
Bayesian model selection approach for colored graphical Gaussian models
We consider a class of colored graphical Gaussian models obtained by pla...
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New Estimation Approaches for the Linear Ballistic Accumulator Model
The Linear Ballistic Accumulator (LBA) model of Brown (2008) is used as ...
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PowerExpectedPosterior Priors as Mixtures of gPriors
One of the main approaches used to construct prior distributions for obj...
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Automated Model Selection with Bayesian Quadrature
We present a novel technique for tailoring Bayesian quadrature (BQ) to m...
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Bayesian Evidence and Model Selection
In this paper we review the concepts of Bayesian evidence and Bayes fact...
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On the normalized power prior
The power prior is a popular tool for constructing informative prior dis...
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Assessing the uncertainty in statistical evidence with the possibility of model misspecification using a nonparametric bootstrap
Empirical evidence, e.g. observed likelihood ratio, is an estimator of t...
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Simulating normalising constants with referenced thermodynamic integration: application to COVID19 model selection
Model selection is a fundamental part of Bayesian statistical inference; a widely used tool in the field of epidemiology. Simple methods such as Akaike Information Criterion are commonly used but they do not incorporate the uncertainty of the model's parameters, which can give misleading choices when comparing models with similar fit to the data. One approach to model selection in a more rigorous way that uses the full posterior distributions of the models is to compute the ratio of the normalising constants (or model evidence), known as Bayes factors. These normalising constants integrate the posterior distribution over all parameters and balance over and under fitting. However, normalising constants often come in the form of intractable, highdimensional integrals, therefore special probabilistic techniques need to be applied to correctly estimate the Bayes factors. One such method is thermodynamic integration (TI), which can be used to estimate the ratio of two models' evidence by integrating over a continuous path between the two unnormalised densities. In this paper we introduce a variation of the TI method, here referred to as referenced TI, which computes a single model's evidence in an efficient way by using a reference density such as a multivariate normal  where the normalising constant is known. We show that referenced TI, an asymptotically exact Monte Carlo method of calculating the normalising constant of a single model, in practice converges to the correct result much faster than other competing approaches such as the method of power posteriors. We illustrate the implementation of the algorithm on informative 1 and 2dimensional examples, and apply it to a popular linear regression problem, and use it to select parameters for a model of the COVID19 epidemic in South Korea.
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