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Yves F. Atchade

  1. Estimation of Network structures from partially observed Markov random fields.

    Tue, 08/16/2011 - 15:01 — SomNambul
    Authors: Yves F. Atchade
    Subjects: Statistics
    Abstract

    We consider the estimation of high-dimensional network structures from
    partially observed Markov random field data using a penalized pseudo-likelihood
    approach. We fit a misspecified model obtained by ignoring the missing data
    problem. We study the consistency of the estimator and derive a bound on its
    rate of convergence. The results obtained relate the rate of convergence of the
    estimator to the extent of the missing data problem. We report some simulation
    results that empirically validate some of the theoretical findings.

  2. Kernel estimators of asymptotic variance for adaptive Markov Chain Monte Carlo.

    Mon, 11/09/2009 - 16:01 — SomNambul
    Authors: Yves F. Atchade
    Subjects: Probability
    Abstract

    In this paper we study kernel methods for the estimation of asymptotic
    variances (or long run variances) for a class of adaptive Markov chains. We
    prove that these estimators are $L^p$-consistent and strongly consistent.
    Although the motivation comes from Markov Chain Monte Carlo, these results
    apply more generally. In the special case of Markov chains, the results improve
    on the existing literature by imposing weaker moments conditions. We illustrate
    the results with applications to the GARCH$(1,1)$ Markov model and to adaptive
    MCMC simulation for Bayesian logistic regression model.

  3. A cautionary tale on the efficiency of some adaptive Monte Carlo Schemes.

    Tue, 11/03/2009 - 16:01 — SomNambul
    Authors: Yves F. Atchade
    Subjects: Computation
    Abstract

    There is a growing interest in the literature for adaptive Markov Chain Monte
    Carlo methods based on sequences of random transition kernels $\{P_n\}$ where
    the kernel $P_n$ is allowed to have an invariant distribution $\pi_n$ not
    necessarily equal to the distribution of interest $\pi$ (target distribution).
    These algorithms are designed such that as $n\to\infty$, $P_n$ converges to
    $P$, a kernel that has the correct invariant distribution $\pi$. Typically, $P$
    is a kernel with good convergence properties, but one that cannot be directly
    implemented.

  4. Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II.

    Tue, 11/03/2009 - 16:01 — SomNambul
    Authors: Gersende Fort, Yves F. Atchade
    Subjects: Probability
    Abstract

    We prove a central limit theorem for a general class of adaptive Markov Chain
    Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We
    discuss in detail the special case of stochastic approximation. We use the
    result to analyze the asymptotic behavior of an adaptive version of the
    Metropolis Adjusted Langevin algorithm with a heavy tailed target density.

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