Estimating Bayes factors via thermodynamic integration and population MCMC

By Ben Calderhead, Mark A. Girolami. 2009

195 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, methodology): “ both (i) \within-temperature" proposals produced by the (simplied) m-MALA algorithm of Girolami and Calderhead (2011), and (ii) \between-temperature" proposals, as described previously by Calderhead and Girolami (2009). We denote the number of samples by n, such that for each of the 31 te”
Estimating the evidence – a review (2011, background): “Calderhead and Girolami (2009) have shown that the discretization error depends on the Kullback– Liebler distance between tj and tj +1 , for j =0, . . ., m − 1.”
The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation (2016, methodology): “Model comparison for systems specified by nonlinear differential equations is known to be profoundly challenging, even when the number of models is small (Calderhead and Girolami 2011).”
Gradient Matching Methods for Computational Inference in Mechanistic Models for Systems Biology: A Review and Comparative Analysis (2015, methodology): “For more details on tempering, see Calderhead and Girolami (2009) and Mohamed et al. (2012). The computational times for the methods from Dondelinger et al. (2013) and Macdonald and Husmeier (2015), in comparison to numerically integrating the ODEs, can be found in Table 2.”
Annealing between distributions by averaging moments (2013, background): “Most work on adapting paths has focused on tuning schedules along a geometric path [15, 16, 17].”
Towards Automatic Model Comparison: An Adaptive Sequential Monte Carlo Approach (2013, methodology): “The rationale behind this particular schedule can be seen in Calderhead and Girolami (2009) and other values of p were also tried while p ≈ 2 performs best in this particular example.”
An adaptive scheduling scheme for calculating Bayes factors with thermodynamic integration using Simpson’s rule (2015, methodology): “Advantages of thermodynamic integration over other methods for calculating marginal likelihoods have been discussed in Calderhead and Girolami (2009), Xu et al. (2010), Eydgahi et al. (2013), Schmidl et al. (2012).”
A taxonomic revision of the Neotropical poison frog genus Ranitomeya (Amphibia: Dendrobatidae) (2011, background): “…the use of harmonic means to calculate the marginal likelihood for model estimation; in particular, harmonic means can favor more parameter-rich models (Lartillot & Philippe 2006) and they can possess a systematic bias capable of significantly skewing Bayes factors (Calderhead & Girolami 2009).”
Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms (2014, methodology): “Attention must be paid to MCMC simulations of non-linear ODEs, as the chains may converge to the wrong mode (see Calderhead and Girolami (2009), for details).”
The Controlled Thermodynamic Integral for Bayesian Model Comparison (2014, methodology): “As shown in Calderhead and Girolami (2009), the Goodwin oscillator induces a highly multi-modal posterior distribution that renders estimation of the model evidence extremely challenging.”