Poisson lognormal convergence

[Isaque Pim]

Dear Nimble users,

I've been using Nimble to model case counts of the West African Ebola outbreak. I'm doing it in the same fashion people model the famous Scotland Lip Cancer dataset. Currently I'm having some trouble trying to make the model converge.

Actually, the basic Poisson lognormal model apparently  presents no MCMC problems. When I add an ORLE term, autocorrelation spikes and the model shows poor efficiency (some betas presenting 0.1 ESS/s).

Here’s a sample of the attached code:

#Simple model, no ORLE 

modelo1_simples <- nimbleCode({

  for (i in 1:N){

    y[i] ~ dpois(mu[i])

    log(mu[i]) <- log(e[i]) + b0 + inprod(X[i,1:p],beta[1:p])

  }

  b0 ~ dnorm(0,0.001)

  beta[1:p] ~ dmnorm(mean = m[1:p], cov = cov[1:p, 1:p])

})

# Model with ORLE

modelo2_ORLE <- nimbleCode({

  for (i in 1:N){

    y[i] ~ dpois(mu[i])

    log(mu[i]) <- log(e[i]) + b0 + inprod(X[i,1:p],beta[1:p]) + u[i]

    u[i] ~ dnorm(0, tau.b)

  }

  tau.b ~ dgamma(1,0.01)

  b0 ~ dnorm(0,0.001) 

  beta[1:p] ~ dmnorm(mean = m[1:p], cov = cov[1:p, 1:p])

})

And I’m running quite long chains: 300,000 iter; 200,000 burnin; thinning = 10.

As another example, take a look at the traceplot for the same beta for each model

Any suggestions on how to deal with the problem? Could it be model misspecification?

Code and data attached. 

Thanks,

Isaque

[Chris Paciorek]

I suspect the mean of the u's is trading off with b0. You might try a centered parameterization:

u[i] ~ dnorm(b0, tau)

Or you might devise a joint sampler for b0 and the u's jointly - we have an example on this in

some materials for our short courses.

Or you might try HMC using our new beta release of nimble and the associated nimbleHMC package.

-Chris

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