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Activity Number: 308 - Highlights in Bayesian Analysis: Innovations in Bayesian Learning
Type: Invited
Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #320472
Title: Fast and Accurate Estimation of Non-Nested Binomial Hierarchical Models Using Variational Inference
Author(s): Max Goplerud*
Companies: University of Pittsburgh
Keywords: hierarchical models; variational Bayes; marginal augmentation; scalable statistical methodology

Inference for non-linear hierarchical models with non-nested effects can be challenging and computationally burdensome on large datasets. This paper provides two contributions to scalable and accurate inference. First, I derive a new mean-field variational algorithm for estimating binomial logistic hierarchical models with an arbitrary number of non-nested random effects. Second, I propose "marginally augmented variational Bayes'' (MAVB) that further improves the initial approximation through a step of Bayesian post-processing. I prove that MAVB provides a guaranteed improvement in the approximation quality at low computational cost and induces dependencies that were assumed away by the initial factorization assumptions.

I apply these techniques to a study of voter behavior using a high-dimensional application of the popular approach of multilevel regression and post-stratification (MRP). Existing estimation took hours whereas the algorithms proposed run in minutes. The posterior means are well-recovered even under strong factorization assumptions. Applying MAVB further improves the approximation by partially correcting the under-estimated variance.

Authors who are presenting talks have a * after their name.

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