Journal ArticleDOI
Monte Carlo Estimation of Bayesian Credible and HPD Intervals
Ming-Hui Chen,Qi-Man Shao +1 more
TLDR
In this article, a Markov chain Monte Carlo (MCMC) sampling algorithm is used to estimate Bayesian credible and highest probability density (HPD) intervals for parameters of interest and provides a simple Monte Carlo approach to approximate these Bayesian intervals when a sample of the relevant parameters can be generated from their respective marginal posterior distribution using a sample from an importance sampling distribution.Abstract:
This article considers how to estimate Bayesian credible and highest probability density (HPD) intervals for parameters of interest and provides a simple Monte Carlo approach to approximate these Bayesian intervals when a sample of the relevant parameters can be generated from their respective marginal posterior distribution using a Markov chain Monte Carlo (MCMC) sampling algorithm. We also develop a Monte Carlo method to compute HPD intervals for the parameters of interest from the desired posterior distribution using a sample from an importance sampling distribution. We apply our methodology to a Bayesian hierarchical model that has a posterior density containing analytically intractable integrals that depend on the (hyper) parameters. We further show that our methods are useful not only for calculating the HPD intervals for the parameters of interest but also for computing the HPD intervals for functions of the parameters. Necessary theory is developed and illustrative examples—including a si...read more
Citations
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Journal ArticleDOI
Analysis and design of RNA sequencing experiments for identifying isoform regulation
TL;DR: In this paper, a mixture-of-isoforms (MISO) model was proposed to estimate expression of alternatively spliced exons and isoforms and assesses confidence in these estimates.
Book
Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan
TL;DR: Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan provides an accessible approach to Bayesian data analysis, as material is explained clearly with concrete examples.
Analysis and design of RNA sequencing experiments for identifying isoform regulation
TL;DR: The mixture-of-isoforms (MISO) model is developed, a statistical model that estimates expression of alternatively spliced exons and isoforms and assesses confidence in these estimates, providing a probabilistic framework for RNA-seq analysis and functional insights into pre-mRNA processing.
Journal ArticleDOI
Current status of methods for defining the applicability domain of (quantitative) structure-activity relationships. The report and recommendations of ECVAM Workshop 52.
Tatiana I. Netzeva,Andrew Worth,Tom Aldenberg,Romualdo Benigni,Mark T. D. Cronin,Paola Gramatica,Joanna Jaworska,Scott Kahn,Gilles Klopman,Carol A. Marchant,Glenn J. Myatt,Nina Nikolova-Jeliazkova,Grace Patlewicz,Roger Perkins,David W. Roberts,Terry W Schultz,David T. Stanton,Johannes J.M. van de Sandt,Weida Tong,Gilman Veith,Chihae Yang +20 more
TL;DR: This is the 52nd report of a series of workshops organised by the European Centre for the Validation of Alternative Methods (ECVAM) to provide a source of input to the development of an OECD Guidance Document on (Q)SAR Validation.
Journal ArticleDOI
Power prior distributions for regression models
Joseph G. Ibrahim,Ming-Hui Chen +1 more
TL;DR: In this paper, the authors propose a general class of prior distributions for arbitrary regression models, called power prior distributions, which are based on the idea of raising the likelihood function of the historical data to the power ao, where 0 < ao < 1.
References
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Journal ArticleDOI
Stastical Decision Theory and Bayesian Analysis.
Malay Ghosh,James O. Berger +1 more
Journal ArticleDOI
Sampling-Based Approaches to Calculating Marginal Densities
TL;DR: In this paper, three sampling-based approaches, namely stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm, are compared and contrasted in relation to various joint probability structures frequently encountered in applications.
Journal Article
Sampling-based approaches to calculating marginal densities
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