## Bayesian Analysis

### Variational Message Passing for Elaborate Response Regression Models

#### Abstract

We build on recent work concerning message passing approaches to approximate fitting and inference for arbitrarily large regression models. The focus is on regression models where the response variable is modeled to have an elaborate distribution, which is loosely defined to mean a distribution that is more complicated than common distributions such as those in the Bernoulli, Poisson and Normal families. Examples of elaborate response families considered here are the Negative Binomial and $t$ families. Variational message passing is more challenging due to some of the conjugate exponential families being non-standard and numerical integration being needed. Nevertheless, a factor graph fragment approach means the requisite calculations only need to be done once for a particular elaborate response distribution family. Computer code can be compartmentalized, including that involving numerical integration. A major finding of this work is that the modularity of variational message passing extends to elaborate response regression models.

#### Article information

Source
Bayesian Anal., Volume 14, Number 2 (2019), 371-398.

Dates
First available in Project Euclid: 25 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.ba/1527213628

Digital Object Identifier
doi:10.1214/18-BA1098

Mathematical Reviews number (MathSciNet)
MR3934090

Zentralblatt MATH identifier
07045435

Subjects
Primary: 62F15: Bayesian inference 62J05: Linear regression
Secondary: 62G08: Nonparametric regression

#### Citation

McLean, M. W.; Wand, M. P. Variational Message Passing for Elaborate Response Regression Models. Bayesian Anal. 14 (2019), no. 2, 371--398. doi:10.1214/18-BA1098. https://projecteuclid.org/euclid.ba/1527213628

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