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Zero Variance Markov Chain Monte Carlo for Bayesian Estimators


Author Info

  • Antonietta Mira

    (Department of Economics, University of Insubria, Italy)

  • Daniele Imparato

    (Department of Economics, University of Insubria, Italy)

  • Reza Solgi

    (Istituto di Finanza, Universita di Lugano)

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    A general purpose variance reduction technique for Markov chain Monte Carlo (MCMC) estimators, based on the zero-variance principle introduced in the physics literature, is proposed to evaluate the expected value, of a function f with respect to a, possibly unnormalized, probability distribution . In this context, a control variate approach, generally used for Monte Carlo simulation, is exploited by replacing f with a di erent function, ~ f. The function ~ f is constructed so that its expectation, under , equals f , but its variance with respect to  is much smaller. Theoretically, an optimal re-normalization f exists which may lead to zero variance; in practice, a suitable approximation for it must be investigated. In this paper, an ecient class of re-normalized ~ f is investigated, based on a polynomial parametrization. We nd that a low-degree polynomial (1st, 2nd or 3rd degree) can lead to dramatically huge variance reduction of the resulting zero-variance MCMC estimator. General formulas for the construction of the control variates in this context are given. These allow for an easy implementation of the method in very general settings regardless of the form of the target/posterior distribution (only di erentiability is required) and of the MCMC algorithm implemented (in particular, no reversibility is needed).

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    Bibliographic Info

    Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf1109.

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    Length: 29 pages
    Date of creation: Mar 2011
    Date of revision:
    Handle: RePEc:ins:quaeco:qf1109

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    Related research

    Keywords: Control variates; GARCH models; Logistic regression; Metropolis-Hastings algorithm; Variance reduction;

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