In this talk, we lay the ground for Markov Chain Monte Carlo (MCMC) methods to inferring the posterior distribution, after looking into the limitations posed by the analytical approach. We demonstrate how MCMC works and use it to solve a Bayesian regression problem and introduce concepts related to causal inference. Before doing so, we have a quick tutorial on using Pyro as a probabilistic programming language.
Pattern recognition and machine learning,
This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning. No previous knowledge of pattern recognition or …
Variational Inference: A Review for Statisticians,
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this paper, we review variational inference (VI), a method from machine learning that approximates probability densities …