Marginal likelihood estimation via power posteriors

By Nial Friel, Anthony N. Pettitt. 2008

360 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, background): “Conditional on an inverse temperature parameter t, the ‘power posterior’ for parameters θ given data y is defined as p.θ|y, t/∝p.y|θ/t p.θ/ (Friel and Pettitt, 2008).”
Approximate Bayesian computational methods (2011, background): “ficult to calibrate (Cucala et al. 2009; Friel and Pettitt 2008)”
Pseudo-Marginal Bayesian Inference for Gaussian Processes (2013, background): “Even though it is possible to sample f relatively efficiently, the estimation of marginal likelihoods from MCMC simulations is generally challenging [39], [40] and only guarantees of estimator”
Improving power posterior estimation of statistical evidence (2012, methodology): “(5) Estimation of the evidence is a non-trivial task for most sta i ical models and there has been considerable effort in the literature to find algorithms and methods f or this purpose.”
Bayesian fractional posteriors (2016, background): “from fractional Bayes factors in objective Bayesian model selection [48], data-dependent priors for sparse estimation [41, 42], to marginal likelihood approximation [19] and posterior simulation [20].”
Improving marginal likelihood estimation for Bayesian phylogenetic model selection. (2011, methodology): “This approach generalizes the method suggested by Friel and Pettitt (2008), which corresponds to the special case α = 0.25, and is analogous to the sigmoidal function proposed by Lepage et al. (2007) in a model-switch TI framework.”
Estimating the Marginal Likelihood Using the Arithmetic Mean Identity (2017, methodology): “Friel and Pettitt (2008) proposed the power posterior method, inspired by ideas from the path sampling, which had been proposed by Gelman and Meng (1998), and based on samples from a distribution proportional to the likelihood raised to a power t times the prior density function.”
Gradient Matching Methods for Computational Inference in Mechanistic Models for Systems Biology: A Review and Comparative Analysis (2015, methodology): “5) This method was included in the study by González et al. (2013), and the results in this review are from the original paper.”
An adaptive scheduling scheme for calculating Bayes factors with thermodynamic integration using Simpson’s rule (2015, methodology): “The power posterior method exploits ideas from path sampling (Gelman and Meng 1998) in the form of thermodynamic integration and has been introduced in Lartillot and Philippe (2006), Friel and Pettitt (2008).”
Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes (2008, background): “It is convenient to fix a geometric path between the prior and posterior, which we do in our implementation, although other sequences are possible [3].”
Bayesian inference of chemical kinetic models from proposed reactions (2015, neutral): “A number of methods exist in the literature for this purpose (Chib and Jeliazkov, 2001; Friel and Pettitt, 2008; Kass and Raftery, 1995; Newton and Raftery, 1994), but they are computationally taxing.”
The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation (2016, methodology): “Following the presentation of Friel and Pettitt (2008), the power posterior is defined as p ( θ | y , t ) = p ( y | θ ) t p ( θ )/ Z t ( y ), where the normalizing constant is given by Z t ( y ) = (cid:7) p ( y | θ ) t p ( θ ) d θ .”
The Controlled Thermodynamic Integral for Bayesian Model Comparison (2014, methodology): “Friel and Pettitt (2008) originally employed a simple trapezoidal rule whereby the (inverse) temperature domain t ∈ [0, 1] was partitioned using 0 = t0 t1 · · · tm = 1 and the (log-)evidence was approximated by log(p(y)) ≈ m−1∑ i=0 (ti+1 − ti) 2 [Eθ|y,ti log(p(y|θ)) + Eθ|y,ti+1 log(p(y|θ))].”
Unified Framework to Evaluate Panmixia and Migration Direction Among Multiple Sampling Locations (2010, methodology): “Studies of path sampling have recently led to an alternative method of estimating marginal likelihoods (thermodynamic integration) (Gelman and Meng 1998; Lartillot and Philippe 2006; Friel and Pettitt 2005, 2008).”
The Thermodynamic Variational Objective (2019, background): “The integrand in (9) is typically estimated by long running Markov chain Monte Carlo chains computed at different values of ⇡ (z) [21, 22].”
Estimating Bayes factors via thermodynamic integration and population MCMC (2009, methodology): “In order to calculate the marginal likelihood using thermodynamic integration, however, we define the power-posterior as in (Friel and Pettitt, 2008) and (Lartillot and Philippe, 2006) pt(θ |y) = p(y | θ)t p(θ) z(y | t) , where z(y | t) = ∫ θ p(y | θ)t p(θ)dθ .”