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Statistica Sinica 4(1994), 127-142


THE LAPLACIAN T-APPROXIMATION

IN BAYESIAN INFERENCE


Tom Leonard, John S. J. Hsu*, and Christian Ritter


University of Wisconsin-Madison
and University of California at Santa Barbara*


Abstract: A remarkably accurate approximation is proposed for a marginal density, for finite sample situations where the tails of the posterior density are not accurately represented by a more standard Laplacian approximation. An approximation is developed for the posterior density of an arbitrary linear combination of the means, in the context of the Bayesian analysis of the multi-parameter Fisher-Behrens problem. Advantages of Laplacian methods for non-linear regression problems when compared with sampling based methods, are discussed.



Key words and phrases: Marginal posterior density, Laplacian approximations, importance sampling, Behrens-Fisher problem, non-linear regression, Grid-based Gibbs sampler, Metropolis algorithm.



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