Bayesian Analysis of Graphical Models of Marginal Independence for Three Way Contingency Tables - Claudia Tarantola; Ioannis Ntzoufras (Università degli Studi di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi (EPMQ), 2012)
This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. Each marginal independence model corresponds to a particular factorization of the cell probabilities and a conjugate analysis based on Dirichlet prior can be performed. We illustrate a comprehensive Bayesian analysis of such models, involving suitable choices of prior parameters, estimation, model determination, as well as the allied computational issues. The posterior distributions of the marginal log-linear parameters is indirectly obtained using simple Monte Carlo schemes. The methodology is illustrated using two real data sets.
Keywords: 330; graphical models; marginal log-linear parameterization; Monte Carlo computation; order decomposability; power prior approach