Finishing Comparison Parametric And Nonparametric

[x] Inverse gamma priors on variances 36888da
[x] Uniform prior on standard deviations 75df941
[x] Mean plot for parametric fit 75df941
[x] Convergence diagnostics for both parametric and nonparametric MCMC, using similar visual layout 75df941
Oh, Jeromy Anglim has a rather nice collection of jags links

On Variance Priors for the Parametric MCMC

Gelman recommends uniform priors on standard deviations for the noise terms: in the .bugs file we have

stdQ ~ dunif(0,100)
stdR ~ dunif(0,100)
# as "precision" tau instead of stdev sigma
iQ <- 1/(stdQ*stdQ);
iR <- 1/(stdR*stdR);

Where these enter the model as

for(t in 1:(N-1)){
    mu[t] <- x[t] + exp(r0 * (1 - x[t]/K)* (x[t] - theta) )
      x[t+1] ~ dnorm(mu[t],iQ)
}


for(t in 1:(N)){
    y[t] ~ dnorm(x[t],iR)
}

Note that dnorm in JAGS notation is defined in terms of the mean and the precision (reciprocal of the variance), rather than standard deviation (e.g. in R’s dnorm function), see the JAGS manual, particularly Table 6.1 pg 29, below. Note that the standard deviation has the uniform prior, not the precision.

Also try inverse gamma priors,

iQ ~ dgamma(0.0001,0.0001)
iR ~ dgamma(0.0001,0.0001)

(Precision is Gamma distributed when the variances are inverse-gamma distributed.

Both are quite uniformative, results appear quite comparable.

Markov Chain Monte Carlo Convergence Analysis

Add for both parametric and non-parametric cases
Extra long runs before finalizing analysis
Some examples with R code

A variety of tools from coda package. Of course these methods are designed from toy problems and cannot guarentee convergence.

Traceplots, density plots
Running mean, autocorrelation plots autocorr.plot
Metropolis acceptance/rejection rate rejectionRate
Multiple chain diagonostics: Gelman-Rubin gelman.diag, gelman.plot
Geweke (compare means between different sections) geweke.diag
Raferty-Lewis raferty.diag
Heidelberg and Welch heidel.diag