James M. Flegal

  1. Exact sampling for intractable probability distributions via a Bernoulli factory.

    Authors: James M. Flegal, Radu Herbei
    Subjects: Computation
    Abstract

    Many applications in the field of statistics require Markov chain Monte Carlo
    methods. Determining appropriate starting values and run lengths can be both
    analytically and empirically challenging. A desire to overcome these problems
    has led to the development of exact, or perfect, sampling algorithms which
    convert a Markov chain into an algorithm that produces i.i.d.\ samples from the
    stationary distribution. Unfortunately, very few of these algorithms have been
    developed for the intractable distributions that arise in statistical
    applications, which typically have uncountable support.

  2. Batch Means and Spectral Variance Estimators in Markov Chain Monte Carlo.

    Authors: James M. Flegal, Galin L. Jones
    Subjects: Statistics
    Abstract

    Calculating a Monte Carlo standard error (MCSE) is an important step in the
    statistical analysis of the simulation output obtained from a Markov chain
    Monte Carlo experiment. For example, it can be used to provide a rigorous
    method for terminating the simulation. An MCSE is usually based on an estimate
    of the variance of the asymptotic normal distribution. We consider spectral and
    batch means methods for estimating this variance. In particular, we establish
    conditions which guarantee that these estimators are strongly consistent as the

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