I obtained posterior samples for a parameter of interest, \lambda, using Stan. I would like to use this posterior as a prior for another model. The distribution looks like a beta distribution so I wrote a Stan model to approximate the beta parameters for \lambda. I could use this beta distribution …

[image] JordanLO: Instead of just passing in the posterior means or medians, could I pass in the posterior samples Stan’s not set up to do this in a single run. [image] JordanLO: … just want to check it is doing what I think it is doing. I.e., my prior is a beta(a,b) and this includes th…

I could be wrong, but I think that the issue with passing a[M] and b[M] is that the prior on lambda now has M contributions to the log posterior. You really want a single contribution to the log posterior that integrates over all the values of a and b. You could try something like target += beta_lu…

I tried this and it did not work. But, I don’t think we want to subtract \log(M). If Stan is using p(\lambda \mid a_1, b_1) \times \dots p(\lambda \mid a_M, b_M) as the prior, I think we want to replace this with [p(\lambda \mid a_1, b_1) \times \dots p(\lambda \mid a_M, b_M)]^{1/M}. I tried the fo…

Investigate mixture approximations. That’s the closest you’ll get. E.g. the RBesT had good implementations including for multivariate normal (remember a-posteriori some parameters will be correlated, even if they weren’t in your initial prior).

See Robert Grant - stats This works but the code is inefficient and alpha in R and still in progress in Stata/Mata. Thence to Rcpp next year. Also I have yet to do side-by-side comparisons with VAEs, GANs and all those popoular methods. It will be a helluiva lot easier than mixtures, where you have…

Posterior from STAN model as prior for another model

Modeling

jsocolar November 10, 2024, 2:08pm 7

You might be able to quickly and efficiently achieve the inference you want via importance sampling using the previous MCMC samples as your proposal distribution. See Updating model based on new data via PSIS

Topic		Replies	Views
Including a posterior from previous experiment for a coefficient Modeling	2	458	September 15, 2020
Fit a beta distribution that captures correlation in the fitted parameters? Modeling rstan , techniques , fitting-issues , specification	6	1939	January 13, 2022
How to use prior from a sample? Modeling pystan , stan , priors	5	631	October 25, 2023
Priors Not Having an Effect on Posterior Samples Modeling rstan , priors	5	187	March 17, 2025
Composing Stan models (posterior as next prior) General	28	7848	February 6, 2020

Posterior from STAN model as prior for another model

Related topics