Approximate Bayesian Computation for Smoothing

• Activity Number: 565
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): James Martin*+
• Companies: University College London
• Keywords: Approximate Bayesian Computation (ABC) ; sequential Monte Carlo (SMC) ; smoothing ; likelihood-free methods

Abstract

We consider the use of Approximate Bayesian Computation (ABC) for performing inference with respect to the hidden state process in a hidden Markov model (HMM) where the conditional observation density, or likelihood, of an observation given the hidden state is analytically intractable. In particular, we focus on the smoothing problem, where the goal is to perform inference with respect to historical values of the state, given the entire observation process. The proposed method uses ABC to construct a likelihood-free approximation of the HMM, the accuracy of which can be controlled to arbitrary precision through a control parameter. I will present theoretical results that quantify the error associated with estimating expectations of additive functionals with respect to the resulting ABC approximation of the smoothing distribution. Under appropriate regularity assumptions, this error is shown to be linear in both the ABC control parameter and the length of the observation record. I will also present and discuss the results of numerical tests, where we adopt a forward-only sequential Monte Carlo (SMC) scheme to estimate such expectations, quantifying the combined ABC and SMC errors.