Referenced Thermodynamic Integration for Bayesian Model Selection: Application to COVID-19 Model Selection
Model selection is a fundamental part of the applied Bayesian statistical methodology. Metrics such as the Akaike Information Criterion are commonly used in practice to select models but do not incorporate the uncertainty of the models' parameters and can give misleading choices. One approach t...
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Main Authors | , , , , |
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Format | Journal Article |
Language | English |
Published |
08.09.2020
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Subjects | |
Online Access | Get full text |
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Summary: | Model selection is a fundamental part of the applied Bayesian statistical
methodology. Metrics such as the Akaike Information Criterion are commonly used
in practice to select models but do not incorporate the uncertainty of the
models' parameters and can give misleading choices. One approach that uses the
full posterior distribution is to compute the ratio of two models' normalising
constants, known as the Bayes factor. Often in realistic problems, this
involves the integration of analytically intractable, high-dimensional
distributions, and therefore requires the use of stochastic methods such as
thermodynamic integration (TI). In this paper we apply a variation of the TI
method, referred to as referenced TI, which computes a single model's
normalising constant in an efficient way by using a judiciously chosen
reference density. The advantages of the approach and theoretical
considerations are set out, along with explicit pedagogical 1 and 2D examples.
Benchmarking is presented with comparable methods and we find favourable
convergence performance. The approach is shown to be useful in practice when
applied to a real problem - to perform model selection for a semi-mechanistic
hierarchical Bayesian model of COVID-19 transmission in South Korea involving
the integration of a 200D density. |
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DOI: | 10.48550/arxiv.2009.03851 |