prior distribution as samples

[Xulong Wang]

Hi Stan,

I have a hierarchical model, in which I have the complete sample pool for one of the hyperparameter's prior distribution, instead of a parametric formula. In this case, this prior is very formative. I am not clear how Stan handles this. Do I have to first fit the prior samples with a parametric distribution? 

Best,

Xulong

[Krzysztof Sakrejda]

On Thursday, August 20, 2015 at 10:32:23 AM UTC-4, Xulong Wang wrote:

Hi Stan,

I have a hierarchical model, in which I have the complete sample pool for one of the hyperparameter's prior distribution, instead of a parametric formula. In this case, this prior is very formative. I am not clear how Stan handles this. Do I have to first fit the prior samples with a parametric distribution? 

Yes, that's likely the best way to do it at the moment, though it can have some issues. I think some folks (Michael and Ben I think) pointed out on a previous question that marginal posteriors used as priors are throwing out a lot of information (e.g., about covariance).

Krzysztof
 

Best,

Xulong

[Michael Betancourt]

Yes.  Look into Sequential Monte Carlo if you want to use samples as a prior.

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[Xulong Wang]

After reading a sequential monte carlo document, together with several previous posts in the mailing list. I would fit the samples to a parametric distribution using methods of moments and continue with Stan.

Thanks Michael and Krzysztof for your quick and precise points.

[Daniel Lakeland]

On Thursday, August 20, 2015 at 11:40:25 AM UTC-7, Xulong Wang wrote:

After reading a sequential monte carlo document, together with several previous posts in the mailing list. I would fit the samples to a parametric distribution using methods of moments and continue with Stan.

You might take the samples, input them into a Stan program that fits the parametric distribution, and then use the average of the posterior samples of the parameters from this Stan run as constants defining the priors in your next Stan run?

That is, if method of moments doesn't do a good enough job for you.

[Xulong Wang]

Daniel, tried your method. It works great. The sample distribution and estimated distributions overlap perfectly. I actually like your approach much better than MoM, because now everything is within Stan and sampling.