By: Chad Scherrer

Re-posted from: https://informativeprior.com/blog/2021/01-28-measure-theory/index.html

Modern probabilistic modeling puts strong demands on the interface and implementation of libraries for probability distributions. MeasureTheory.jl is an effort to address limitations of existing libraries. In this post, we'll motivate the need for a new library and give an overview of the approach and its benefits.

By: Chad Scherrer

Re-posted from: https://informativeprior.com/blog/2021/01-25-symbolic-simplification/index.html

Upcoming features in Soss.jl include static model simplification. After a one-time compilation cost, posterior log-densities for many models become constant cost, independent of the number of observations. Bayesian analysis for such models can easily scale to big data. The symbolic representation of the posterior log-density can also be useful for pedagogical purposes.

By: Chad Scherrer

Re-posted from: https://cscherrer.github.io/post/variational-importance-sampling/

Lots of distributions are easy to evaluate (the density), but hard to sample. So when we need to sample such a distribution, we need to use some tricks. We’ll see connections between two of these: importance sampling and variational inference, and see a way to use them together for fast inference.
Importance sampling Importance sampling aims to make it easy to compute expected values. Say we have a distribution \(p\), and we’d like to compute the average of some function \(f\) of the distribution (or equivalently, the expected value of a "push-forward along \(f\)").