Estimating Marginal Likelihoods for Mixture and Markov Switching Models Using Bridge Sampling Techniques

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Properties of nested sampling (2008, result): “Frühwirth-Schnatter (2004) uses the same importance function g in both Ẑ1 and Ẑ2, and obtain results similar to ours, namely that Ẑ2 outperforms Ẑ1.”
Safe models for risky decisions (2017, methodology): “To derive the generalized harmonic mean estimator, also known as reciprocal importance sampling estimator (Frühwirth-Schnatter, 2004), we use the following identity:”
Regression Density Estimation With Variational Methods and Stochastic Approximation (2012, methodology): “There are related concerns with some MCMC methods when estimating the marginal likelihood (e.g., see Frühwirth-Schnatter 2004 and the references therein).”
bridgesampling: An R Package for Estimating Normalizing Constants (2017, unknown): “…by: The bridgesampling package computes an approximate relative mean-squared error of the marginal likelihood estimate based on the derivation by Fr¨uhwirth–Schnatter (2004) which takes into account that the samples from the proposal distribution are independent, whereas the samples from the…”
Mixtures of Experts Models (2018, methodology): “For instance, FrühwirthSchnatter & Kaufmann (2008) apply bridge sampling (Frühwirth-Schnatter, 2004) to compute marginal likelihoods for a mixture of experts model with a single covariate (that is q = 1) with up to four components.”