1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
|
R version 2.13.1 (2011-07-08)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
>
> # test batching (blen) and spacing (nspac) together
>
> epsilon <- 1e-15
>
> library(mcmc)
>
> RNGkind("Marsaglia-Multicarry")
> set.seed(42)
>
> n <- 100
> rho <- 0.5
> beta0 <- 0.25
> beta1 <- 1
> beta2 <- 0.5
>
> x1 <- rnorm(n)
> x2 <- rho * x1 + sqrt(1 - rho^2) * rnorm(n)
> eta <- beta0 + beta1 * x1 + beta2 * x2
> p <- 1 / (1 + exp(- eta))
> y <- as.numeric(runif(n) < p)
>
> out <- glm(y ~ x1 + x2, family = binomial())
>
> logl <- function(beta) {
+ if (length(beta) != 3) stop("length(beta) != 3")
+ beta0 <- beta[1]
+ beta1 <- beta[2]
+ beta2 <- beta[3]
+ eta <- beta0 + beta1 * x1 + beta2 * x2
+ p <- exp(eta) / (1 + exp(eta))
+ return(sum(log(p[y == 1])) + sum(log(1 - p[y == 0])))
+ }
>
> out.metro <- metrop(logl, coefficients(out), 1e3, scale = 0.01)
> out.metro$accept
[1] 0.982
>
> out.metro <- metrop(out.metro, scale = 0.1)
> out.metro$accept
[1] 0.795
>
> out.metro <- metrop(out.metro, scale = 0.5)
> out.metro$accept
[1] 0.264
>
> apply(out.metro$batch, 2, mean)
[1] 0.06080257 1.42304941 0.52634149
>
> out.metro <- metrop(logl, as.numeric(coefficients(out)), 1e2,
+ scale = 0.5, debug = TRUE, blen = 5, nspac = 3)
>
> niter <- out.metro$nbatch * out.metro$blen * out.metro$nspac
> niter == nrow(out.metro$current)
[1] TRUE
> niter == nrow(out.metro$proposal)
[1] TRUE
> all(out.metro$current[1, ] == out.metro$initial)
[1] TRUE
> all(out.metro$current[niter, ] == out.metro$final) |
+ all(out.metro$proposal[niter, ] == out.metro$final)
[1] TRUE
>
> .Random.seed <- out.metro$initial.seed
> d <- ncol(out.metro$proposal)
> n <- nrow(out.metro$proposal)
> my.proposal <- matrix(NA, n, d)
> my.u <- double(n)
> ska <- out.metro$scale
> for (i in 1:n) {
+ my.proposal[i, ] <- out.metro$current[i, ] + ska * rnorm(d)
+ if (is.na(out.metro$u[i])) {
+ my.u[i] <- NA
+ } else {
+ my.u[i] <- runif(1)
+ }
+ }
> max(abs(out.metro$proposal - my.proposal)) < epsilon
[1] TRUE
> all(is.na(out.metro$u) == is.na(my.u))
[1] TRUE
> all(out.metro$u[!is.na(out.metro$u)] == my.u[!is.na(my.u)])
[1] TRUE
>
> my.curr.log.green <- apply(out.metro$current, 1, logl)
> my.prop.log.green <- apply(out.metro$proposal, 1, logl)
> all(is.na(out.metro$u) == (my.prop.log.green > my.curr.log.green))
[1] TRUE
> foo <- my.prop.log.green - my.curr.log.green
> max(abs(foo - out.metro$log.green)) < epsilon
[1] TRUE
>
> my.accept <- is.na(my.u) | my.u < exp(foo)
> sum(my.accept) == round(n * out.metro$accept)
[1] TRUE
> if (my.accept[niter]) {
+ all(out.metro$proposal[niter, ] == out.metro$final)
+ } else {
+ all(out.metro$current[niter, ] == out.metro$final)
+ }
[1] TRUE
>
> my.current <- out.metro$current
> my.current[my.accept, ] <- my.proposal[my.accept, ]
> my.current <- rbind(out.metro$initial, my.current[- niter, ])
> max(abs(out.metro$current - my.current)) < epsilon
[1] TRUE
>
> my.path <- matrix(NA, n, d)
> my.path[my.accept, ] <- out.metro$proposal[my.accept, ]
> my.path[! my.accept, ] <- out.metro$current[! my.accept, ]
> nspac <- out.metro$nspac
>
> my.path <- my.path[seq(nspac, niter, by = nspac), ]
>
> foom <- array(as.vector(t(my.path)), c(d, out.metro$blen, out.metro$nbatch))
> boom <- t(apply(foom, c(1, 3), mean))
>
> all(dim(boom) == dim(out.metro$batch))
[1] TRUE
> max(abs(boom - out.metro$batch)) < epsilon
[1] TRUE
>
>
|
