New perspectives for Estimating Normalizing Constants via Posterior Simulation - Rapporto tecnico n.28-2007 - Dipartimento di Statistica, Probabilità e Statistiche Applicate - Università degli Studi di Roma "La Sapienza"

In this paper we propose a new effective tool for evaluating the normalizing constant of an arbitrary density function with the aid of an arbitrary MC or MCMC sampling scheme. The new original estimators proposed here stem from the idea of suitably perturbing the original target density function whose normalizing constant has to be evaluated in such a way that the perturbed density has the same original normalizing constant plus a known arbitrary positive mass. The proposed estimators can be easily implemented sharing the original simplicity of the harmonic mean estimator of Newton and Raftery (1994) yielding consistent MC or MCMC estimators based only on a simulated sample from the distribution proportional to the original density. However, under fairly general sufficient conditions, they avoid the infinite variance shortcoming. Effectiveness is illustrated through controlled simulated examples with distributions in dimension one up to one hundred, as well as on a more practical context of real data sets. Extensions to the ratio of constants are discussed together with relations of the new proposed approach with bridge sampling and path sampling. Key Words: Normalizing constant; MCMC; Integrated Likelihood; Generalized Harmonic Mean; Bridge Sampling; Path Sampling; Bayesian inference