Fast methods for posterior inference of two-group normal-normal models

10/06/2021
by   Philip Greengard, et al.
0

We describe a class of algorithms for evaluating posterior moments of certain Bayesian linear regression models with a normal likelihood and a normal prior on the regression coefficients. The proposed methods can be used for hierarchical mixed effects models with partial pooling over one group of predictors, as well as random effects models with partial pooling over two groups of predictors. We demonstrate the performance of the methods on two applications, one involving U.S. opinion polls and one involving the modeling of COVID-19 outbreaks in Israel using survey data. The algorithms involve analytical marginalization of regression coefficients followed by numerical integration of the remaining low-dimensional density. The dominant cost of the algorithms is an eigendecomposition computed once for each value of the outside parameter of integration. Our approach drastically reduces run times compared to state-of-the-art Markov chain Monte Carlo (MCMC) algorithms. The latter, in addition to being computationally expensive, can also be difficult to tune when applied to hierarchical models.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/09/2020

A Fast Linear Regression via SVD and Marginalization

We describe a numerical scheme for evaluating the posterior moments of B...
research
05/08/2020

Dynamic Shrinkage Priors for Large Time-varying Parameter Regressions using Scalable Markov Chain Monte Carlo Methods

Time-varying parameter (TVP) regression models can involve a huge number...
research
02/26/2018

Conjugate Bayes for probit regression via unified skew-normals

Regression models for dichotomous data are ubiquitous in statistics. Bes...
research
10/23/2017

A hierarchical Bayesian model for measuring individual-level and group-level numerical representations

A popular method for indexing numerical representations is to compute an...
research
02/27/2019

Bayesian Effect Selection in Structured Additive Distributional Regression Models

We propose a novel spike and slab prior specification with scaled beta p...
research
11/15/2019

Asymptotically Exact Variational Bayes for High-Dimensional Binary Regression Models

State-of-the-art methods for Bayesian inference on regression models wit...
research
05/20/2019

Exploring helical dynamos with machine learning

We use ensemble machine learning algorithms to study the evolution of ma...

Please sign up or login with your details

Forgot password? Click here to reset