Exponential tilting in Bayesian asymptotics.
We use exponential tilting to obtain versions of asymptotic formulae for Bayesian computation that do not involve conditional maxima of the likelihood function, yielding a more stable computational procedure and significantly reducing computational time. In particular we present an alternative version of the Laplace approximation for a marginal posterior density. Implementation of the asymptotic formulae and a modified signed root based importance sampler are illustrated with an example.
Department of Nutrition and Food Sciences, Faculty of Agricultural and Food Sciences, American University of Beirut, P.O. Box 11-0236, Riad El Solh 1107-2020 Beirut, Lebanon , sk157@aub.edu.lb.
S A
SA
Kharroubi
Department of Statistical Science, University College London, London WC1E 6BT, U.K. , t.sweeting@ucl.ac.uk.
T J
TJ
Sweeting
Approximate Bayesian inference; Exponential tilting; Higher-order asymptotic theory; Importance sampling; Laplace approximation; Signed root loglikelihood ratio