Comparison of Bayesian Credible Intervals to Frequentist Confidence Intervals

Gray, Kathy; Hampton, Brittany Star; Silveti-Falls, Tony; McConnell, Allison; Bausell, Casey

doi:10.22237/jmasm/1430453220

Cited by 18 publications

(16 citation statements)

References 7 publications

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“…While the DP-Drop had the best performance in terms of credible interval coverage, we note that the DP-Drop 95% credible intervals do not always maintain 95% frequentist coverage probabilities. While in certain scenarios, Bayesian credible intervals can achieve nominal frequentist coverage probabilities, in general, there is no guarantee that a 95% Bayesian credible interval will maintain 95% frequentist coverage probability, as coverage probability depends on the prior distribution and sample size, as well as other factors (Wasserman, 2011;Gray et al, 2015). In these simulations with nonignorable dropout, coverage is lower than expected since the estimates of change over time for subjects that dropout early, and therefore have fewer observations, are necessarily shrunk towards subjects with more information.…”

Section: Resultsmentioning

confidence: 99%

A Dirichlet Process Mixture Model for Non-Ignorable Dropout

Moore¹,

Carlson²,

MaWhinney³

et al. 2020

Bayesian Anal.

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Longitudinal cohorts are a valuable resource for studying HIV disease progression; however, dropout is common in these studies. Subjects often fail to return for visits due to disease progression, loss to follow-up, or death. When dropout depends on unobserved outcomes, data are missing not at random, and results from standard longitudinal data analyses can be biased. Several methods have been proposed to adjust for non-ignorable dropout; however, many of these approaches rely on parametric assumptions about the distribution of dropout times and the functional form of the relationship between the outcome and dropout time. More flexible approaches may be needed when the distribution of dropout times does not follow a known distribution or violates proportional hazards assumptions, or when the relationship between the outcome and dropout times does not have a simple polynomial form. We propose a Bayesian semi-parametric Dirichlet process mixture model to flexibly model the relationship between dropout time and the outcome and show that more accurate inference can be obtained by nonparametrically modeling the distribution of subject-specific effects as well as the distribution of dropout times. Results from simulation studies as well as an application to a longitudinal HIV cohort study database illustrate the strengths of our Bayesian semi-parametric approach.

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Section: Resultsmentioning

confidence: 99%

A Dirichlet Process Mixture Model for Non-Ignorable Dropout

Moore¹,

Carlson²,

MaWhinney³

et al. 2020

Bayesian Anal.

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“… (a)Why does the paper use only confidence intervals, not credible intervals? I understand that the central limit theorem is a frequentist concept (Gray et al ., ) but, since this paper is about Bayesian methods, I wonder where the term ‘credible interval’ applies. (b)What is the contextual definition of the ‘meeting time’ of the chains? The mathematical definition is provided, but I think that stating the definition in plain text would also be helpful. (c)Why is the convergence speed measured as the ‘average meeting time’ in the figures?…”

Section: Discussion On the Paper By Jacob O’leary And Atchadémentioning

confidence: 99%

Unbiased Markov Chain Monte Carlo Methods with Couplings

Jacob

OʼLeary²,

Atchadé

2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

115

138

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Summary Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to ∞. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel. We discuss practical couplings for popular MCMC algorithms. We establish the theoretical validity of the estimators proposed and study their efficiency relative to the underlying MCMC algorithms. Finally, we illustrate the performance and limitations of the method on toy examples, on an Ising model around its critical temperature, on a high dimensional variable‐selection problem, and on an approximation of the cut distribution arising in Bayesian inference for models made of multiple modules.

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“…For example, Bayesian credible intervals can be estimated while incorporating information from a prior distribution. 23 Oftentimes, researchers would really prefer the information provided in a credible interval, and they should feel empowered to use this method to present their findings (see Table 1).…”

Section: Failure To Recognize Problematicmentioning

confidence: 99%