Estimating the Integrated Likelihood via Posterior Simulation Using the Harmonic Mean Identity

By Adrian E. Raftery, Michael A. Newton, J. Satagopan, Pavel N. Krivitsky. 2006

345 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c44b89fa2594b797a7e24b3fb38ee06085af6b3d

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Citations in the corpus

Improving the accuracy of demographic and molecular clock model comparison while accommodating phylogenetic uncertainty. (2012, methodology): “with density function 9) Equation (7) suggests a method-of-moments estimate of γ as ˆ γ = s 2 and ˆ ‘ max = ˉ ‘ + s 2 , where ˉ ‘ and s 2 are the sample mean and variance of the posterior log likelihoods (Raftery et al. 2007).”
Functional traits shape ontogenetic growth trajectories of rain forest tree species (2011, methodology): “First, forMax, Dopt andK, we built a linear model where the significant functional traits among the 17 were selected by the Bayesian information criterion (BIC, Schwarz 1978) using the R package glmulti (Calcagno 2011).”
A survey of Bayesian predictive methods for model assessment, selection and comparison (2012, methodology): “(145) This form avoids the use of plug-in estimate in estimation of peff , but this variance estimate can be unstable due to the long tail of the χ2ν distribution (Raftery et al., 2007; Carlin and Spiegelhalter, 2007).”
Accurate model selection of relaxed molecular clocks in bayesian phylogenetics. (2012, methodology): “We note that a posterior simulation-based analog of the Bayesian information criterion through Markov chain Monte Carlo has also been proposed (Raftery et al. 2007), an approach that has a more direct Bayesian justification but requires specification of a sample size for each parameter, which may…”
Efficient sampling of atomic configurational spaces. (2009, background): “Note, however, that advance knowledge of the global minimum is not required and was not used in the nested sampling simulations.”
Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning (2019, methodology): “The weight for each cycle wi is estimated using the harmonic mean method (Green, 1995; Raftery et al., 2006):”
Estimating the Marginal Likelihood Using the Arithmetic Mean Identity (2017, background): “…(2001)), important-weighted marginal density estimators (see Chen (1994), Chen (2005)), and others (see, e.g. Meng and Wong (1996), Raftery (1996), Lewis and Raftery (1997), Han and Carlin (2001), Raftery et al. (2007), Friel and Pettitt (2008), Lenk (2009), Xie et al. (2011), Weinberg (2012)).”
Mixtures of Experts Models (2018, methodology): “The models are compared through the AICM, the posterior simulation-based analogue of Akaike’s Information Criterion (AIC) (Akaike, 1973; Raftery et al. , 2007).”
Variational free energy and the Laplace approximation (2007, methodology): “Estimating the marginal likelihood via MCMC sampling and the harmonic mean identity Following Raftery et al. (2006); consider data y, a likelihood function p(y|ϑ,m) for a model m and a prior distribution p(ϑ|m).”
Estimating Bayes factors via thermodynamic integration and population MCMC (2009, methodology): “We consider two methods based on importance sampling ideas, the Prior Arithmetic Mean estimator (McCulloch and Rossi, 1991) and the Posterior Harmonic Mean estimator (Newton and Raftery, 1994; Raftery et al., 2007).”