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George Casella

  1. Shrinkage Confidence Procedures.

    Fri, 03/23/2012 - 15:01 — SomNambul
    Authors: George Casella, J. T. Gene Hwang
    Subjects: Methodology
    Abstract

    The possibility of improving on the usual multivariate normal confidence was
    first discussed in Stein (1962). Using the ideas of shrinkage, through Bayesian
    and empirical Bayesian arguments, domination results, both analytic and
    numerical, have been obtained. Here we trace some of the developments in
    confidence set estimation.

  2. Discussion of "Estimating Random Effects via Adjustment for Density Maximization" by C. Morris and R. Tang.

    Mon, 08/22/2011 - 15:01 — SomNambul
    Authors: George Casella, Claudio Fuentes
    Subjects: Methodology
    Abstract

    Discussion of "Estimating Random Effects via Adjustment for Density
    Maximization" by C. Morris and R. Tang [arXiv:1108.3234]

  3. Consistency of objective Bayes factors as the model dimension grows.

    Wed, 10/20/2010 - 15:01 — SomNambul
    Authors: George Casella, Elías Moreno, F. Javier Girón
    Subjects: Statistics
    Abstract

    In the class of normal regression models with a finite number of regressors,
    and for a wide class of prior distributions, a Bayesian model selection
    procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer.
    Statist. Assoc. 104 (2009) 1261--1271]. However, in models where the number of
    parameters increases as the sample size increases, properties of the Bayes
    factor are not totally understood. Here we study consistency of the Bayes
    factors for nested normal linear models when the number of regressors increases
    with the sample size.

  4. Estimation in Dirichlet random effects models.

    Fri, 02/26/2010 - 16:01 — SomNambul
    Authors: George Casella, Minjung Kyung, Jeff Gill
    Subjects: Statistics
    Abstract

    We develop a new Gibbs sampler for a linear mixed model with a Dirichlet
    process random effect term, which is easily extended to a generalized linear
    mixed model with a probit link function. Our Gibbs sampler exploits the
    properties of the multinomial and Dirichlet distributions, and is shown to be
    an improvement, in terms of operator norm and efficiency, over other commonly
    used MCMC algorithms.

  5. Introducing Monte Carlo Methods with R Solutions to Odd-Numbered Exercises.

    Tue, 01/19/2010 - 16:01 — SomNambul
    Authors: George Casella, Christian P. Robert
    Subjects: Methodology
    Abstract

    This is the solution manual to the odd-numbered exercises in our book
    "Introducing Monte Carlo Methods with R", published by Springer Verlag on
    December 10, 2009, and made freely available to everyone.

  6. A History of Markov Chain Monte Carlo--Subjective Recollections from Incomplete Data--.

    Mon, 08/31/2009 - 17:16 — SomNambul
    Authors: Christian Robert, George Casella
    Subjects: Computation
    Abstract

    In this note we attempt to trace the history and development of Markov chain
    Monte Carlo (MCMC) from its early inception in the late 1940's through its use
    today. We see how the earlier stages of the Monte Carlo (MC, not MCMC) research
    have led to the algorithms currently in use. More importantly, we see how the
    development of this methodology has not only changed our solutions to problems,
    but has changed the way we think about problems.

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