Approximate Bayesian Forecasting

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.

Isolated Pulsar Population Synthesis with Simulation-based Inference

“…In the past few years, SBI has successfully challenged traditional approaches such as approximate Bayesian computation (e.g., Rubin 1984;Beaumont et al 2002;Dean et al 2011;Frazier et al 2017) in those areas of science that rely on complex simulators, which lead to intractable likelihoods. The existence of such a simulator, essentially acting as a forward model, is the only requirement for SBI.…”