h(x)}{g(x)} \le M
\end{equation*}`
for all `$x$`.

.pull-right[
<img src="sim_files/figure-html/unnamed-chunk-14-1.png" style="display: block; margin: auto;" />
]

`$M g(x)$` is an _envelope_ for `$h(x)$`.

---

.pull-left[
Suppose
{{content}}
]
--

* we want to sample from a density proportional to `$h$`;
{{content}}
--

* we can find a density `$g$` and a constant `$M$` such that

* `$M g(x)$` is an envelope for `$h(x)$`;
    * it is easy to sample from `$g$`.
{{content}}
--

Then we can
{{content}}
--

* sample `$X$` from `$g$` and `$Y|X=x$` from `$\text{U}(0,Mg(x))$`
  to get a pair `$(X,Y)$` uniformly distributed on `$\mathcal{G}_{Mg}$`;
{{content}}
--

* repeat until the pair `$(X,Y)$` satisfies `$Y \le h(X)$`.

.pull-right[
The resulting pair `$(X,Y)$` is uniformly distributed on
`$\mathcal{G}_h$`;
{{content}}
]
--

Therefore the marginal density of the resulting `$X$` is

`$$f_X(x) = \frac{h(x)}{\int h(y) dy}$$`.

---

The number of draws from the uniform distribution on
`$\mathcal{G}_{Mg}$` needed until we obtain a pair in `$\mathcal{G}_h$`
is independent of the final pair.
{{content}}
--

The number of draws has a geometric distribution
with success probability

`\begin{equation*}
  p = \frac{|\mathcal{G}_h|}{|\mathcal{G}_{Mg}|}
  = \frac{\int h(y) dy}{M \int g(y) dy}
  = \frac{\int h(y) dy}{M}
\end{equation*}`

since `$g$` is a probability density.

`$p$` is the _acceptance probability_.

The expected number of draws needed is

`\begin{equation*}
  E[\text{number of draws}] = \frac{1}{p}
  = \frac{M \int g(y) dy}{\int h(y) dy}
  = \frac{M}{\int h(y) dy}.
\end{equation*}`

If `$h$` is also a proper density, then `$p = 1/M$` and

`\begin{equation*}
  E[\text{number of draws}] = \frac{1}{p} = M
\end{equation*}`

---

#### The Basic Algorithm

.pull-left[
The rejection, or accept/reject, sampling algorithm:

&nbsp;&nbsp; **repeat**<BR>
&nbsp;&nbsp;&nbsp;&nbsp; **Generate**
independent `$X \sim g$` and `$U \sim \text{U}[0,1]$`<BR>
&nbsp;&nbsp;**until** `$U M g(X) \le h(X)$`<BR>
&nbsp;&nbsp;**return** `$X$`<BR>
]

.pull-right[
Alternate forms of the test:

`\begin{align*}
  U &\le \frac{h(X)}{M g(X)}\\
  \log(U) &\le \log(h(X)) - \log(M) - \log(g(X))
\end{align*}`
{{content}}
]
--

Care may be needed to ensure numerical stability.

---

#### Example: Normal Distribution with Cauchy Envelope

Suppose

* `$h(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}$` is the standard normal density
* `$g(x) = \frac{1}{\pi(1 + x^2)}$` is the standard Cauchy density

Then

`\begin{equation*}
  \frac{h(x)}{g(x)}
  = \sqrt{\frac{\pi}{2}} (1+x^2)e^{-x^2/2}
  \le \sqrt{\frac{\pi}{2}} (1+1^2)e^{-1^2/2}
  = \sqrt{2\pi e^{-1}}
  = 1.520347
\end{equation*}`

The resulting accept/reject algorithm is

&nbsp;&nbsp; **repeat**<BR>
&nbsp;&nbsp;&nbsp;&nbsp; **Generate**
independent standard Cauchy `$X$` and `$U \sim \text{U}[0,1]$`<BR>
&nbsp;&nbsp;**until** `$U \le \frac{e^{1/2}}{2}(1+X^2)e^{-X^2/2}$`<BR>
&nbsp;&nbsp;**return** `$X$`

---

#### Squeezing

.pull-left[
Performance can be improved by _squeezing_:
{{content}}
]
--

Accept if point is inside the triangle:

.pull-right[
Squeezing _can_ speed up generation.
{{content}}
]
--

Squeezing _will_ complicate the code (making errors more likely).

---

#### Rejection Sampling for Discrete Distributions

For simplicity, just consider integer valued random variables.

* If `$h$` and `$g$` are probability mass functions on the integers
  and `$h(x)/g(x)$` is bounded, then the same algorithm can be used.

* If `$p$` is a probability mass function on the integers then
  `$$h(x) = p(\lfloor x \rfloor)$$`
  is a probability density.

* If `$X$` has density `$h$`, then `$Y = \lfloor X \rfloor$` has PMF `$p$`.

---

#### Example: Poisson Distribution with Cauchy Envelope

.pull-left[
Suppose
{{content}}
]
--

* `$p$` is the PMF of a Poisson distribution with mean 5
{{content}}
--

* `$g$` is the Cauchy density with location 5 and scale 3.
{{content}}
--

* `$h(x) = p(\lfloor x \rfloor)$`
{{content}}

Then, by careful analysis or graphical examination, `$h(x) \le 2 g(x)$`
for all `$x$`.

.pull-right[
<img src="sim_files/figure-html/unnamed-chunk-16-1.png" style="display: block; margin: auto;" />
]

---

#### Comments

The Cauchy density is often a useful envelope.

More efficient choices are often possible.

Location and scale need to be chosen appropriately.

If the target distribution is non-negative, a truncated Cauchy can be
used.

Careful analysis is needed to produce generators for a parametric
family (e.g. all Poisson distributions).

Graphical examination can be very helpful in guiding the analysis.

Carefully tuned envelopes combined with squeezing can produce very
efficient samplers.

Errors in tuning and squeezing will produce garbage.

---

.pull-left[
### Ratio-of-Uniforms Method

#### Basic Method
{{content}}
]
--

Introduced by Kinderman and Monahan (1977).
{{content}}
--

Suppose

* `$h(x) \ge 0$` for all `$x$`
* `$\int h(x) dx < \infty$`
{{content}}
--

Let `$(V, U)$` be uniform on

`\begin{equation*}
  \mathcal{C}_h = \{(v,u): 0 < u \le \sqrt{h(v/u)}\}
\end{equation*}`
{{content}}
--

Then `$X = V/U$` has density `$f(x) = h(x)/\int h(y) dy$`.

.pull-right[
For `$h(x) = e^{-x^2/2}$` the region `$\mathcal{C}_h$` looks like

<img src="sim_files/figure-html/unnamed-chunk-17-1.png" style="display: block; margin: auto;" />
{{content}}
]
--

In this example:
{{content}}
--

* The region is bounded.
{{content}}
--

* The region is convex.

---

#### Properties

The region `$\mathcal{C}_h$` is convex if `$h$` is _log concave_.

The region `$\mathcal{C}_h$` is bounded if `$h(x)$` and `$x^2 h(x)$` are
bounded.

Let

`\begin{align*}
  u^* &= \max_x \sqrt{h(x)}\\
  v_-^* &= \min_x x \sqrt{h(x)}\\
  v_+^* &= \max_x x \sqrt{h(x)}
\end{align*}`

Then `$\mathcal{C}_h$` is contained in the rectangle
`$[v_-^*,v_+^*]\times[0,u^*]$`.

---

.pull-left[
The simple Ratio-of-Uniforms algorithm based on rejection sampling
from the enclosing rectangle is

&nbsp;&nbsp; **repeat**<BR>
&nbsp;&nbsp;&nbsp;&nbsp; **Generate** `$U \sim \text{U}[0,u^*]$`<BR>
&nbsp;&nbsp;&nbsp;&nbsp; **Generate** `$V \sim \text{U}[v_-^*,v_+^*]$`<BR>
&nbsp;&nbsp; **until** `$U^2 \le h(V/U)$`<BR>
&nbsp;&nbsp; **return** `$X = V/U$`
]

.pull-right[
If `$h = e^{-x^2/2}$` then
`\begin{align*}
  u^* &= 1\\
  v_-^* &= -\sqrt{2e^{-1}}\\
  v_+^* &= \sqrt{2e^{-1}}
\end{align*}`
{{content}}
]
--

and the expected number of draws is

`\begin{equation*}
  \frac{\text{area of rectangle}}{\text{area of} \,\mathcal{C}_h}
  = \frac{u^*(v_+^*-v_-^*)}{\frac{1}{2}\int h(x)dx}
  = \frac{2\sqrt{2e^{-1}}}{\sqrt{\pi/2}} = 1.3688
\end{equation*}`
{{content}}
--

Various squeezing methods are possible.
{{content}}
--

Other approaches to sampling from `$\mathcal{C}_h$` are also possible.

---

#### Relation to Rejection Sampling

.pull-left[
Ratio of Uniforms with rejection sampling from the enclosing rectangle
is equivalent to ordinary rejection sampling using an envelope density

`\begin{equation*}
  g(x) \propto
  \begin{cases}
    \left(\frac{v_-^*}{x}\right)^2 & x < v_-^*/u^*\\
    (u^*)^2 & v_-^*/u^* \le x \le v_+^*/u^*\\
    \left(\frac{v_+^*}{x}\right)^2 & x > v_+^*/u^*
  \end{cases}
\end{equation*}`
]

.pull-right[
This is sometimes called a _table mountain density_

<img src="sim_files/figure-html/unnamed-chunk-18-1.png" style="display: block; margin: auto;" />
]

---

#### Generalizations

A more general form of the basic result:

For any `$\mu$` and any `$r > 0$` let

`\begin{equation*}
  \mathcal{C}_{h,\mu, r}
  = \{(v,u): 0 < u \le h(v/u^r+\mu)^{1/(r+1)}\}
\end{equation*}`

If `$(U,V)$` is uniform on `$\mathcal{C}_{h,\mu, r}$`, then
`$X = V/U^r + \mu$` has density `$f(x) = h(x)/\int h(y)dy$`.

* `$\mu$` and `$r$` can be chosen to minimize the rejection probability.

* `$r = 1$` seems adequate for most purposes.

* Choosing `$\mu$` equal to the mode of `$h$` can help.

---

For the Gamma distribution with `$\alpha = 30$`,

---

### Adaptive Rejection Sampling

.pull-left[
First introduced by Gilks and Wild (1992).
{{content}}
]
--

#### Convexity
{{content}}
--

A set `$C$` is convex if `$\lambda x + (1-\lambda)y \in C$` for all
`$x, y \in C$` and `$\lambda \in [0, 1]$`.
{{content}}
--

`$C$` can be a subset or `$\Real$`, or `$\Real^n$`, or any other set where
the _convex combination_

`\begin{equation*}
  \lambda x + (1-\lambda)y    
\end{equation*}`

makes sense.

.pull-right[
A real-valued function `$f$` on a convex set `$C$` is convex if

`\begin{equation*}
  f(\lambda x + (1 - \lambda) y) \le \lambda f(x) + (1-\lambda) f(y)
\end{equation*}`

`$x, y \in C$` and `$\lambda \in [0, 1]$`.
{{content}}
]
--

`$f(x)$` is concave if `$-f(x)$` is convex, i.e. if

`\begin{equation*}
  f(\lambda x + (1 - \lambda) y) \ge \lambda f(x) + (1-\lambda) f(y)
\end{equation*}`

`$x, y \in C$` and `$\lambda \in [0, 1]$`.
{{content}}
--

A concave function is always below its tangent.

---

#### Log Concave Densities

.pull-left[
A density `$f$` is _log concave_ if `$\log f$` is a concave function.
{{content}}
]
--

Many densities are log concave:
{{content}}
--

* normal densities;
{{content}}
--

* `$\text{Gamma}(\alpha, \beta)$` with `$\alpha \ge 1$`;
{{content}}
--

* `$\text{Beta}(\alpha,\beta)$` with `$\alpha \ge 1$` and `$\beta \ge 1$`.
{{content}}
--

.pull-right[
Some are not but may be related to ones that are:
{{content}}
]
--

The `$t$` densities
are not, but if

`\begin{align*}
  X|Y=y &\sim \text{N}(0,1/y)\\
  Y &\sim \text{Gamma}(\alpha, \beta)
\end{align*}`

then
{{content}}
--

* the marginal distribution of `$X$` is `$t$` for suitable choice of
  `$\beta$`,
{{content}}
--

* and the joint distribution of `$X$` and `$Y$` has density
  `$$f(x,y) \propto \sqrt{y}e^{-\frac{y}{2}x^2}y^{\alpha-1}e^{-y/\beta} = y^{\alpha-1/2}e^{-y(\beta+x^2/2)}$$`
  which is log concave for `$\alpha \ge 1/2$`

---

#### Tangent Approach

.pull-left[
Suppose

* `$f$` is log concave;
* `$f$` has an interior mode
{{content}}
]
--

Need log density, derivative at two points, one each side of the mode

* piece-wise linear envelope of log density
* piece-wise exponential envelope of density
* if first point is not accepted, can use to make better envelope

.pull-right[
<img src="sim_files/figure-html/unnamed-chunk-20-1.png" style="display: block; margin: auto;" />
]

---

#### Secant Approach

.pull-left[
<img src="sim_files/figure-html/unnamed-chunk-21-1.png" style="display: block; margin: auto;" />
]

.pull-right[
* Need three points to start
* Do not need derivatives
* Get larger rejection rates
{{content}}
]
--

Both approaches need numerical care

---

### Notes and Comments

Many methods depend on properties of a particular distribution.

Inversion is one general method that can often be used.

Other general-purpose methods are

* rejection sampling;
* adaptive rejection sampling;
* ratio-of-uniforms.

---

Some references:

> Devroye, L. (1986). _Non-Uniform Random Variate Generation_,
> Springer-Verlag, New York.

> Gentle, J. E. (2003). _Random Number Generation and Monte Carlo
> Methods_, Springer-Verlag, New York.

> Hoermann, W., Leydold, J., and Derflinger, G. (2004).  [_Automatic
>  Nonuniform Random Variate
>  Generation_](https://statmath.wu.ac.at/arvag/monograph/index.html),
>  Springer-Verlag, New York.

Still an area of active research:

> Karney, C.F.F. (2016). "Sampling Exactly from the Normal
> Distribution."  _ACM Transactions on Mathematical Software_ 42 (1).

---

### Random Variate Generators in R

Generators for most standard distributions are available

* `rnorm`: normal
* `rgamma`: gamma
* `rt`: `$t$`
* `rpois`: Poisson
* etc.

Most use standard algorithms from the literature.

Source code is in `src/nmath/` in the [source
tree](https://svn.r-project.org/R/trunk/).

---

The normal generator can be configured by `RNGkind`.

Options are

* Kinderman-Ramage
* Buggy Kinderman-Ramage (available for reproducing results)
* Ahrens-Dieter
* Box-Muller
* Inversion (the current default)
* user-supplied

---
layout: true
## Generating Random Vectors and Matrices
---

Sometimes generating random vectors can be reduced to a series of
univariate generations.

One approach is conditioning:
`\begin{equation*}
  f(x,y,z) = f_{Z|X,Y}(z|x,y) f_{Y|X}(y|x) f_X(x)
\end{equation*}`

So we can generate

* `$X$` from `$f_X(x)$`
* `$Y|X=x$` from `$f_{Y|X}(y|x)$`
* `$Z|X=x,Y=y$` from `$f_{Z|X,Y}(z|x,y)$`

---

.pull-left[
#### Example

Suppose `$(X_1,X_2,X_3) \sim \text{Multinomial}(n,p_1,p_2,p_3)$`.
{{content}}
]
--

Then

`\begin{align*}
  X_1 &\sim \text{Binomial}(n, p_1)\\
  X_2 | X_1 = x_1 &\sim \text{Binomial}(n - x_1, p_2/(p_2+p_3))\\
  X_3 | X_1 = x_1, X_2 = x_2 &= n - x_1 - x_2
\end{align*}`

.pull-right[
#### Example

Suppose `$X, Y$` bivariate normal
`$(\mu_X, \mu_Y, \sigma_X^2, \sigma_Y^2, \rho)$`.
{{content}}
]
--

Then

`\begin{align*}
  X &\sim \text{N}(\mu_X,\sigma_X^2)\\
  Y|X=x &\sim \text{N}\left(\mu_Y + \rho\frac{\sigma_Y}{\sigma_X}(x-\mu_X),
  \sigma_Y^2(1-\rho^2)\right)
\end{align*}`
{{content}}
--
Conditioning can be used for a multivariate normal of any dimension.

---

.pull-left[
For some distributions special methods are available.
{{content}}
]
--

Some general methods extend to multiple dimensions.
{{content}}
--

### Multivariate Normal Distribution
{{content}}
--

Alternative to conditioning: use linear transformations.
{{content}}
--

Suppose `$Z_1, \dots, Z_d$` are independent standard normals,
`$\mu_1, \dots \mu_d$` are constants, and `$A$` is a constant `$d \times d$`
matrix.

.pull-right[
Let

`\begin{align*}
  Z &= \
      \begin{bmatrix}
        Z_1\\
        \vdots\\
        Z_d
      \end{bmatrix}
    & \mu &= 
            \begin{bmatrix}
              \mu_1\\
              \vdots\\
              \mu_d
            \end{bmatrix}
\end{align*}`
{{content}}
]
--

and set

`\begin{equation*}
  X = \mu + A Z
\end{equation*}`
{{content}}
--

Then `$X$` is multivariate normal with mean vector `$\mu$` and covariance
matrix `$A A^T$`,

`\begin{equation*}
  X \sim \text{MVN}_d(\mu, A A^T)
\end{equation*}`

---

To generate `$X \sim \text{MVN}_d(\mu, \Sigma)$`, we can

* find a matrix `$A$` such that `$A A^T = \Sigma$`
--

* generate elements of `$Z$` as independent standard normals 
--

* compute `$X = \mu + A Z$`

The Cholesky factorization is one way to choose `$A$`.

If we are given `$\Sigma^{-1}$`, then we can

* decompose `$\Sigma^{-1} = L L^T$`
--

* solve `$L^T Y = Z$`
--

* compute `$X = \mu + Y$`

---

### Spherically Symmetric Distributions

.pull-left[
A joint distribution is called spherically symmetric (about the
origin) if it has a density of the form

`\begin{equation*}
  f(x) = g(x^T x) = g(x_1^2 + \dots + x_d^2).
\end{equation*}`
{{content}}
]
--

If the distribution of `$X$` is spherically symmetric, then

`\begin{align*}
  R &= \sqrt{X^T X}\\
  Y &= X/R
\end{align*}`

are independent,
{{content}}
--

* `$Y$` is uniformly distributed on the surface of the unit sphere.
{{content}}
--

* `$R$` has density proportional to `$g(r^2)r^{d-1}$` for `$r > 0$`.

.pull-right[
We can generate `$X \sim f$` by
{{content}}
]
--

* generating `$Z \sim \text{MVN}_d(0, I)$` and setting
  `$Y = Z / \sqrt{Z^T Z}$`
{{content}}
--

* generating `$R$` from the density proportional to `$g(r^2)r^{d-1}$`
  by univariate methods.

---

### Elliptically Contoured Distributions

A density `$f$` is elliptically contoured if
`\begin{equation*}
  f(x) = \frac{1}{\sqrt{\det \Sigma}} g((x-\mu)^T\Sigma^{-1}(x-\mu))
\end{equation*}`
for some vector `$\mu$` and symmetric positive definite matrix `$\Sigma$`.

Suppose `$Y$` has spherically symmetric density `$g(y^Ty)$` and
`$AA^T = \Sigma$`.

Then `$X = \mu + A Y$` has density `$f$`.

---

### Wishart Distribution

Suppose `$X_1, \dots X_n$` are independent and
`$X_i \sim \text{MVN}_d(\mu_i,\Sigma)$`.

Let

`\begin{equation*}
  W = \sum_{i=1}^{n} X_i X_i^T
\end{equation*}`

--
Then `$W$` has a non-central Wishart distribution
`$\text{W}(n, \Sigma, \Delta)$` where `$\Delta = \sum \mu_i\mu_i^T$`.

If `$X_i \sim \text{MVN}_d(\mu,\Sigma)$` and

`\begin{equation*}
  S = \frac{1}{n-1}\sum_{i=1}^n (X_i -\overline{X})(X_i -\overline{X})^T
\end{equation*}`

is the sample covariance matrix, then
`$(n-1) S \sim \text{W}(n-1, \Sigma, 0)$`.

---

Suppose `$\mu_i = 0$`, `$\Sigma = A A^T$`, and `$X_i = A Z_i$` with
`$Z_i \sim \text{MVN}_d(0,I)$`.

Then `$W = AVA^T$` with

`\begin{equation*}
  V = \sum_{i=1}^n Z_i Z_i^T
\end{equation*}`

_Bartlett decomposition_: In the Cholesky factorization of `$V$`

* all elements are independent;
* the elements below the diagonal are standard normal;
* the square of the `$i$`-th diagonal element is `$\chi^2_{n+1-i}$`.

If `$\Delta \neq 0$` let `$\Delta = B B^T$` be its Cholesky factorization,
let `$b_i$` be the columns of `$B$` and let `$Z_1,\dots,Z_n$` be independent
`$\text{MVN}_d(0,I)$` random vectors.

Then for `$n \ge d$`

`\begin{equation*}
  W = \sum_{i=1}^d(b_i + A Z_i)(b_i + A Z_i)^T +
  \sum_{i=d+1}^n A Z_i Z_i^T A^T
  \sim \text{W}(n, \Sigma, \Delta)
\end{equation*}`

---

### Rejection Sampling

.pull-left[
Rejection sampling can in principle be used in any dimension.
{{content}}
]
--

A general envelope that is sometimes useful is based on generating `$X$` as

`\begin{equation*}
  X = b + A Z/Y
\end{equation*}`
{{content}}
--

where

* `$Z$` and `$Y$` are independent
* `$Z \sim \text{MVN}_d(0, I)$`
* `$Y^2 \sim \text{Gamma}(\alpha, 1/\alpha)$`, a scalar
* `$b$` is a vector of constants
* `$A$` is a matrix of constants
{{content}}
--

This is a kind of multivariate `$t$` random vector.

.pull-right[
This often works in modest dimensions.
{{content}}
]
--

Specially tailored envelopes can sometimes be used in higher
dimensions.
{{content}}
--

Without special tailoring, rejection rates tend to be too high to be
useful.

---

### Ratio of Uniforms

The ratio-of-uniforms method also works in `$\Real^d$`:

Suppose

* `$h(x) \ge 0$` for all `$x$`
* `$\int h(x) dx < \infty$`

Let

$$
  \mathcal{C}_h =
  \{(v,u): v \in \Real^d, 0 < u \le \sqrt[d+1]{h(v/u + \mu)}\}
$$

for some `$\mu$`. If `$(V,U)$` is uniform on `$\mathcal{C}_h$`, then
`$X = V/U+\mu$` has density `$f(x) = h(x)/\int h(y) dy$`.

If `$h(x)$` and `$\Norm{x}^{d+1}h(x)$` are bounded, then `$\mathcal{C}_h$`
is bounded.

If `$h(x)$` is log concave then `$\mathcal{C}_h$` is convex.

---

.pull-left[
Rejection sampling from a bounding hyper rectangle works in modest
dimensions.
{{content}}
]
--

It will not work for dimensions larger than 8 or so:
{{content}}
--

* The shape of `$\mathcal{C}_h$` is vaguely spherical.
{{content}}
--

* The volume of the unit sphere in `$d$` dimensions is
  `$$V_d = \frac{\pi^{d/2}}{\Gamma(d/2 + 1)}$$`
{{content}}
--

* The ratio of this volume to the volume of the enclosing hyper
  cube, `$2^d$` tends to zero very fast:

.pull-right[
<img src="sim_files/figure-html/unnamed-chunk-22-1.png" style="display: block; margin: auto;" />
]

---

### Order Statistics

.pull-left[
The order statistics for a random sample `$X_1,\dots,X_n$` from
`$F$` are the ordered values

`\begin{equation*}
  X_{(1)} \le X_{(2)} \le \dots \le X_{(n)}
\end{equation*}`
{{content}}
]
--

* We can simulate them by ordering the sample.
{{content}}
--

* Faster `$O(n)$` algorithms are available for individual order
  statistics, such as the median.

.pull-right[
If `$U_{(1)} \le \dots \le U_{(n)}$` are the order statistics of a
random sample from the `$\text{U}[0,1]$` distribution, then

`\begin{align*}
  X_{(1)} &= F^-(U_{(1)})\\
          &\;\;\vdots\\
  X_{(n)} &= F^-(U_{(n)})
\end{align*}`

are the order statistics of a random sample from `$F$`.
]

---

.pull-left[
For a sample of size `$n$` the marginal distribution of `$U_{(k)}$` is

`\begin{equation*}
  U_{(k)} \sim \text{Beta}(k, n-k+1).
\end{equation*}`
{{content}}
]
--

Suppose `$k < \ell$`. Then
{{content}}
--

* `$U_{(k)}/U_{(\ell)}$` is independent of
  `$U_{(\ell)}, \dots, U_{(n)}$`.
{{content}}
--

* `$U_{(k)}/U_{(\ell)}$` has a `$\text{Beta}(k, \ell-k)$`
  distribution.
{{content}}
--

We can use this to generate any subset or all order statistics.

.pull-right[
Let `$V_1, \dots, V_{n+1}$` be independent exponential random variables
with the same mean and let

`\begin{equation*}
  W_k = \frac{V_1+\dots+V_k}{V_1+\dots+V_{n+1}}
\end{equation*}`
{{content}}
]
--

Then `$W_1, \dots, W_n$` has the same joint distribution as
`$U_{(1)}, \dots, U_{(n)}$`.

---

### Homogeneous Poisson Process

For a homogeneous Poisson process with rate `$\lambda$` on `$\Real^d$`:

* The number of points `$N(A)$` in a set `$A$` is Poisson with mean
  `$\lambda|A|$`.

* If `$A$` and `$B$` are disjoint then `$N(A)$` and `$N(B)$` are
  independent.

Conditional on `$N(A) = n$`, the `$n$` points are uniformly distributed on
`$A$`.

---

We can generate a Poisson process on `$[0,t]$` by generating exponential
variables `$T_1, T_2,\dots$` with rate `$\lambda$` and computing

`\begin{equation*}
  S_k = T_1+\dots+T_k
\end{equation*}`

until `$S_k > t$`.

The values `$S_1, \dots, S_{k-1}$` are the points in the Poisson process
realization.

---

### Inhomogeneous Poisson Processes

For an inhomogeneous Poisson process with rate `$\lambda(x)$` on `$\Real^d$`:

* The number of points `$N(A)$` in a set `$A$` is Poisson with mean
  `$\int_A\lambda(x) dx$`.

* If `$A$` and `$B$` are disjoint then `$N(A)$` and `$N(B)$` are
  independent.

Conditional on `$N(A) = n$`, the `$n$` points in `$A$` are a random sample
from a distribution with density `$\lambda(x)/\int_A\lambda(y)dy$`.

---

To generate an inhomogeneous Poisson process on `$[0,t]$` we can

* Let `$\Lambda(s) = \int_0^s\lambda(x)dx$`.

* Generate arrival times `$S_1, \dots, S_N$` for a homogeneous
  Poisson process with rate one on `$[0,\Lambda(t)]$`.

* Compute arrival times of the inhomogeneous process as
  $$ \Lambda^{-1}(S_1),\dots,\Lambda^{-1}(S_N). $$

---

If `$\lambda(x) \le M$` for all `$x$`, then we can generate an
inhomogeneous Poisson process with rate `$\lambda(x)$` by
_thinning_:

* Generate a homogeneous Poisson process with rate `$M$` to obtain
  points `$X_1, \dots, X_N$`.

* Independently delete each point `$X_i$` with probability
  `$1-\lambda(X_i)/M$`.

The remaining points form a realization of an inhomogeneous Poisson
process with rate `$\lambda(x)$`.

If `$N_1$` and `$N_2$` are independent inhomogeneous Poisson processes
with rates `$\lambda_1(x)$` and `$\lambda_2(x)$`, then their superposition
`$N_1+N_2$` is an inhomogeneous Poisson process with rate
`$\lambda_1(x)+\lambda_2(x)$`.

---

### Other Processes

Many other processes can be simulated from their definitions:

* Cox processes (doubly stochastic Poisson process)
* Poisson cluster processes
* ARMA, ARIMA processes
* GARCH processes

Continuous time processes, such as Brownian motion and diffusions,
require discretization of time.

Other processes may require Markov chain methods

* Ising models
* Strauss process
* interacting particle systems

---
layout: true
## Variance Reduction
---

.pull-left[
Most simulations involve estimating integrals or expectations:
`\begin{align*}
  \theta &= \int h(x) f(x) dx & \text{mean}\\
  \theta &= \int 1_{\{X \in A\}} f(x) dx & \text{probability}\\
  \theta &= \int (h(x) - E[h(X)])^2 f(x) dx & \text{variance}\\
  &\;\;\vdots
\end{align*}`
{{content}}
]
--

The _crude simulation_, or _crude Monte Carlo_, or
_naive Monte Carlo_, approach:
{{content}}
--

* Sample `$X_1,\dots,X_N$` independently from `$f$`
{{content}}
--

* Estimate `$\theta$` by `$\widehat{\theta}_N = \frac{1}{N} \sum h(X_i)$`.

.pull-right[
If `$\sigma^2 = \Var(h(X))$`, then
`$\Var(\widehat{\theta}_N) = \frac{\sigma^2}{N}$`.
{{content}}
]
--

To reduce the error we can:
{{content}}
--

* Increase `$N$`: requires CPU time and clock time; diminishing
  returns.
{{content}}
--

* try to reduce `$\sigma^2$`: requires thinking time, programming
  effort.
{{content}}
--

Methods that reduce `$\sigma^2$` are called

* tricks;
* swindles;
* Monte Carlo methods.

---

### Control Variates

.pull-left[
Suppose we have a random variable `$Y$` with mean `$\theta$` and a
correlated random variable `$W$` with known mean `$E[W]$`.
{{content}}
]
--

Then for any constant `$b$`

`\begin{equation*}
  \widetilde{Y} = Y - b(W-E[W])
\end{equation*}`

has mean `$\theta$`.
{{content}}
--

`$W$` is called a _control variate_.

.pull-right[
* Choosing `$b=1$` often works well if the correlation is positive
  and `$\theta$` and `$E[W]$` are close.
{{content}}
]
--

* The value of `$b$` that minimizes the variance of `$\widetilde{Y}$`
  is `$\Cov(Y,W)/\Var(W)$`.
{{content}}
--

* We can use a guess or a pilot study to estimate `$b$`.
{{content}}
--

* We can also estimate `$b$` from the same data used to compute `$Y$`
  and `$W$`.
{{content}}
--

* This is related to the regression estimator in sampling.

---

#### Example

.pull-left[
Suppose we want to estimate the expected value of the sample median
`$T$` for a sample of size 10 from a `$\text{Gamma}(3,1)$` population.
{{content}}
]
--

Crude estimate:

`\begin{equation*}
  Y = \frac{1}{N}\sum T_i
\end{equation*}`
{{content}}
--

Using the sample mean as a control variate with `$b=1$`:

`\begin{align*}
  \widehat{Y} &= \frac{1}{N}\sum (T_i-\overline{X}_i) + E[\overline{X}_i]\\
  &= \frac{1}{N}\sum (T_i-\overline{X}_i) + \alpha
\end{align*}`

.pull-right[

```r
x <- matrix(rgamma(100000, 3), ncol = 10)
md <- apply(x, 1, median)
mn <- apply(x, 1, mean)
mean(md)
## [1] 2.727918
mean(md - mn) + 3
## [1] 2.723364
sd(md)
## [1] 0.6091441
sd(md - mn)
## [1] 0.3588795
```
{{content}}
]
--

The standard deviation is cut roughly in half.

{{content}}
--

The optimal `$b$` seems close to 1.

---

.pull-left[
#### Another Approach

The expected value of the median of a sample from a standard normal
distribution is zero.
{{content}}
]
--

* Generate uniform `$[0, 1]$` samples.
{{content}}
--

* Generate gamma samples and normal samples by inversion.
{{content}}
--

* Use the medians `$\widetilde{X}_i$` of the normal samples as a control
  variate:

`\begin{equation*}
  \widehat{Y} = \frac{1}{N}\sum (T_i - \widetilde{X}_i)
\end{equation*}`

.pull-right[

```r
## uniform samples
u <- matrix(runif(100000), ncol = 10)

## gamma samples and medians
x <- qgamma(u, 3)
md <- apply(x, 1, median)

## normal samples and medians
nx <- qnorm(u)
nmd <- apply(nx, 1, median)

## crude estimate
mean(md)
## [1] 2.7338
sd(md)
## [1] 0.6055229

## control variate estimate
mean(md - nmd)
## [1] 2.730465
sd(md - nmd)
## [1] 0.2417076
```
{{content}}
]

Another example is available [here](../gamcont.html).

---

#### Control Variates and Probability Estimates

.pull-left[
Suppose `$T$` is a test statistic and we want to estimate
`$\theta = P(T \le t)$`.
{{content}}
]
--

Crude Monte Carlo:

`\begin{equation*}
  \widehat{\theta} = \frac{\#\{T_i \le t\}}{N}
\end{equation*}`
{{content}}
--

Suppose `$S$` is "similar" to `$T$` and `$P(S \le t)$` is known.  Use

`\begin{align*}
  \widehat{\theta} &= \frac{\#\{T_i \le t\} - \#\{S_i \le t\}}{N} + P(S \le t)\\
  &= \frac{1}{N}\sum Y_i + P(S \le t)
\end{align*}`

with `$Y_i = 1_{\{T_i \le t\}} - 1_{\{S_i \le t\}}$`.

.pull-right[
If `$S$` mimics `$T$`, then `$Y_i$` is usually zero.
{{content}}
]
--

Could use this to calibrate

`\begin{equation*}
  T = \frac{\text{median}}{\text{interquartile range}}
\end{equation*}`

for normal data using the `$t$` statistic.

---

### Importance Sampling

Suppose we want to estimate

`\begin{equation*}
  \theta = \int h(x) f(x) dx
\end{equation*}`

for some density `$f$` and some function `$h$`.

Crude Mote Carlo samples `$X_1,\dots,X_N$` from `$f$` and uses

`\begin{equation*}
  \widehat{\theta} = \frac{1}{N} \sum h(X_i)
\end{equation*}`

If the region where `$h$` is large has small probability under `$f$` then
this can be inefficient.

---

An alternative: Sample `$X_1,\dots X_n$` from `$g$` that puts more
probability near the "important" values of `$x$` and compute

`\begin{equation*}
  \widetilde{\theta} = \frac{1}{N}\sum h(X_i)\frac{f(X_i)}{g(X_i)}
\end{equation*}`

Then, if `$g(x) > 0$` when `$h(x)f(x) \neq 0$`,
`\begin{equation*}
  E[\widetilde{\theta}] = \int h(x) \frac{f(x)}{g(x)} g(x) dx
  = \int h(x) f(x) dx = \theta
\end{equation*}`

and

$$
  \Var(\widetilde{\theta}) = 
  \frac{1}{N} \int \left(h(x)\frac{f(x)}{g(x)} - \theta\right)^2 g(x) dx =
  \frac{1}{N} \left( \int \left(h(x)\frac{f(x)}{g(x)}\right)^2 g(x) dx -
    \theta^2\right)
$$

The variance is minimized by `$g(x) \propto |h(x)f(x)|$`

---

#### Importance Weights

Importance sampling is related to stratified and weighted sampling in
sampling theory.

The function `$w(x) = f(x)/g(x)$` is called the _weight function_.

Alternative estimator:

`\begin{equation*}
  \theta^* = \frac{\sum h(X_i) w(X_i)}{\sum w(X_i)}
\end{equation*}`

This is useful if `$f$` or `$g$` or both are unnormalized densities.

Importance sampling can be useful for computing expectations with
respect to posterior distributions in Bayesian analyses.

Importance sampling can work very well if the weight function is
bounded.

Importance sampling can work very poorly if the weight function is
unbounded---it is easy to end up with infinite variances.

---

#### Computing Tail Probabilities

.pull-left[
Suppose `$\theta = P(X \in R)$` for some region `$R$`.
{{content}}
]
--

Suppose we can find `$g$` such that `$f(x)/g(x) < 1$` on `$R$`.
{{content}}
--

Then

`\begin{equation*}
  \widetilde{\theta} = \frac{1}{N} \sum 1_R(X_i)\frac{f(X_i)}{g(X_i)}
\end{equation*}`

.pull-right[
The variance is

`\begin{align*}
  \renewcommand{\Var}{\text{Var}}
  \Var(\widetilde{\theta})
  &= \frac{1}{N}\left(\int_R \left(\frac{f(x)}{g(x)}\right)^2 g(x) dx -
     \theta^2\right)\\
  &= \frac{1}{N}\left(\int_R \frac{f(x)}{g(x)} f(x) dx - \theta^2\right)\\
  &< \frac{1}{N}\left(\int_R f(x) dx - \theta^2\right)\\
  &= \frac{1}{N}(\theta-\theta^2) = \Var(\widehat{\theta})
\end{align*}`
]

---

For computing `$P(X>2)$` where `$X$` has a standard Cauchy distribution we
can use a shifted distribution:

```r
y <- rcauchy(10000, 3)
tt <- ifelse(y > 2, 1, 0) * dcauchy(y) / dcauchy(y, 3)
mean(tt)
## [1] 0.1490259
sd(tt)
## [1] 0.1637507
```

The asymptotic standard deviation for crude Monte Carlo is
approximately

```r
sqrt(mean(tt) * (1 - mean(tt)))
## [1] 0.356114
```

A _tilted_ density `$g(x) \propto f(x) e^{\beta x}$` can also be
useful.

---

### Antithetic Variates

Suppose `$S$` and `$T$` are two unbiased estimators of `$\theta$` with the
same variance `$\sigma^2$` and correlation `$\rho$`, and compute

`\begin{equation*}
  V = \frac{1}{2}(S+T)
\end{equation*}`

Then

`\begin{equation*}
  \Var(V) = \frac{\sigma^2}{4}(2+2\rho) = \frac{\sigma^2}{2}(1+\rho)
\end{equation*}`

Choosing `$\rho < 0$` reduces variance.

Such negatively correlated pairs are called _antithetic
  variates_.

---

.pull-left[
Suppose we can choose between generating independent `$T_1,\dots,T_{N}$`

`\begin{equation*}
  \widehat{\theta} = \frac{1}{N}\sum_{i=1}^N T_i
\end{equation*}`

or independent pairs `$(S_1,T_1),\dots,(S_{N/2},T_{N/2})$` and computing

`\begin{equation*}
  \widetilde{\theta} = \frac{1}{N} \sum_{i=1}^{N/2}(S_i+T_i)
\end{equation*}`
{{content}}
]
--

If `$\rho < 0$`, then
`$\Var(\widetilde{\theta}) < \Var(\widehat{\theta})$`.

.pull-right[
If `$T = f(U)$`, `$U \sim \text{U}[0,1]$`, and `$f$` is monotone, then
`$S = f(1-U)$` is negatively correlated with `$T$` and has the same
marginal distribution.
{{content}}
]
--

If inversion is used to generate variates, computing `$T$` from
`$U_1, \dots$` and `$S$` from `$1-U_1, \dots$` often works.
{{content}}
--

Some uniform generators provide an option in the seed to switch
between returning `$U_i$` and `$1-U_i$`.

---

#### Example

For estimating the expected value of the median for samples of size 10
from the `$\text{Gamma}(3,1)$` distribution:

```r
u <- matrix(runif(50000), ncol = 10)
x1 <- qgamma(u, 3)
x2 <- qgamma(1 - u, 3)
md1 <- apply(x1, 1, median)
md2 <- apply(x2, 1, median)
sqrt(2) * sd((md1 + md2) / 2)
## [1] 0.09582766
```
--

Control variates helps further a bit but need `$b = 0.2$` or so.

```r
mn1 <- apply(x1, 1, mean)
mn2 <- apply(x2, 1, mean)
sqrt(2) * sd((md1 + md2 - 0.2 * (mn1 + mn2)) / 2)
## [1] 0.08880972
```

---

.pull-left[
### Latin Hypercube Sampling
{{content}}
]
--

Suppose we want to compute

`\begin{equation*}
  \theta = E[f(U_1,\dots,U_d)]
\end{equation*}`

with `$(U_1,\dots,U_d)$` uniform on `$[0,1]^d$`.
{{content}}
--

For each `$i$` 
{{content}}
--

* independently choose permutation `$\pi_i$` of `$\{1, \dots, N\}$`
{{content}}
--

* generate `$U_i^{(j)}$` uniformly on
  `$[\pi_i(j)/N, (\pi_i(j)+1)/N]$`.
{{content}}
--

For `$d = 2$` and `$N = 10$`:
--

.pull-right[
<img src="sim_files/figure-html/unnamed-chunk-30-1.png" style="display: block; margin: auto;" />
{{content}}
]
--

This is a random Latin square design.
{{content}}
--

In many cases this reduces variance compared to unrestricted random
sampling (Stein, 1987; Avramidis and Wilson, 1995; Owen, 1992, 1998)

---

### Common Variates and Blocking

.pull-left[
Suppose we want to estimate `$\theta = E[S] - E[T]$`
{{content}}
]
--

One approach is to chose independent samples `$T_1,\dots,T_N$` and
`$S_1,\dots,S_M$` and compute

`\begin{equation*}
  \widehat{\theta} =
  \frac{1}{M}\sum_{i=1}^M S_i - \frac{1}{N}\sum_{i=1}^N T_i
\end{equation*}`
--

.pull-right[
Suppose `$S = S(X)$` and `$T=T(X)$` for some `$X$`.
{{content}}
]
--

Instead of generating independent `$X$` values for `$S$` and `$T$` we may be
able to
{{content}}
--

* use the common `$X$` values to generate pairs
  `$(S_1,T_1),\dots,(S_N,T_N)$`;
{{content}}
--

* compute
  $$ \widetilde{\theta} = \frac{1}{N}\sum_{i=1}^N(S_i-T_i).$$

---

This use of _paired comparisons_ is a form of _blocking_.

This idea extends to comparisons among more than two statistics.

In simulations, we can often do this by using the same random variates
to generate `$S_i$` and `$T_i$`.  This is called using _common variates_.

This is easiest to do if we are using inversion; this, and the ability
to use antithetic variates, are two strong arguments in favor of
inversion.

Using common variates may be harder when rejection-based methods are
involved.

In importance sampling, using

`\begin{equation*}
  \theta^* = \frac{\sum h(X_i)w(X_i)}{\sum w(X_i)}
\end{equation*}`

can be viewed as a paired comparison; for some forms of `$h$` is can
have lower variance than the estimator that does not normalize by the
sum of the weights.

---

### Conditioning or Rao-Blackwellization

.pull-left[
Suppose we want to estimate `$\theta = E[X]$`
{{content}}
]
--

If `$X, W$` are jointly distributed, then

`\begin{equation*}
  \theta = E[X] = E[E[X|W]]
\end{equation*}`
{{content}}
--

and

`\begin{align*}
  \Var(X) &= E[\Var(X|W)] + \Var(E[X|W])\\
          &\ge  \Var(E[X|W])
\end{align*}`

.pull-right[
Suppose we can compute `$E[X|W]$`.
{{content}}
]
--

Then we can 
{{content}}
--

* generate `$W_1, \dots, W_N$`;
{{content}}
--

* compute
  `$$\widetilde{\theta} = \frac{1}{N} \sum E[X|W_i].$$`

---

This is often useful in Gibbs sampling.

Variance reduction is not guaranteed if `$W_1,\dots,W_N$` are not
independent.

Conditioning is particularly useful for density estimation:

If we can compute `$f_{X|W}(x|w)$` and generate `$W_1,\dots,W_N$`, then

`\begin{equation*}
  \widehat{f}_X(x) = \frac{1}{N}\sum f_{X|W}(x|W_i)
\end{equation*}`

is much more accurate than, say, a kernel density estimate based on a
sample `$X_1,\dots,X_N$`.

---

#### Example

Suppose we want to estimate `$\theta = P(X > t)$` where `$X=Z/W$` with
`$Z,W$` independent, `$Z \sim \text{N}(0,1)$` and `$W > 0$`.

Then

`\begin{equation*}
  P(X>t|W=w) = P(Z > tw) = 1-\Phi(tw)  
\end{equation*}`

So we can estimate `$\theta$` by generating `$W_1,\dots,W_N$` and computing

`\begin{equation*}
  \widetilde{\theta} = \frac{1}{N}\sum (1 - \Phi(tW_i))
\end{equation*}`

---

### Independence Decomposition

Suppose `$X_1,\dots,X_n$` is a random sample from a `$\text{N}(0,1)$`
distribution and

`\begin{equation*}
  \widetilde{X} = \text{median}(X_1,\dots,X_n)
\end{equation*}`

We want to estimate
`$\theta = \Var(\widetilde{X}) = E[\widetilde{X}^2]$`.

Crude Monte Carlo estimate: generate independent medians
`$\widetilde{X}_1,\dots,\widehat{X}_N$` and compute

`\begin{equation*}
  \widehat{\theta} = \frac{1}{N}\sum \widetilde{X}_i^2
\end{equation*}`

---

An alternative: Write

`\begin{equation*}
  \widetilde{X} = (\widetilde{X}-\overline{X})+\overline{X}
\end{equation*}`

`$(\widetilde{X}-\overline{X})$` and `$\overline{X}$` are independent, for
example by Basu's theorem.

`\begin{equation*}
  E[\widetilde{X}^2|\overline{X}]
  = \overline{X}^2 + E[(\widetilde{X}-\overline{X})^2]
\end{equation*}`

and

`\begin{equation*}
  \theta = \frac{1}{n} + E[(\widetilde{X}-\overline{X})^2]
\end{equation*}`

So we can estimate `$\theta$` by generating pairs
`$(\widetilde{X}_i,\overline{X}_i)$` and computing

`\begin{equation*}
  \widetilde{\theta} = \frac{1}{n} +
  \frac{1}{N}\sum(\widetilde{X}_i-\overline{X}_i)^2
\end{equation*}`

Generating these pairs may be more costly than generating medians
alone.

---

#### Example

Estimates:

```r
x <- matrix(rnorm(100000), ncol = 10)
mn <- apply(x, 1, mean)
md <- apply(x, 1, median)
mean(md^2)
## [1] 0.1371412
1 / 10 + mean((md - mn)^2)
## [1] 0.1382007
```

Asymptotic standard errors:

```r
sd(md^2)
## [1] 0.1977867
sd((md - mn)^2)
## [1] 0.05864061
```

---

### Princeton Robustness Study

> D. F. Andrews, P. J. Bickel, F. R. Hampel, P. J. Huber,
> W. H. Rogers, and J. W. Tukey, _Robustness of Location Estimates_,
> Princeton University Press, 1972.

Suppose `$X_1, \dots, X_n$` are a random sample from a symmetric density

`\begin{equation*}
  f(x-m).    
\end{equation*}`

We want an estimator `$T(X_1,\dots,X_n)$` of `$m$` that is

* accurate;
--

* robust (works well for a wide range of `$f$`'s).

---

The study considers many estimators, various different distributions.

All estimators are unbiased and _affine equivariant_, i.e.

`\begin{align*}
  E[T] &= m\\
  T(aX_1+b,\dots, aX_n+b) &= aT(X_1,\dots,X_n)+b
\end{align*}`

for any constants `$a, b$`.

We can thus take `$m = 0$` without loss of generality.

---

#### Distributions Used in the Study

.pull-left[
Distributions considered were all of the form

`\begin{equation*}
  X = Z/V
\end{equation*}`

with `$Z \sim \text{N}(0,1)$`, `$V > 0$`, and `$Z, V$` independent.
]

.pull-right[
Some examples:
{{content}}
]
--

* `$V \equiv 1$` gives `$X \sim \text{N}(0,1)$`.
{{content}}
--

* Contaminated normal:
  `$$V = \begin{cases} c & \text{with probability} \,  \alpha\\ 1 & \text{with probability} \, 1-\alpha \end{cases}$$`
{{content}}
--

* Double exponential:  `$V \sim f_V(v) = v^{-3} e^{-v^{-2}/2}$`
{{content}}
--

* Cauchy: `$V = |Y|$` with `$Y \sim \text{N}(0,1)$`.
{{content}}
--

* `$t_\nu$`: `$V \sim \sqrt{\chi^2_\nu/\nu}$`.

---

The conditional distribution `$X|V=v$` is `$\text{N}(0,1/v^2)$`.

Study generates `$X_i$` as `$Z_i/V_i$`.

Let

`\begin{align*}
  \widehat{X} &= \frac{\sum X_i V_i^2}{\sum V_i^2} &
  \widehat{S}^2 &= \frac{1}{n-1}\sum(X_i-\widehat{X})^2V_i^2 &
  C_i = \frac{X_i - \widehat{X}}{\widehat{S}}.
\end{align*}`

Then `$X_i = \widehat{X} + \widehat{S} C_i$`, and

`\begin{equation*}
  T(X) = \widehat{X} + \widehat{S} T(C)
\end{equation*}`

Can show that `$\widehat{X}, \widehat{S}, C$` are conditionally
independent given `$V$`.

---

#### Estimating Variances

.pull-left[
Suppose we want to estimate `$\theta = \Var(T) = E[T^2]$`.
{{content}}
]
--

Then

`\begin{align*}
  \theta &= E[(\widehat{X}+\widehat{S} T(C))^2]\\
         &= E[\widehat{X}^2 + 2 \widehat{S} \widehat{X} T(C) +
            \widehat{S}^2 T(C)^2]\\
         &= E[E[\widehat{X}^2 + 2 \widehat{S}\widehat{X}T(C) +
            \widehat{S}^2 T(C)^2|V]]
\end{align*}`
{{content}}
--

and

`\begin{align*}
  E[\widehat{X}^2|V] &= \frac{1}{\sum V_i^2}\\
  E[\widehat{X}|V] &= 0\\
  E[\widehat{S}^2|V] &= 1
\end{align*}`

.pull-right[
So

`\begin{equation*}
  \theta = E\left[\frac{1}{\sum V_i^2}\right] + E[T(C)^2]
\end{equation*}`
{{content}}
]
--

The strategy:
{{content}}
--

* Compute `$E[T(C)^2]$` by crude Monte Carlo
{{content}}
--

* Compute `$E\left[\frac{1}{\sum V_i^2}\right]$` the same way or
  analytically.

---

Some exact calculations:

* If `$V_i \sim \sqrt{\chi^2_\nu/\nu}$`, then
`\begin{equation*}
  E\left[\frac{1}{\sum V_i^2}\right] =
  E\left[\frac{\nu}{\chi^2_{n\nu}}\right]
  = \frac{\nu}{n\nu -2}
\end{equation*}`

* Contaminated normal:
`\begin{equation*}
  E\left[\frac{1}{\sum V_i^2}\right] =
  \sum_{r=0}^n \binom{n}{r} \alpha^r(1-\alpha)^{n-r}\frac{1}{n-r+rc}
\end{equation*}`

#### Comparing Variances

If `$T_1$` and `$T_2$` are two estimators, then

`\begin{equation*}
  \Var(T_1) - \Var(T_2) = E[T_1(C)^2] - E[T_2(C)^2]
\end{equation*}`

We can reduce variances further by using common variates.

---

#### Estimating Tail Probabilities

.pull-left[
Suppose we want to estimate

`\begin{align*}
  \theta &= P(T(X) > t)\\
    &= P(\widehat{X} + \widehat{S} T(C) > t)\\
    &= E\left[P\left(\left.\sqrt{\sum V_i^2}\frac{t - \widehat{X}}{\widehat{S}}
      < \sqrt{\sum V_i^2} T(C)\right| V, C\right)\right]\\
    &= E\left[F_{t,n-1}\left(\sqrt{\sum V_i^2} T(C)\right)\right]
\end{align*}`

where `$F_{t,n-1}$` is the CDF of a non-central `$t$` distribution (the
parameter `$t$` is not the usual non-centrality parameter).
]

.pull-right[
This CDF can be evaluated numerically, so we can estimate `$\theta$` by

`\begin{equation*}
  \widehat{\theta}_N =
  \frac{1}{N} \sum_{k=1}^N
  F_{t,n-1}\left(T(C^{(k)})\sqrt{\sum {V_i^{(k)}}^2}\right)
\end{equation*}`
{{content}}
]
--

An alternative is to condition on `$V, C, \widehat{S}$` and use the
conditional normal distribution of `$\widehat{X}$`.

//adapted from Emi Tanaka's gist at //https://gist.github.com/emitanaka/eaa258bb8471c041797ff377704c8505