Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques*

SUMMARYNested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is asymptotically Gaussian. We show that the asymptotic variance of the nested sampling approximation typically grows linearly with the dimension of the parameter. We discuss the applicability and efficiency of nested sampling in realistic problems, and we compare it with two current methods for computing marginal likelihood. We propose an extension that avoids resorting to Markov chain Monte Carlo to obtain the simulated points.

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“…As in Frühwirth-Schnatter (2004), we consider the example of the posterior distribution on (µ, σ) associated with the normal mixture…”

Section: ·2 a Mixture Examplementioning

confidence: 99%

Properties of nested sampling

Chopin¹,

Robert²

2010

Biometrika

107

129

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“…Most of the methodological literature focusses on models with constant probabilities of Markov switching, including the seminal paper by Hamilton (1989), as well as the subsequent contributions by Chauvet (1998), Kim and Nelson (1999), Frühwirth-Schnatter (2004), Sims and Zha (2006), Sims et al (2008) and Hubrich and Tetlow (2015).…”

Section: Introductionmentioning

confidence: 99%

Macroeconomic Implications of Oil Price Fluctuations: A Regime-Switching Framework for the Euro Area

Holm‐Hadulla

Hubrich

2017

FEDS

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We investigate whether the response of the macro-economy to oil price shocks undergoes episodic changes. Employing a regime-switching vector autoregressive model we identify two regimes that are characterized by qualitatively different patterns in economic activity and inflation following oil price shocks in the euro area. In the normal regime, oil price shocks trigger only limited and short-lived adjustments in these variables. In the adverse regime, by contrast, oil price shocks are followed by sizeable and sustained macroeconomic fluctuations, with inflation and economic activity moving in the same direction as the oil price. The responses of inflation expectations and wage growth point to second-round effects as a potential driver of the dynamics characterising the adverse regime. The systematic response of monetary policy works against such second-round effects in the adverse regime but is insufficient to fully offset them. The model also delivers (conditional) probabilities for being (staying) in either regime, which may help interpret oil price fluctuations -and inform deliberations on the adequate policy response -in real-time.JEL Classification: E31, E52, C32

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“…permutations of the parameter vector result to the same likelihood. In case of non-identifiable mixture components, an extra effort should be provided, in order to take into account the underlying symmetry of the posterior distribution (Neal, 1999;Frühwirth-Schnatter, 2004). This does not apply in our setup, that is, no "label switching" (see, e.g., Jasra et al, 2005) takes place.…”

Section: Discussionmentioning

confidence: 99%

Improved variational Bayes inference for transcript expression estimation

Papastamoulis

Hensman²,

Glaus³

et al. 2014

Statistical Applications in Genetics and Molecular Biology

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RNA-seq studies allow for the quantification of transcript expression by aligning millions of short reads to a reference genome. However, transcripts share much of their sequence, so that many reads map to more than one place and their origin remains uncertain. This problem can be dealt using mixtures of distributions and transcript expression reduces to estimating the weights of the mixture. In this paper, variational Bayesian (VB) techniques are used in order to approximate the posterior distribution of transcript expression. VB has previously been shown to be more computationally efficient for this problem than Markov chain Monte Carlo. VB methodology can precisely estimate the posterior means, but leads to variance underestimation. For this reason, a novel approach is introduced which integrates the latent allocation variables out of the VB approximation. It is shown that this modification leads to a better marginal likelihood bound and improved estimate of the posterior variance. A set of simulation studies and application to real RNA-seq datasets highlight the improved performance of the proposed method.

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Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques*

Cited by 178 publications

References 64 publications

Properties of nested sampling

Properties of nested sampling

Macroeconomic Implications of Oil Price Fluctuations: A Regime-Switching Framework for the Euro Area

Improved variational Bayes inference for transcript expression estimation

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