Title: Approximate Bayesian forecasting
Authors: David Frazier - Monash University (Australia)
Worapree Ole Maneesoonthorn - University of Melbourne (Australia)
Gael Martin - Monash University (Australia) [presenting]
Brendan McCabe - The University of Liverpool (United Kingdom)
Abstract: Approximate Bayesian Computation (ABC) has become an increasingly prominent tool for conducing inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function. ABC inference requires only that one can simulate pseudo data from the assumed data generating process underlying the observed data, for given draws of the parameters from the prior. Parameter draws that produce a 'match' between the pseudo and observed data are retained and used to estimate the posterior distribution, with the accuracy of the resultant estimate of the exact (but inaccessible) posterior dependent on the informativeness of the summary statistics used in the matching. We focus on the use of ABC not as a tool for parametric inference, but as a means of generating probabilistic forecasts; or for conducting what we refer to as 'approximate Bayesian forecasting'. The three key issues explored are: i) the loss of forecast accuracy incurred when using an approximate rather than an exact forecast distribution; ii) the role played in approximate Bayesian forecasting by posterior consistency; and iii) the use of forecasting criteria to inform the selection of ABC summaries. A range of time series models, including those in which latent variables, and discrete variables, feature are used to illustrate the methodology.