Bayesian Inference for the Inverse Problem and Applications

• Activity Number: 164
• Type: Contributed
• Date/Time: Monday, August 3, 2009 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Huei-Wen Teng*+
• Companies: Penn State University
• Keywords: Bayesian Inference ; Inverse problem ; Dirichlet Process ; Markov chain Monte Carlo simulation

Abstract

This paper is concerned with making inferences for deconvolutions and integral equations. Using a Bayesian perspective, we propose a standard Markov Chain Monte Carlo MC2 approach and an extension of it, the Markov Chain Monte Carlo, Monte Carlo MC3 approach. In the MC2 approach, the likelihood is calculated using a Monte Carlo approximation to the integral. In the MC3 approach, the draws, used for the Monte Carlo approximation to the integral, are retained and updated as part of the Markov Chain Monte Carlo simulation. For illustration purposes, MC2 and MC3 are applied to the deconvolution problem, the moment problem, and several pricing problems in finance. For the pricing problems, we are interested in making inferences for the risk neutral density for European equity options.