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Open Access Publications from the University of California

Scholarly Works (4 results)

  • Article
  • Peer Reviewed
UC Irvine Previously Published Works (2005)

We describe a method for estimating the marginal likelihood, based on CHIB (1995) and CHIB and JELIAZKOV (2001), when simulation from the posterior distribution of the model parameters is by the accept reject Metropolis-Hastings (ARMH) algorithm. The method is developed for one-block and multiple-block ARMH algorithms and does not require the (typically) unknown normalizing constant of the proposal density. The problem of calculating the numerical standard error of the estimates is also considered and a procedure based on batch means is developed. Two examples, dealing with a multinomial logit model and a Gaussian regression model with non-conjugate priors, are provided to illustrate the efficiency and applicability of the method.

    Cover page: Accept-reject Metropolis-Hastings sampling and marginal likelihood estimation
    • Article
    • Peer Reviewed
    UC Santa Barbara Previously Published Works (1989)
    Let R denote the population multiple correlation coefficient of one variable on the other (m-1), in a m-variate normal —2 distribution. Bayes estimator of R, given only the sample 2 multiple correlation coefficient R, is derived with respect to the squared error loss function and a Beta prior distribution.-2 These results are then related to the Bayes estimates of R /(1-_o R), a parameter considered recently by Muirhead (1985). The ideas are illustrated and the effect of various parameters studied through numerical examples. A Monte Carlo study indicates that the sampling mean squared error of the Bayes estimator is lower than that of R2, for plausible prior distributions. © 1989, Taylor & Francis Group, LLC. All rights reserved.
      Cover page: Bayes estimation of the multiple correlation coefficient
      • Article
      • Peer Reviewed
      UC Santa Barbara Previously Published Works (1987)
        Cover page: Another Look at Some Results on the Recursive Estimation in the General Linear Model
        • Article
        • Peer Reviewed
        UC Santa Barbara Previously Published Works (1988)
        In this paper the prediction problem is considered for linear regression models with elliptical errors when the Bayes prior is non-informative. We show that the Bayes prediction density under the elliptical errors assumption is exactly the same as that obtained with normally distributed errors. Thus, assuming that the errors have a normal distribution, when the true distribution is elliptical, will not lead to incorrect predictive inferences if the error variance structure is correctly specified. This extends the results of Zellner (1976). Finally, based on Monte Carlo numerical integration procedures, computations are provided in a model with multiplicative heteroscedasticity. © 1988.
          Cover page: Bayes prediction in regressions with elliptical errors
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