Title :
Multidimensional Laplace formulas for nonlinear Bayesian estimation
Author :
Bui Quang, Paul ; Musso, C. ; Le Gland, F.
Author_Institution :
Onera - The French Aerosp. Lab., Palaiseau, France
Abstract :
The Laplace method and Monte Carlo methods are techniques to approximate integrals which are useful in nonlinear Bayesian computation. When the model is one-dimensional, Laplace formulas to compute posterior expectations and variances have been proposed by Tierney, Kass and Kadane (1989). We provide in this article formulas for the multidimensional case. We demonstrate the accuracy of these formulas and show how to use them in importance sampling to design an importance density function which reduces the Monte Carlo error.
Keywords :
Bayes methods; importance sampling; Laplace method; Monte Carlo error; Monte Carlo method; importance density function; importance sampling; multidimensional Laplace formulas; nonlinear Bayesian computation; nonlinear Bayesian estimation; posterior expectations; Approximation methods; Bayesian methods; Computational modeling; Monte Carlo methods; Numerical models; Optimized production technology; Probability density function; Laplace method; Monte Carlo methods; Nonlinear Bayesian estimation; importance sampling;
Conference_Titel :
Signal Processing Conference (EUSIPCO), 2012 Proceedings of the 20th European
Print_ISBN :
978-1-4673-1068-0
