Approximate Bayesian Forecasting

TL;DR

This paper explores how Approximate Bayesian Computation (ABC) can be effectively used for probabilistic forecasting, demonstrating that it produces nearly identical forecasts to exact methods more efficiently in complex models.

Contribution

It introduces the concept of approximate Bayesian forecasting, analyzing its theoretical properties, performance in state space models, and methods for selecting summaries in empirical applications.

Findings

ABC provides nearly identical forecasts to exact methods.

Forecasting with ABC is computationally more efficient.

Forecast quality can be assessed using proper scoring rules.

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. y identical to those produced by the exact predictive, and in a fraction of the time required to produce predictions via an exact method.