Basic MCMC DiagnosticsSTAT8810, Fall 2017

M.T. Pratola

November 19, 2017

Today

TraceplotsConvergence DiagnosticsEffective Sample Size

Basic MCMC Diagnostics

• MCMC is an algorithm that generates (approximate) samplesfrom the posterior distribution of interest.

• We would like to check, to some degree, if our samples are anygood.

• This is a difficult problem. Most methods in the literature areunivariate.

• Run multiple chains: do they agree with eachother?• Run a long chain: is the chain transient or stationary?• Insightful plots are helpful.• Strategy: check for (obvious) ways it might have failed, rather

than checking (guaranteeing) that it worked.

Traceplots

• First place to start. This is simply a plot of the sample versusits index.

• Plot should show stationary behavior - constant mean/median,constant variance, no trend.

• Often, this is called the “fat marker” test.• Check the autocorrelation by making an ACF plot. The ACF

should decay rapidly.• Ideally, we want independent draws from the posterior.

Examplesource("dace.sim.r")set.seed(88)n=10k=1rhotrue=0.2lambdaytrue=1design=as.matrix(runif(n))l1=list(m1=outer(design[,1],design[,1],"-"))l.dez=list(l1=l1)R=rhogeodacecormat(l.dez,c(rhotrue))$RL=chol(R)u=rnorm(nrow(R))z=t(L)%*%u

# now set up our observed data:y=zl1=list(m1=outer(design[,1],design[,1],"-"))l.dez=list(l1=l1)

Examplesource("regression.r")pi=list(az=5,bz=5,rhoa=rep(1,k),rhob=rep(5,k))

# Run MCMC using a proposal width of 1e-5 for# the rho parameters.mh=list(rr=1e-5)

# regress works as follows:# Adapt for first 50% of iterations -- here that is 2500.# Further burn-in is draws up to start of last# iterations -- here that is 2501--4000.# last is number of draws to take as posterior samples.# Here that is 4001--5000.

fit=regress(y,l.dez,5000,pi,mh,last=1000,adapt=FALSE)

#### Bayesian Gaussian Process Interpolation model## The last 999 samples from the posterior will be reported## The stepwidth for uniform corr. param proposal distn is rr= 1e-05## Prior params: az= 5 bz= 5## ----------------------------------------------------------------###### 0.04 percent complete0.06 percent complete0.08 percent complete0.1 percent complete0.12 percent complete0.14 percent complete0.16 percent complete0.18 percent complete0.2 percent complete0.22 percent complete0.24 percent complete0.26 percent complete0.28 percent complete0.3 percent complete0.32 percent complete0.34 percent complete0.36 percent complete0.38 percent complete0.4 percent complete0.42 percent complete0.44 percent complete0.46 percent complete0.48 percent complete0.5 percent complete0.52 percent complete0.54 percent complete0.56 percent complete0.58 percent complete0.6 percent complete0.62 percent complete0.64 percent complete0.66 percent complete0.68 percent complete0.7 percent complete0.72 percent 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