R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1 Patched (2005-08-04), ISBN 3-900051-07-0

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> invisible(options(echo = TRUE))
> 
> foo <- read.table(url("http://www.stat.umn.edu/geyer/PhD/F03/logit.txt"),
+     header = TRUE)
> 
> x <- foo
> x$y <- NULL
> x <- as.matrix(x)
> x <- cbind(1, x)
> dimnames(x) <- NULL
> y <- foo$y
> 
> lupost <- function(beta) {
+     eta <- x %*% beta
+     p <- 1 / (1 + exp(- eta))   # note: works even when eta is Inf or -Inf
+     logl <- sum(log(p[y == 1])) + sum(log(1 - p[y == 0]))
+     return(logl + sum(dnorm(beta, 0, 2, log = TRUE)))
+ }
> 
> library(mcmc)
> set.seed(42)
> beta.init <- rep(0, ncol(x))
> out <- metrop(lupost, beta.init, blen = 100, nbatch = 1e2, scale = 0.4)
> out$accept
[1] 0.232
> 
> fred <- function(z) {
+     sally <- 1 / (1 + exp(- z[1]))
+     c(sally, sally^2)
+ }
> 
> out <- metrop(out, nbatch = 1e3, outfun = fred)
> out$accept
[1] 0.23566
> 
> # plot(out$batch[ , 1])
> # plot(out$batch[ , 2])
> # acf(out$batch[ , 1])
> # acf(out$batch[ , 2])
> # barely signif lag-1, double batch length?
> 
> mu.hat <- mean(out$batch[ , 1])
> mu.mcse <- sd(out$batch[ , 1]) / sqrt(out$nbatch)
> print(mu.hat)
[1] 0.6577262
> print(mu.mcse)
[1] 0.0008380032
> 
> var.hat <- mean(out$batch[ , 2] - mu.hat^2)
> ##### bogus
> var.mcse <- sd(out$batch[ , 2] - mu.hat^2) / sqrt(out$nbatch)
> ##### right
> delta1 <- out$batch[ , 1] - mean(out$batch[ , 1])
> delta2 <- out$batch[ , 2] - mean(out$batch[ , 2])
> var.mcse.ok <- sqrt(mean((delta2 - 2 * mu.hat * delta1)^2) / out$nbatch)
> print(var.hat)
[1] 0.004427835
> print(var.mcse)
[1] 0.001103689
> print(var.mcse.ok)
[1] 6.48155e-05
> 
> sigma.hat <- sqrt(var.hat)
> sigma.mcse <- var.mcse / (2 * sigma.hat)
> sigma.mcse.ok <- var.mcse.ok / (2 * sigma.hat)
> print(sigma.hat)
[1] 0.06654198
> print(sigma.mcse)
[1] 0.008293178
> print(sigma.mcse.ok)
[1] 0.0004870272
> 
> ##### looks like merely doubling the batch length should do it
> 
> out <- metrop(out, blen = 250, outfun = fred)
> out$accept
[1] 0.234812
> 
> mu.hat <- mean(out$batch[ , 1])
> mu.mcse <- sd(out$batch[ , 1]) / sqrt(out$nbatch)
> print(mu.hat)
[1] 0.6566396
> print(mu.mcse)
[1] 0.0005460812
> 
> var.hat <- mean(out$batch[ , 2] - mu.hat^2)
> ##### bogus
> var.mcse <- sd(out$batch[ , 2] - mu.hat^2) / sqrt(out$nbatch)
> ##### right
> delta1 <- out$batch[ , 1] - mean(out$batch[ , 1])
> delta2 <- out$batch[ , 2] - mean(out$batch[ , 2])
> var.mcse.ok <- sqrt(mean((delta2 - 2 * mu.hat * delta1)^2) / out$nbatch)
> print(var.hat)
[1] 0.004376975
> print(var.mcse)
[1] 0.0007199504
> print(var.mcse.ok)
[1] 4.002801e-05
> 
> sigma.hat <- sqrt(var.hat)
> sigma.mcse <- var.mcse / (2 * sigma.hat)
> sigma.mcse.ok <- var.mcse.ok / (2 * sigma.hat)
> print(sigma.hat)
[1] 0.06615871
> print(sigma.mcse)
[1] 0.005441085
> print(sigma.mcse.ok)
[1] 0.000302515
> 
> print(out$nbatch)
[1] 1000
> print(out$blen)
[1] 250
> print(out$nspac)
[1] 1
> print(out$nburn)
NULL
> print(out$nbatch * out$blen)
[1] 250000
> 
> proc.time()
[1] 42.42  0.09 42.93  0.00  0.00
>