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Expand scale-mixtures #46

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brandonwillard opened this issue Jul 22, 2022 · 1 comment
Open

Expand scale-mixtures #46

brandonwillard opened this issue Jul 22, 2022 · 1 comment
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exact posterior gibbs important mathematical relations refactoring A change that improves the codebase but doesn't necessarily introduce a new feature sampler steps

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@brandonwillard
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brandonwillard commented Jul 22, 2022

After #45, we need to add a scale-mixture-expansion step to the sampler-generating process.

We can start by implementing the Polya-gamma expansion for negative-binomials and Bernoulli random variables. This will work together to produce nbinom_normal_posterior and bern_normal_posterior in #45, after expansion and subsequent detection of the resulting normal-normal posterior.

On a related note, we'll need to start walking through "graph rewrite space" in a more reasonable way. For instance, a scale-mixture expansion might aid in the construction of a sampler where one wasn't possible before (e.g. we don't have a sampler for the unexpanded term in our "database"). On the other hand, when there is a sampler for a term that can be expanded, we will need to consider the samplers resulting from both expanding and not expanding.

@brandonwillard brandonwillard added important refactoring A change that improves the codebase but doesn't necessarily introduce a new feature sampler steps gibbs exact posterior mathematical relations labels Jul 22, 2022
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A directly relevant Discussion has been started here: aesara-devs/aesara#1082 (comment).

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exact posterior gibbs important mathematical relations refactoring A change that improves the codebase but doesn't necessarily introduce a new feature sampler steps
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