Approximate Models and Robust Decisions

By James A. Watson, Christopher C. Holmes. 2014

91 citations recorded by the source corpus.

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 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. Firstly, in a strong sense via an information (Kullback-Leibler) divergence around the approximating model. Or using a nonparametric model extension, again centred at 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 methods are agnostic to this position.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9e0d8dc37de22c12dc332c0919e25907a2c7f4d6

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Citations in the corpus

Ambiguity Aversion and Model Misspecification: An Economic Perspective (2016, methodology): “This minimization problem is essentially a special case of an optimization problem with a relative entropy penalty that emerges in a variety of areas of applied mathematics and essentially follows from Theorem 4.1 in Watson and Holmes (2016).”
Minimizing Sensitivity to Model Misspecification (2018, methodology): “Also related are the literatures on statistical decision theory (e.g., Wald, 1950, Chamberlain 2000, Watson and Holmes, 2016, Hansen and Marinacci, 2016, and especially Hansen and Sargent, 2008) and the literature on sensitivity analysis in statistics and economics (e.g., Rosenbaum and Rubin, 1983,…”
Assigning a value to a power likelihood in a general Bayesian model (2017, background): “See, for example, Royall & Tsou (2003), Zhang (2006a), Zhang (2006b), Jiang & Tanner (2008), Bissiri, Holmes & Walker (2016), Walker & Hjort (2001), Watson & Holmes (2016), Miller & Dunson (2015), Grünwald & van Ommen (2014), Syring & Martin (2015), and more generally Hansen & Sargent (2008).”