slice sampler reached maximum number of contractions

[Sara Euzzor]

Hi everyone, 

I am trying to fit a quite complex model in Nimble, and when trying to improve the convergence of certain parameters I encountered a problem with the slice sampler. 

I am using a slice sampler for the standard deviations of a spline (modelled as a Multivariate Normal Distribution as specified in Just Another Gibbs Additive Modeler: Interfacing JAGS and mgcv | Journal of Statistical Software ), and the problem arose when I started using an elliptic sampler for the coefficient of said spline. 

The response is a multivariate (3 responses) constrained dataset (represents percentage of people using object A,B,C so should sum to < 1). I am modelling it by transforming into count data and using a beta-binomial distribution. 

I have tried simplifying the model so that it contains only an intercept and a spline for GDP, but the problem persisted. 

As a last resort, I am simulating response data using a known intercept, standard deviation (which is then used to simulate known spline coefficients), and concentration (to control the variability of the beta-binomial).  

I am then fitting the model. The error message still comes up. Most parameters are retrieved correctly from the model. The first standard deviation (which penalizes the wigglines of the non-linear basis functions) always ends up converging at 0 though. 

I have included the Rscript with the simulated code. Can anyone spot any mistakes or find a cause of the problems with the slice sampler? I have noticed that it fails when the current value is a point of maximum of the posterior density but can't really find a theoretical justification for that.

Many thanks, 

Sara

[Chris Paciorek]

Hi Sara,

It looks like the lambda values are getting stuck in the slice sampling. They stay at the same value for multiple iterations. I think this is when the warnings about contractions are emitted. I suspect it's because somehow the values of the b_gdp values are such that other possible lambda values are not feasible, so that both lambda values get stuck until the b_gdp values shift some. I don't know why this particular combination of samplers is causing that to happen. Another difficulty is that in some cases lambda_1 seems to drift down towards zero and not sample from larger values after it does that.

You might try HMC via nimbleHMC here. I tried it briefly and it seems to help somewhat, but still mixes slowly for some of the parameters (particularly lambda_1) so you may need to run it for a while. If you try it you need to add `buildDerivs=TRUE` as the last argument when creating `dmybetabin3` and calling `nimbleModel`.

-chris

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