Bayesian inference for logistic models using Polya-Gamma latent variables

05/02/2012
by   Nicholas G. Polson, et al.
0

We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Polya-Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effects models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that: (1) circumvent the need for analytic approximations, numerical integration, or Metropolis-Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Polya-Gamma distribution, are implemented in the R package BayesLogit. In the technical supplement appended to the end of the paper, we provide further details regarding the generation of Polya-Gamma random variables; the empirical benchmarks reported in the main manuscript; and the extension of the basic data-augmentation framework to contingency tables and multinomial outcomes.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/03/2021

Bayesian Inference for Gamma Models

We use the theory of normal variance-mean mixtures to derive a data augm...
research
09/06/2019

A Pólya-Gamma Sampler for a Generalized Logistic Regression

In this paper we introduce a novel Bayesian data augmentation approach f...
research
08/23/2016

Softplus Regressions and Convex Polytopes

To construct flexible nonlinear predictive distributions, the paper intr...
research
06/18/2015

Dependent Multinomial Models Made Easy: Stick Breaking with the Pólya-Gamma Augmentation

Many practical modeling problems involve discrete data that are best rep...
research
10/09/2013

Improved Bayesian Logistic Supervised Topic Models with Data Augmentation

Supervised topic models with a logistic likelihood have two issues that ...
research
11/13/2020

Ultimate Pólya Gamma Samplers – Efficient MCMC for possibly imbalanced binary and categorical data

Modeling binary and categorical data is one of the most commonly encount...
research
05/24/2020

A New Spatial Count Data Model with Bayesian Additive Regression Trees for Accident Hot Spot Identification

The identification of accident hot spots is a central task of road safet...

Please sign up or login with your details

Forgot password? Click here to reset