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Adrian Dobra

  1. Dynamic Markov Bases.

    Mon, 03/28/2011 - 15:01 — SomNambul
    Authors: Adrian Dobra
    Subjects: Computation
    Abstract

    We present a computational approach for generating Markov bases for multi-way
    contin- gency tables whose cells counts might be constrained by fixed marginals
    and by lower and upper bounds. Our framework includes tables with structural
    zeros as a particular case. In- stead of computing the entire Markov basis in
    an initial step, our framework finds sets of local moves that connect each
    table in the reference set with a set of neighbor tables. We construct a Markov
    chain on the reference set of tables that requires only a set of local moves at
    each iteration.

  2. Relational models for contingency tables.

    Tue, 03/01/2011 - 16:01 — SomNambul
    Authors: Adrian Dobra, Anna Klimova, Tamás Rudas
    Subjects: Methodology
    Abstract

    The paper considers general multiplicative models for complete and incomplete
    contingency tables that generalize log-linear and several other models and are
    entirely coordinate free. Sufficient conditions of the existence of maximum
    likelihood estimates under these models are given, and it is shown that the
    usual equivalence between multinomial and Poisson likelihoods holds if and only
    if an overall effect is present in the model.

  3. Bayesian inference for general Gaussian graphical models with application to multivariate lattice data.

    Tue, 05/25/2010 - 15:01 — SomNambul
    Authors: Adrian Dobra, Alex Lenkoski, Abel Rodriguez
    Subjects: Methodology
    Abstract

    We introduce efficient Markov chain Monte Carlo methods for inference and
    model determination in multivariate and matrix-variate Gaussian graphical
    models. Our framework is based on the G-Wishart prior for the precision matrix
    associated with graphs that can be decomposable or non-decomposable. We extend
    our sampling algorithms to a novel class of conditionally autoregressive models
    for sparse estimation in multivariate lattice data, with a special emphasis on
    the analysis of spatial data.

  4. A conjugate prior for discrete hierarchical log-linear models.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: Hélène Massam, Jinnan Liu, Adrian Dobra
    Subjects: Statistics
    Abstract

    In Bayesian analysis of multi-way contingency tables, the selection of a
    prior distribution for either the log-linear parameters or the cell
    probabilities parameters is a major challenge. In this paper, we define a
    flexible family of conjugate priors for the wide class of discrete hierarchical
    log-linear models, which includes the class of graphical models. These priors
    are defined as the Diaconis--Ylvisaker conjugate priors on the log-linear
    parameters subject to "baseline constraints" under multinomial sampling.

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