Integrated likelihood computation methods

Zhao, Zhenyu; Severini, Thomas A.

doi:10.1007/s00180-016-0677-z

Cited by 11 publications

(7 citation statements)

References 33 publications

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“…In the literature, there exist variants of the estimators in Eqs. (38) and (46). These corrected estimators are attempts to improve the efficiency (e.g., remove the infinite variance cases, specially in the harmonic estimator) by restricting the integration to a smaller subset of X (usually chosen in high posterior/likelihood-valued regions) generally denoted by B ⊂ X .…”

Section: Standard Ismentioning

confidence: 99%

Marginal likelihood computation for model selection and hypothesis testing: an extensive review

Llorente¹,

Martino²,

Delgado³

et al. 2020

Preprint

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This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many applications in statistics, applied mathematics, signal processing and machine learning. This article provides a comprehensive study of the state-of-the-art of the topic. We highlight limitations, benefits, connections and differences among the different techniques. Problems and possible solutions with the use of improper priors are also described. Some of the most relevant methodologies are compared through theoretical comparisons and numerical experiments.

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Section: Standard Ismentioning

confidence: 99%

Marginal likelihood computation for model selection and hypothesis testing: an extensive review

Llorente¹,

Martino²,

Delgado³

et al. 2020

Preprint

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“…For probit models and MCMC sampling with augmented variables, Fox (2010, p. 190) and Zhang et al (2019) exploit the closed form of the marginal likelihood of the augmented variables to obtain different kinds of marginal DICs. Zhao and Severini (2017) relatedly describe and compare a variety of other methods for computing integrated likelihoods. Our approach is closest to their "direct method" of importance sampling (see their Section 3.1.2), with importance density chosen to be similar to what they call the "weighted likelihood function."…”

Section: Dicmentioning

confidence: 99%

Bayesian Comparison of Latent Variable Models: Conditional Versus Marginal Likelihoods

2019

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Typical Bayesian methods for models with latent variables (or random effects) involve directly sampling the latent variables along with the model parameters. In high-level software code for model definitions (using, e.g., BUGS, JAGS, Stan), the likelihood is therefore specified as conditional on the latent variables. This can lead researchers to perform model comparisons via conditional likelihoods, where the latent variables are considered model parameters. In other settings, however, typical model comparisons involve marginal likelihoods where the latent variables are integrated out. This distinction is often overlooked despite the fact that it can have a large impact on the comparisons of interest. In this paper, we clarify and illustrate these issues, focusing on the comparison of conditional and marginal Deviance Information Criteria (DICs) and Watanabe-Akaike Information Criteria (WAICs) in psychometric modeling. The conditional/marginal distinction corresponds to whether the model should be predictive for the clusters that are in the data or for new clusters (where "clusters" typically correspond to higherlevel units like people or schools). Correspondingly, we show that marginal WAIC corresponds to leave-one-cluster out (LOcO) cross-validation, whereas conditional WAIC corresponds to leave-one-unit out (LOuO). These results lead to recommendations on the general application of the criteria to models with latent variables.

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“…The computational cost of the Monte Carlo-based algorithm for probability models used in this paper is moderate, and its efficiency can be improved with parallel computing. For complex or high dimensional model evidence calculation, MCMC-based algorithms, including Chib and Jeliazkov [43] and nested sampling [44] may be preferable as discussed in the recent review literature [45,46,47].…”

Section: Bayesian Evidence Calculationmentioning

confidence: 99%

The effect of prior probabilities on quantification and propagation of imprecise probabilities resulting from small datasets

Zhang

Shields

2018

Computer Methods in Applied Mechanics and Engineering

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This paper outlines a methodology for Bayesian multimodel uncertainty quantification (UQ) and propagation and presents an investigation into the effect of prior probabilities on the resulting uncertainties. The UQ methodology is adapted from the information-theoretic method previously presented by the authors (Zhang and Shields, 2018) to a fully Bayesian construction that enables greater flexibility in quantifying uncertainty in probability model form. Being Bayesian in nature and rooted in UQ from small datasets, prior probabilities in both probability model form and model parameters are shown to have a significant impact on quantified uncertainties and, consequently, on the uncertainties propagated through a physics-based model. These effects are specifically investigated for a simplified plate buckling problem with uncertainties in material properties derived from a small number of experiments using noninformative priors and priors derived from past studies of varying appropriateness. It is illustrated that prior probabilities can have a significant impact on multimodel UQ for small datasets and inappropriate (but seemingly reasonable) priors may even have lingering effects that bias probabilities even for large datasets. When applied to uncertainty propagation, this may result in probability bounds on response quantities that do not include the true probabilities.

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Integrated likelihood computation methods

Cited by 11 publications

References 33 publications

Marginal likelihood computation for model selection and hypothesis testing: an extensive review

Marginal likelihood computation for model selection and hypothesis testing: an extensive review

Bayesian Comparison of Latent Variable Models: Conditional Versus Marginal Likelihoods

The effect of prior probabilities on quantification and propagation of imprecise probabilities resulting from small datasets

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