I have a multivariate distribution parametrized by a vector mu and a Cholesky decomposed covariance matrix sigma = L.L^T. Pretty much the same as in the docs . Now I want to update the prior whenever I have new data available, but the examples do not cover how to do this for cases where the paramete…

You mean the updating prior using interpolation? Yeah that wouldnt work in your case with a vector prior. But maybe you can parameterized on the things like eta of LKJCorr and update that instead?

Oh maybe try something like: [image] Performance speedup for updating posterior with new data Questions I had a look at your code. Unfortunately, I dont see much more room to improve the speed, as the Interpolation rv always need to reinitialized, and the bottom neck in th…

Thank you, I think I mostly get it. I can get the means of each set of trace samples for Xi in X = [X1, …Xn] and then use a student-t distribution to approximate the actual distribution over X. Assuming that my understand is correct, there are two questions: How would I provide the n mean values…

Maybe it would be easier if you can share your code and indicate which are the parameters you would like to do posterior update.

A notebook can be found here . [image] junpenglao: maybe you can parameterized on the things like eta of LKJCorr and update that instead I doubt that the way I’ve done this in the notebook is correct because I wasn’t sure what the right way to approximate LKJCholeskyCov was.

Hmmm i see. In theory you can always approximate the latent freeRVs (not necessary the RV you wrote down, as pymc3 sample in the nonbounded real space) with a distribution, but it would involves changing the model quite a bit…

Thanks for your reply. Could you please elaborate a little more? I understand your comment about approximating latent free RVs but do you have any ideas on how I could go about modeling that?

@junpenglao I re-parametrized my model, like so: with pm.Model() as model1: mu = pm.InverseGamma('mu', 3., 1., shape=shape) eta = pm.Gamma('eta', 3., 1.) sd_dist = pm.HalfCauchy('sd_dist', 2.5) packed_L = pm.LKJCholeskyCov('packed_L', n=shape, eta=eta, sd_dist=sd_dist) L = …

Sorry about the non response. we did not directly model the var parameters on the diag - but maybe you can model the diag and the corr matrix separately.

Thanks, is there a reason for this choice of design?

Drawing from posterior of a Multivariate Distribution

Questions

junpenglao December 6, 2018, 2:34pm 3

Oh maybe try something like:

Topic		Replies	Views
Updating multivariate priors Questions	11	3550	March 12, 2019
Can traces be used as priors? Questions	5	2462	September 12, 2019
Prior propagation by nonparametric copulas Sharing	0	1234	April 26, 2019
Incremental updates with independent multi-dimensional parameters Questions	0	506	October 12, 2020
How to use the posterior distribution of one model as a prior distribution for another model General	19	2060	April 9, 2024

Drawing from posterior of a Multivariate Distribution

Related topics