Gael Martin | Monash University

Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function. In this paper, 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 four key issues explored are: i) the loss of forecast accuracy incurred when using an approximate rather than an exact predictive; ii) the role played in approximate Bayesian forecasting by posterior consistency; iii) the importance of (particle) filtering in approximate Bayesian forecasting in latent variable models; and iv) the use of forecasting criteria to inform the selection of ABC summaries in empirical settings. A range of time series models, including those in which latent variables, and discrete variables, feature are used to illustrate the methodology, for both simulated and empirical data. The primary finding of the paper is that ABC can provide a computationally efficient means of generating probabilistic forecasts that are nearly identical to those produced by the exact predictive, and in a fraction of the time required to produce predictions via an exact method.

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