Bayesian inference in theory is composable: a posterior distribution of one model can be a prior for another one. Can this be achieved in Stan? Specifically, if I have an output sample matrix from one Stan model, can I turn it into a multivariate prior in another Stan model?

Thanks @maxbiostat ! I’ll roll that paper and the code into our working group to study.

@Ara_Winter - Side note, here’s a potentially relevant paper: https://osf.io/jrjd2/ - “Cumulative science via Bayesian posterior passing, an introduction.”

You set a_0, however, you could also estimate it. In your experience, what is typically done?

You may also want to follow Omega.jl where composability is a main feature (i.e. condition on predicates). It looks to be quite experimental and the author recommends using Stan if your model is expressible in Stan. zenna/Omega.jl/blob/master/docs/src/omegavsotherppls.md # Omega vs other Pr…

Typically, a_0 is fixed. But you’re absolutely right it can be estimated. You just need to be careful about the normalising constant: c(a_0) = \int_{\Theta} L(D \mid \theta)^{a_0}\pi(\theta)d\theta. See this note for discussion and examples. The paper I linked above also has a section with discussi…

[image] betanalpha: but let me warn that they typically hemorrhage information Note that the power prior approach also suffers from this information leakage. For a few models, we know how to set a_0 such that some “information-optimality” is satistified (see this paper).

Hi, I am having a similar issue. I am estimating the matrix A in a model where y = Ax + e with e an error term, and x an y given vectors (len(x)<len(y)). I have several (x;y) couples and would like to iterate the estimation on each couple using as prior of the i+1-th iteration the posterior of the…

Hi! Just to pick this discussion up, I am trying to reproduce the power prior with ‘random’ a0 for a simple regression example. It works with the unnormalized version. I am unsure, however, how to include the normalizing constant c(a0) as mentioned by max. Currently, I am thinking along the lines o…

Depending on the model you might be able to write c(a_0) in closed form. Otherwise, bridge sampling is a good way to go. I have.a manuscript in the works that deals with this. PM me if you are interested.

Hi max, yes, I’d be interested! It seems I cannot send you a PM (the composer throws an error, ‘you cannot send a PM to that user’), so I reply here. My first example would be a simple regression model, but later on it will become more complicated (mostly SEMs). I’ve attached a small example where…

Composing Stan models (posterior as next prior)

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b_j13 November 20, 2019, 4:01pm 26

Thank you - Power Prior for a Hierarchical Model in Stan

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Composing Stan models (posterior as next prior)

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