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View Code? Open in Web Editor NEWR package for general Metropolis Hastings sampling
Home Page: cran.r-project.org/web/packages/MHadaptive/
License: Other
R package for general Metropolis Hastings sampling
Home Page: cran.r-project.org/web/packages/MHadaptive/
License: Other
Hi,
For pedagogical reasons, I wanted to use different MCMC samplers to sample from a multivariate normal [the goal was to show that MCMC is great and all, but nothing beats sampling directly]. Here is the code for the analysis I wanted to present:
set.seed(666^3)
M <- 1E4
K <- 31
Mu <- rnorm(K, mean = 0, sd = 10)
P <- qr.Q(qr(matrix(rnorm(K^2), K)))
SS <- crossprod(P, P*(K:1))
target <- function(x){
mvtnorm::dmvnorm(x, mean = Mu, sigma = SS, log = TRUE)
}
########
indep.samples <- MASS::mvrnorm(n = M, mu = Mu, Sigma = SS)
MH1 <- mcmc::metrop(target, initial = rnorm(K), nbatch = M)
MH1.samples <- MH1$batch
MH2 <- MHadaptive::Metro_Hastings(li_func = target,
pars = rnorm(K),
burn_in = 1000,
iterations = M + round(.1 * M))
MH2
MH2.samples <- MH2$trace
library(rstan)
mvmodel <- '
data{
int <lower=0> k;
matrix[k , k] Sigma;
vector[k] mu;
}
parameters{
vector[k] x;
}
model{
x ~ multi_normal(mu, Sigma);
}
'
stan.data <- list(
k = K,
mu = Mu,
Sigma = SS
)
StanRun <- stan(model_code = mvmodel, data = stan.data, iter = M, chains = 2 )
Stan.samples <- extract(StanRun, 'x')$x
Means <- list(
indep = data.frame(est = colMeans(indep.samples), truth = Mu, sampler = "indep"),
MH = data.frame(est = colMeans(MH1.samples), truth = Mu, sampler = "MH"),
adapMH = data.frame(est = colMeans(MH2.samples), truth = Mu, sampler = "adaptMH"),
Stan = data.frame(est = colMeans(Stan.samples), truth = Mu, sampler = "Stan")
)
####
## mean squared error and mean relative error
lapply(Means, function(dt) mean((dt$truth-dt$est)^2))
lapply(Means, function(dt) mean((dt$truth-dt$est)/dt$truth))
###
mean.results <- do.call(rbind, Means)
mean.results$sampler <- factor(mean.results$sampler,
levels = sort(levels(as.factor(mean.results$sampler)), FALSE) )
library(ggplot2)
p0 <- ggplot(mean.results,
aes(x = sampler, y = (truth-est)/truth,
fill = sampler, colour = sampler) ) +
stat_summary(fun.data = mean_se, size = 1.5) +
scale_x_discrete("Sampler") +
scale_y_continuous(expression((mu-hat(mu))/mu),
expand = c(0, 0)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
NULL
p0
p1 <- ggplot(mean.results,
aes(x = sampler, y = (truth-est)/truth,
fill = sampler) ) +
geom_boxplot(position = "dodge") +
scale_x_discrete("Sampler") +
scale_y_continuous(expression((mu-hat(mu))/mu),
expand = c(0, 0)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
NULL
p1
p2 <- ggplot(mean.results,
aes(x = truth, y = est,
fill = sampler, colour = sampler) ) +
geom_point() +
scale_x_continuous(expression(mu)) +
scale_y_continuous(expression(hat(mu))) +
geom_abline(intercept = 0, slope = 1, linetype = "dashed") +
theme_bw() +
NULL
p2
It's a bit long, I know, and includes stuff unrelated to MHadaptive, but I wanted to show the whole thing for transparency. It seems to me that Metro_Hastings()
does exceptionally badly in this example, and I can't think of a reason why this would be. Am I employing the function incorrectly? Am I perhaps computing the wrong quantities?
Thanks in advance
Elevating issues out of TODO file. I am not sure how easy this is, but further development on adaptive functionality would be nice.
Elevating the item from TODO file. This would be really important for diagnostics and serious (publishable) results
May I please elevate the excellent todo items you have listed in the file. This would be really important and helpful for comparing performance across packages and alleviate the need for custom plot functions.
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