123 research outputs found
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
Lexis: An R Class for Epidemiological Studies with Long-Term Follow-Up
The Lexis class in the R package Epi provides an object-based framework for managing follow-up time on multiple time scales, which is an important feature of prospective epidemiological studies with long duration. Follow-up time may be split either into fixed time bands, or on individual event times and the split data may be used in Poisson regression models that account for the evolution of disease risk on multiple time scales. The summary and plot methods for Lexis objects allow inspection of the follow-up times.
Using Lexis Objects for Multi-State Models in R
The Lexis class in the R package Epi provides tools for creation, manipulation and display of data from multi-state models. Transitions between states are described by rates (intensities); Lexis objects represent this kind of data and provide tools to show states and transitions annotated by relevant summary numbers. Data can be transformed to a form that allows modelling of several transition rates with common parameters.
Lexis: An R Class for Epidemiological Studies with Long-Term Follow-Up
The Lexis class in the R package Epi provides an object-based framework for managing follow-up time on multiple time scales, which is an important feature of prospective epidemiological studies with long duration. Follow-up time may be split either into fixed time bands, or on individual event times and the split data may be used in Poisson regression models that account for the evolution of disease risk on multiple time scales. The summary and plot methods for Lexis objects allow inspection of the follow-up times
Using Lexis Objects for Multi-State Models in R
The Lexis class in the R package Epi provides tools for creation, manipulation and display of data from multi-state models. Transitions between states are described by rates (intensities); Lexis objects represent this kind of data and provide tools to show states and transitions annotated by relevant summary numbers. Data can be transformed to a form that allows modelling of several transition rates with common parameters
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
Quantification of Empirical Determinacy: The Impact of Likelihood Weighting on Posterior Location and Spread in Bayesian Meta-Analysis Estimated with JAGS and INLA
Correction: On Bayesian modeling of censored data in JAGS
Following the publication of the original article [1], the authors identified errors in the model specifications 1 and 2. The correct models are given below
How vague is vague? How informative is informative? Reference analysis for Bayesian metaâanalysis
Meta-analysis provides important insights for evidence-based medicine by synthesizing evidence from multiple studies which address the same research question. Within the Bayesian framework, meta-analysis is frequently expressed by a Bayesian normal-normal hierarchical model (NNHM). Recently, several publications have discussed the choice of the prior distribution for the between-study heterogeneity in the Bayesian NNHM and used several âvagueâ priors. However, no approach exists to quantify the informativeness of such priors, and thus, we develop a principled reference analysis framework for the Bayesian NNHM acting at the posterior level. The posterior reference analysis (post-RA) is based on two posterior benchmarks: one induced by the improper reference prior, which is minimally informative for the data, and the other induced by a highly anticonservative proper prior. This approach applies the Hellinger distance to quantify the informativeness of a heterogeneity prior of interest by comparing the corresponding marginal posteriors with both posterior benchmarks. The post-RA is implemented in the freely accessible R package ra4bayesmeta and is applied to two medical case studies. Our findings show that anticonservative heterogeneity priors produce platykurtic posteriors compared with the reference posterior, and they produce shorter 95% credible intervals (CrI) and optimistic inference compared with the reference prior. Conservative heterogeneity priors produce leptokurtic posteriors, longer 95% CrI and cautious inference. The novel post-RA framework could support numerous Bayesian meta-analyses in many research fields, as it determines how informative a heterogeneity prior is for the actual data as compared with the minimally informative reference prior
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