Statistical Science

Approximate Models and Robust Decisions

James Watson and Chris Holmes

Full-text: Open access

Abstract

Decisions based partly or solely on predictions from probabilistic models may be sensitive to model misspecification. Statisticians are taught from an early stage that “all models are wrong, but some are useful”; however, little formal guidance exists on how to assess the impact of model approximation on decision making, or how to proceed when optimal actions appear sensitive to model fidelity. This article presents an overview of recent developments across different disciplines to address this. We review diagnostic techniques, including graphical approaches and summary statistics, to help highlight decisions made through minimised expected loss that are sensitive to model misspecification. We then consider formal methods for decision making under model misspecification by quantifying stability of optimal actions to perturbations to the model within a neighbourhood of model space. This neighbourhood is defined in either one of two ways. First, in a strong sense via an information (Kullback–Leibler) divergence around the approximating model. Second, using a Bayesian nonparametric model (prior) centred on the approximating model, in order to “average out” over possible misspecifications. This is presented in the context of recent work in the robust control, macroeconomics and financial mathematics literature. We adopt a Bayesian approach throughout although the presentation is agnostic to this position.

Article information

Source
Statist. Sci. Volume 31, Number 4 (2016), 465-489.

Dates
First available in Project Euclid: 19 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ss/1484816572

Digital Object Identifier
doi:10.1214/16-STS592

Keywords
Computational decision theory model misspecification D-open problem Kullback–Leibler divergence robustness Bayesian nonparametrics

Citation

Watson, James; Holmes, Chris. Approximate Models and Robust Decisions. Statist. Sci. 31 (2016), no. 4, 465--489. doi:10.1214/16-STS592. https://projecteuclid.org/euclid.ss/1484816572.


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