Non-Centered Reparameterisation for the Negative Binomial Distribution?

Questions
1

A typical suggestion that I see with model specification is switching between centered and non-centered representations for scale parameters e.g., see here: https://twiecki.io/blog/2017/02/08/bayesian-hierchical-non-centered/

The intution I have behind this is that, for the centered model, the posterior looks very different for different values of scale parameters, making it a nightmare to sample from.

I’m basically have the same issue, but I’m using a negative binomial output distribution with an unknown dispersion parameter. I place a prior over this dispersion, similar to placing a prior over the scale parameter, but I suppose that the posterior is different to different values of this parameter, giving issues. For example, I noticed an approximate 2x speed-up from changing my model to use a fixed dispersion rather than having a prior over the dispersion.

I’m wondering if this could be caused by a similar issue with centered parameterisations for scale parameters, or instead perhaps the prior I place on the dispersion is ‘poor’ in some respect.

Thanks :slight_smile:

2

centered and non-centered is for latent variables - for observed (i.e., likelihood) it doesnt make much sense usually. I think your reasoning about poor prior for dispersion is correct - try assigning more informative prior usually helps.

1 Like
3

Cool, thanks. Is there any best practice for setting the prior for dispersion?

4

Hi @MrinankSharma,
You can take a look at https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations, I think it’ll be useful :wink:

5

Hello,

This is a very useful post and reply. Could you please provide an example of centered and non-centered parameterization for latent negative binomial? I know what to do for Normal but I cannot figure out what should be done for negative binomial.

Thanks

6

latent negative binomial probably wont make much differences when you try to run inference, i suggest you try to see if there is alternative implementation that does not need a latent discrete variable first.