Bayesian Analysis

Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models

Ioannis Ntzoufras, Claudia Tarantola, and Monia Lupparelli

Full-text: Open access

Abstract

We introduce a novel Bayesian approach for quantitative learning for graphical log-linear marginal models. These models belong to curved exponential families that are difficult to handle from a Bayesian perspective. The likelihood cannot be analytically expressed as a function of the marginal log-linear interactions, but only in terms of cell counts or probabilities. Posterior distributions cannot be directly obtained, and Markov Chain Monte Carlo (MCMC) methods are needed. Finally, a well-defined model requires parameter values that lead to compatible marginal probabilities. Hence, any MCMC should account for this important restriction. We construct a fully automatic and efficient MCMC strategy for quantitative learning for such models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm that employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformation. We exploit a conditional conjugate setup to build an efficient proposal on probability parameters. The proposed methodology is illustrated by a simulation study and a real dataset.

Article information

Source
Bayesian Anal., Volume 14, Number 3 (2019), 777-803.

Dates
First available in Project Euclid: 11 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.ba/1560240028

Digital Object Identifier
doi:10.1214/18-BA1128

Mathematical Reviews number (MathSciNet)
MR3960771

Zentralblatt MATH identifier
07089626

Keywords
graphical models marginal log-linear parameterisation Markov Chain Monte Carlo computation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Ntzoufras, Ioannis; Tarantola, Claudia; Lupparelli, Monia. Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models. Bayesian Anal. 14 (2019), no. 3, 777--803. doi:10.1214/18-BA1128. https://projecteuclid.org/euclid.ba/1560240028


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Supplemental materials

  • Supplementary Material: Electronic for the Paper “Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models”. The Supplementary Material includes details for the Jacobian calculations (Appendix A) and details for the construction of M and C matrices (Appendices B and C respectively). Finally, some additional results for the illustrated examples of Section 5 are provided in Appendix D.