arXiv subjects

Martyn Plummer

Publications and source records attributed to Martyn Plummer.

4 recordsLinked to original sources

arXiv2025

Bayesian measures of leverage and influence

Leverage and influence are regression diagnostics that are used to measure the sensitivity of parameter estimates to changes in the data. In this article, Bayesian leverage and influence diagnostics are derived from a local sensitivity framework in which the case weights of individual observations are perturbed. The resulting diagnostics can be applied to any Bayesian model and are easy to estimate using Markov Chain Monte Carlo. Bayesian measures of leverage and influence are closely related to predictive information criteria that are commonly used for Bayesian model choice. The penalty terms for these information criteria can be reinterpreted in terms of local sensitivity diagnostics. This connection helps to understand differences between the various information criteria that have been proposed in the literature. A comparison between leverage and influence measures leads to a new diagnostic for outlier detection. By considering multivariate case weight perturbations, groups of observations can be highlighted that are collectively outliers. This may suggest ways to improve the model. A diagnostic for sensitivity to the learning rate is also proposed that may be interpreted as a measure of prior-data conflict. This diagnostic can be adapted to measure cross-conflict between different parts of the data.

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arXiv2021

Quantification of empirical determinacy: the impact of likelihood weighting on posterior location and spread in Bayesian meta-analysis estimated with JAGS and INLA

The popular Bayesian meta-analysis expressed by Bayesian normal-normal hierarchical model (NNHM) synthesizes knowledge from several studies and is highly relevant in practice. Moreover, NNHM is the simplest Bayesian hierarchical model (BHM), which illustrates problems typical in more complex BHMs. Until now, it has been unclear to what extent the data determines the marginal posterior distributions of the parameters in NNHM. To address this issue we computed the second derivative of the Bhattacharyya coefficient with respect to the weighted likelihood, defined the total empirical determinacy (TED), the proportion of the empirical determinacy of location to TED (pEDL), and the proportion of the empirical determinacy of spread to TED (pEDS). We implemented this method in the R package \texttt{ed4bhm} and considered two case studies and one simulation study. We quantified TED, pEDL and pEDS under different modeling conditions such as model parametrization, the primary outcome, and the prior. This clarified to what extent the location and spread of the marginal posterior distributions of the parameters are determined by the data. Although these investigations focused on Bayesian NNHM, the method proposed is applicable more generally to complex BHMs.

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arXiv2020

A Note on Bayesian Modeling Specification of Censored Data in JAGS

Just Another Gibbs Sampling (JAGS) is a convenient tool to draw posterior samples using Markov Chain Monte Carlo for Bayesian modeling. However, the built-in function dinterval() to model censored data misspecifies the computation of deviance function, which may limit its usage to perform likelihood based model comparison. To establish an automatic approach to specify the correct deviance function in JAGS, we propose a simple alternative modeling strategy to implement Bayesian model selection for analysis of censored outcomes. The proposed approach is applicable to a broad spectrum of data types, which include survival data and many other right-, left- and interval-censored Bayesian model structures.

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arXiv2016

A Bayesian information criterion for singular models

We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher-information matrices may fail to be invertible along other competing submodels. Such singular models do not obey the regularity conditions underlying the derivation of Schwarz's Bayesian information criterion (BIC) and the penalty structure in BIC generally does not reflect the frequentist large-sample behavior of their marginal likelihood. While large-sample theory for the marginal likelihood of singular models has been developed recently, the resulting approximations depend on the true parameter value and lead to a paradox of circular reasoning. Guided by examples such as determining the number of components of mixture models, the number of factors in latent factor models or the rank in reduced-rank regression, we propose a resolution to this paradox and give a practical extension of BIC for singular model selection problems.

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