## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 8, Number 1 (2014), 1113-1151.

### Mean field variational Bayes for continuous sparse signal shrinkage: Pitfalls and remedies

Sarah E. Neville, John T. Ormerod, and M. P. Wand

#### Abstract

We investigate mean field variational approximate Bayesian inference for models that use continuous distributions, Horseshoe, Negative-Exponential-Gamma and Generalized Double Pareto, for sparse signal shrinkage. Our principal finding is that the most natural, and simplest, mean field variational Bayes algorithm can perform quite poorly due to posterior dependence among auxiliary variables. More sophisticated algorithms, based on special functions, are shown to be superior. Continued fraction approximations via Lentz’s Algorithm are developed to make the algorithms practical.

#### Article information

**Source**

Electron. J. Statist. Volume 8, Number 1 (2014), 1113-1151.

**Dates**

First available in Project Euclid: 7 August 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1407415580

**Digital Object Identifier**

doi:10.1214/14-EJS910

**Mathematical Reviews number (MathSciNet)**

MR3263115

**Zentralblatt MATH identifier**

1298.62050

**Subjects**

Primary: 62F15: Bayesian inference

Secondary: 62J07: Ridge regression; shrinkage estimators

**Keywords**

Approximate Bayesian inference continued fraction Generalized Double Pareto distribution Horseshoe distribution Lentz’s Algorithm Normal-Exponential-Gamma distribution special function

#### Citation

Neville, Sarah E.; Ormerod, John T.; Wand, M. P. Mean field variational Bayes for continuous sparse signal shrinkage: Pitfalls and remedies. Electron. J. Statist. 8 (2014), no. 1, 1113--1151. doi:10.1214/14-EJS910. https://projecteuclid.org/euclid.ejs/1407415580