Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling

By Andrew Gelman, Xiao-Li Meng. 1998

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Citations in the corpus

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).”
Modern Statistics for Spatial Point Processes * (2007, background): “The path sampling identity (e.g. Gelman & Meng, 1998) log(c /c 0 )= ∫ 1 0 E (s)t(X) (d (s)/ds)T ds (45) provides an alternative and often numerically more stable way of computing a ratio of normalizing constants.”
The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures (2003, methodology): “Several methods that have been proposed for estimating marginal likelihoods are the candidate method (Chib, 1995; and see Neal, 1998), bridge sampling and path sampling (Gelman and Meng, 1998) and the closely related Annealed Importance Sampling (Neal, 2001).”
Learning Sparse FRAME Models for Natural Image Patterns (2014, background): “which can be approximated by averaging over the sampled images {Ĩm} as an application of importance sampling (Gelman and Meng 1998):”
On the stability of sequential Monte Carlo methods in high dimensions (2011, background): “ning on the set {1,2,...,d}. Accordingly, ks(·,·), with s ∈ (φ0,1], will denote the transition kernel preserving πs. This is an analogue to the connection between bridge sampling and path sampling in [30]. 2.2 Conditions We now state the conditions under which we will derive our results. Throughout,”
The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background (2023, background): “The first is thermodynamic integration (e.g., Ogata 1989; Gelman & Meng 1998), which computes Bayesian evidence integrals directly through parallel tempering: we run Nβ MCMC chains that explore variants of the likelihood function raised to different exponents β, then approximate the evidence for…”
Unified Framework to Evaluate Panmixia and Migration Direction Among Multiple Sampling Locations (2010, methodology): “We contrast two different methods to estimate the marginal likelihood: harmonic mean (Newton and Raftery 1994; Kass and Raftery 1995) and path sampling (Gelman and Meng 1998).”
Towards Automatic Model Comparison: An Adaptive Sequential Monte Carlo Approach (2013, methodology): “…p 0 = q 0 /Z 0 to p 1 = q 1 /Z 1 as α increases from zero to one, one can estimate the logarithm of the ratio of their normalizing constants via a simple integral relationship which holds under very mild regularity conditions: where E α denotes expectation under p α ; see Gelman and Meng (1998).”
Bayesian Analysis of Markov Point Processes (2006, methodology): “Keywords: Bayesian inference; Markov chain Monte Carlo; Markov point process; Partially ordered Markov point process; Perfect simulation; Spatial point process; Strauss process.”
Warp Bridge Sampling (2002, methodology): “This is, in some sense, in the spirit of path sampling (e.g., Gelman and Meng 1998), for it attempts to create a “path,” indexed by D, to link p1 to p2.”