Estimating the evidence – a review

By Nial Friel, Jason Wyse. 2011

197 citations recorded by the source corpus.

The model evidence is a vital quantity in the comparison of statistical models under the Bayesian paradigm. This study presents a review of commonly used methods. We outline some guidelines and offer some practical advice. The reviewed methods are compared for two examples; non‐nested Gaussian linear regression and covariate subset selection in logistic regression.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, background): “Recent empirical investigations recommend thermodynamic integration (TI) for this task (e.g. Friel and Wyse (2012)).”
Bayesian Model Comparison for Time-Varying Parameter VARs with Stochastic Volatility (2018, unknown): “Marginal likelihood estimation has generated a large literature; see, for example, Friel and Wyse (2012) and Ardia, Baştürk, Hoogerheide, and van Dijk (2012) for a recent review.”
A survey of Bayesian predictive methods for model assessment, selection and comparison (2012, background): “…tempering with thermodynamic integration and reversible jump MCMC (last one just for Bayes factor or posterior odds) reviewed, for example, in Kass and Raftery (1995); Han and Carlin (2000); Chen, Shao and Ibrahim (2000); Robert and Wraith (2009); Marin and Robert (2010); Friel and Wyse (2012).”
Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan (2014, methodology): “The method presented in this section is just one of many; Friel and Wyse (2012) offer a recent review.”
Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods (2016, methodology): “Approximating the marginal likelihood using Monte Carlo (MC) methods has become popular [Kass and Raftery, 1995; Han and Carlin, 2001; von Toussaint, 2011; Friel and Wyse, 2012; Vrugt et al., 2013].”
Estimating the Marginal Likelihood Using the Arithmetic Mean Identity (2017, background): “Obviously, various other numerical methods have been proposed in the literature to estimate the marginal data density value directly or to compute ratios of two marginal likelihoods (i.e. Bayes factors); for a review see, e.g. Ardia et al. (2012), Friel and Wyse (2012).”
An adaptive scheduling scheme for calculating Bayes factors with thermodynamic integration using Simpson’s rule (2015, methodology): “Overviews over different methods are presented in Friel and Wyse (2012), Kirk et al. (2013).”
A Bayesian information criterion for singular models (2013, methodology): “Mi|Yn/ can be approximated by various Monte Carlo procedures—see Friel and Wyse (2012) for a recent review—but practitioners also often turn to computationally inexpensive proxies that are suggested by large sample theory.”
The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation (2016, methodology): “Recent empirical investigations, including Vyshemirsky and Girolami (2008) and Friel and Wyse (2012), have revealed that TI is among the most promising approach to estimation of model evidence.”
Improving power posterior estimation of statistical evidence (2012, methodology): “We present three examples, the ﬁrst two of which were included in the review paper by Friel and Wyse (2012) where the performance of power posteriors was compared to some other existing methods.”