[R] MCMC gradually slows down

[William Dunlap]

> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Jens Malmros
> Sent: Sunday, November 08, 2009 11:11 AM
> To: r-help at r-project.org
> Subject: [R] MCMC gradually slows down
> 
> Hello,
> 
> I have written a simple Metropolis-Hastings MCMC algorithm for a
> binomial parameter:
> 
> MHastings = function(n,p0,d){
> 	theta = c()

Change that theta <- c() to
      theta <- numeric(n)
and it will go faster.  Growing datasets
can result in a lot of unnecessary memory
management.  The original had an obvious
quadratic quality in the plot of n vs. MHastings(n,.2,2)
and preallocating theta to its final length
made it look linear up to n=100000 and at n=100000
the time for the original was 35 seconds vs 3.75
for the preallocated version.

Bill Dunlap
Spotfire, TIBCO Software
wdunlap tibco.com  

> 	theta[1] = p0
> 	t =1
> 	while(t<=n){
> 		phi = log(theta[t]/(1-theta[t]))
> 		phisim = phi + rnorm(1,0,d)
> 		thetasim = exp(phisim)/(1+exp(phisim))
> 		r = 
> (thetasim)^4*(1-thetasim)^8/(theta[t]^4*(1-theta[t])^8)
> 		if(runif(1,0,1)<r){
> 			theta[t+1] = thetasim
> 		} else {
> 			theta[t+1] = theta[t]
> 		}
> 		t = t+1
> 		if(t%%1000==0) print(t) # diagnostic
> 	}
> 	data.frame(theta)
> }
> 
> The problem is that it gradually slows down. It is very fast in the
> beginning, but slows down and gets very slow as you reach about 50000
> iterations and I need do to plenty more.
> 
> I know there are more fancy MCMC routines available, but I am really
> just interested in this to work.
> 
> Thank you for your help,
> Jens Malmros
> 
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