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

Ioannis Ntzoufras (), Claudia Tarantola () and Monia Lupparelli ()
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Ioannis Ntzoufras: Department of Statistics, Athens University of Economics and Business
Claudia Tarantola: Department of Economics and Management, University of Pavia
Monia Lupparelli: Department of Statistical Sciences, University of Bologna

No 149, DEM Working Papers Series from University of Pavia, Department of Economics and Management

Abstract: Bayesian methods for graphical log-linear marginal models has not been developed in the same extend as traditional frequentist approaches. In this work, we introduce a novel Bayesian approach for quantitative learning for such models. They belong to curved exponential families that are difficult to handle from a Bayesian perspective. Furthermore, 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 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 graphical log-linear marginal models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm which employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformations. By this strategy, we achieve to move within the desired target space. At each step we directly work with well-defined probability distributions. Moreover, we can 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.

Keywords: Graphical Models; Marginal Log-Linear Parameterisation; Markov Chain Monte Carlo Computation. (search for similar items in EconPapers)
JEL-codes: E12 E21 E22 E24 E31 C32 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2018-01
New Economics Papers: this item is included in nep-ecm and nep-mac
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