Reconstruction of Marginal Posterior Densities

Authors: 
Al Erkanli
Duke University

Mar 4 1992

Cubic spline approximations to marginal posterior densities are considered when the member of function evaluations are costly and are kept small in advance. The conditional maximization method of Tierney and Kadane (1986) is used as a reference approximation to the underlying marginal posterior density and a cubic spline function is fitted to the logarithm of this approximation based on few knots scattered judiciously around the relative mode of the full parameter vector. The fit is updated by increasing the knot set sequentially until the threshold number of function evaluations (i.e., the maximum number of knots) is reached. The procedure is illustrated with univariate and two-dimensional examples.

Keywords: 

Bayesian inference, Cubic splines, Laplace's method

Manuscript: 

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