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The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model.
General principles of the Monte Carlo method
John Michael Hammersley and David Christopher Handscomb · 1964
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Evolution of protein molecules
T.H Jukes and C.R. Cantor · 1969
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Nineteen dubious ways to compute the exponential of a matrix
C Moler and C Van Loan · 1978
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Consensusn-trees
Timothy Margush and Fred R McMorris · 1981
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Accurate approximations for posterior moments and marginal densities
Luke Tierney and Joseph B Kadane · 1986
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A Monte Carlo method for high dimensional integration
Yosihiko Ogata · 1989
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Stopping the Gibbs sampler, the use of morphology, and other issues in spatial statistics (Bayesian image restoration, with two applications in spatial statistics)–(discussion)
Adrian E Raftery and Jeffrey D Banfield · 1991
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Approximate Bayesian inference with the weighted likelihood bootstrap
Michael A Newton and Adrian E Raftery · 1994
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Bayes factors
Robert E Kass and Adrian E Raftery · 1995
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Posterior predictive assessment of model fitness via realized discrepancies
Andrew Gelman, Xiao-Li Meng, and Hal Stern · 1996
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Simulating ratios of normalizing constants via a simple identity: a theoretical exploration
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Simulating normalizing constants: from importance sampling to bridge sampling to path sampling
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Estimating the rate of evolution of the rate of molecular evolution
Jeffrey L Thorne, Hirohisa Kishino, and Ian S Painter · 1998
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Nineteen dubious ways to compute the exponential of a matrix, Twenty-Five years later
C Moler and C Van Loan · 2003
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Efficient approximations for learning phylogenetic HMM models from data
Vladimir Jojic, Nebojsa Jojic, Chris Meek, Dan Geiger, Adam Siepel, David Haussler, and David Heckerman · 2004
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Nested sampling
John Skilling · 2004
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Computing Bayes factors using thermodynamic integration
Nicolas Lartillot and Hervé Philippe · 2006
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Nested sampling for general Bayesian computation
John Skilling et al · 2006
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Shotgun stochastic search for “large p” regression
Chris Hans, Adrian Dobra, and Mike West · 2007
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Variational upper bounds for probabilistic phylogenetic models
Ydo Wexler and Dan Geiger · 2007
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Marginal likelihood estimation via power posteriors
Nial Friel and Anthony N Pettitt · 2008
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Clock-constrained tree proposal operators in Bayesian phylogenetic inference
Sebastian Höhna, Michael Defoin-Platel, and Alexei J Drummond · 2008
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Efficiency of Markov chain Monte Carlo tree proposals in Bayesian phylogenetics
Clemens Lakner, Paul Van Der Mark, John P Huelsenbeck, Bret Larget, and Fredrik Ronquist · 2008
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The estimation of tree posterior probabilities using conditional clade probability distributions
Bret Larget · 2013
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Paul O Lewis, Wangang Xie, Ming-Hui Chen, Yu Fan, and Lynn Kuo · 2013
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Monte Carlo Theory, Methods and Examples
Art B. Owen · 2013
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Novel non-parametric models to estimate evolutionary rates and divergence times from heterochronous sequence data
Mathieu Fourment and Edward C Holmes · 2014
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Improving power posterior estimation of statistical evidence
Nial Friel, Merrilee Hurn, and Jason Wyse · 2014
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Black box variational inference
Rajesh Ranganath, Sean Gerrish, and David Blei · 2014
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Mean field variational approximation for continuous-time Bayesian networks
Ido Cohn, Tal El-Hay, Nir Friedman, and Raz Kupferman · 2010
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Yu Fan, Rui Wu, Ming-Hui Chen, Lynn Kuo, and Paul O Lewis · 2010
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Bayesian estimation of divergence times from large sequence alignments
Stéphane Guindon · 2010
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Default Bayesian model determination methods for generalised linear mixed models
Antony M Overstall and Jonathan J Forster · 2010
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Improving marginal likelihood estimation for Bayesian phylogenetic model selection
Wangang Xie, Paul O Lewis, Yu Fan, Lynn Kuo, and Ming-Hui Chen · 2010
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Guided tree topology proposals for Bayesian phylogenetic inference
Sebastian Höhna and Alexei J Drummond · 2011
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An efficient independence sampler for updating branches in Bayesian Markov chain Monte Carlo sampling of phylogenetic trees
Andre J Aberer, Alexandros Stamatakis, and Fredrik Ronquist · 2015
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Genealogical working distributions for Bayesian model testing with phylogenetic uncertainty
Guy Baele, Philippe Lemey, and Marc A Suchard · 2015
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Automatic variational inference in Stan
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Quantifying MCMC exploration of phylogenetic tree space
Chris Whidden and Frederick A Matsen IV · 2015
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Estimating Bayesian phylogenetic information content
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A tutorial on bridge sampling
Quentin F Gronau, Alexandra Sarafoglou, Dora Matzke, Alexander Ly, Udo Boehm, Maarten Marsman, David S Leslie, Jonathan J Forster, Eric-Jan Wagenmakers, and Helen Steingroever · 2017
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Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC
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Stochastic variational inference for Bayesian phylogenetics: A case of CAT model
Tung Dang and Hirohisa Kishino · 2018
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Model selection and parameter inference in phylogenetics using nested sampling
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Systematic exploration of the high likelihood density set of phylogenetic trees
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Generalizing tree probability estimation via Bayesian networks
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