arXiv subjects

David T. Frazier

Publications and source records attributed to David T. Frazier.

57 records · Page 4Linked to original sources

arXiv2018

Approximate Bayesian Forecasting

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.

stat.ME↗

arXiv2018

Asymptotic Properties of Approximate Bayesian Computation

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, its limiting shape, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.

stat.ME↗

arXiv2015

On Consistency of Approximate Bayesian Computation

Approximate Bayesian computation (ABC) methods have become increasingly prevalent of late, facilitating as they do the analysis of intractable, or challenging, statistical problems. With the initial focus being primarily on the practical import of ABC, exploration of its formal statistical properties has begun to attract more attention. The aim of this paper is to establish general conditions under which ABC methods are Bayesian consistent, in the sense of producing draws that yield a degenerate posterior distribution at the true parameter (vector) asymptotically (in the sample size). We derive conditions under which arbitrary summary statistics yield consistent inference in the Bayesian sense, with these conditions linked to identification of the true parameters. Using simple illustrative examples that have featured in the literature, we demonstrate that identification, and hence consistency, is unlikely to be achieved in many cases, and propose a simple diagnostic procedure that can indicate the presence of this problem. We also formally explore the link between consistency and the use of auxiliary models within ABC, and illustrate the subsequent results in the Lotka-Volterra predator-prey model.

stat.CO↗