Statistics Seminar: Theodore Kypraios
Theodore Kypraios, University of Nottingham
Friday 31 January 2014, 1400-1500
A54, Postgraduate Statistics Centre Lecture Theatre
Piecewise Approximate Bayesian Computation (PW-ABC): Exploring Model's Local Dynamic Structure for Efficient Statistical Inference
Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential techniques cannot be used. In such settings, Bayesian inference can be performed using Approximate Bayesian Computation (ABC). However, in spite of many recent developments to ABC methodology, in many applications the computational cost of ABC necessitates the choice of summary statistics and tolerances that can potentially severely bias estimation.
We propose a new "piecewise" ABC approach suitable for discretely observed Markov models that involves writing the posterior density of the parameters as a product of factors, each a function of only a subset of the data, and then using ABC within each factor. The approach has the advantage of side-stepping the need to choose a summary statistic and it enables a stringent tolerance to be set, making the posterior "less approximate". We investigate two methods for estimating the posterior density based on ABC samples for each of the factors and discuss their advantages and disadvantages. We illustrate the piecewise ABC approach for four examples; in each case, the approach enables "exact matching" between simulations and data and offers fast and accurate inference. If time permits, we will also discuss how similar ideas can be used to make inference in ODE models.