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Approximate Bayesian forecasting

David T. Frazier, Worapree Maneesoonthorn, Gael M. Martin and Brendan McCabe

International Journal of Forecasting, 2019, vol. 35, issue 2, 521-539

Abstract: 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 link between the theoretical behavior of the ABC posterior and that of the ABC-based predictive; (ii) the use of proper scoring rules to measure the (potential) loss of forecast accuracy when using an approximate rather than an exact predictive; (iii) the performance of approximate Bayesian forecasting in state space models; and (iv) the use of forecasting criteria to inform the selection of ABC summaries in empirical settings. 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.

Keywords: Bayesian prediction; Likelihood-free methods; Predictive merging; Proper scoring rules; Particle filtering; Jump-diffusion models (search for similar items in EconPapers)
Date: 2019
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