Bayesian estimation of the Bonferroni index from a Pareto-type I population

2001 ◽  
Vol 10 (1-3) ◽  
pp. 41-48 ◽  
Author(s):  
G. M. Giorgi ◽  
M. Crescenzi
Keyword(s):  
Bayesian Estimation ◽  
Type I ◽  
Bonferroni Index

scholarly journals Bayesian estimation of the parameters of the bivariate generalized exponential distribution using accelerated life testing under censoring data

2015 ◽  
Vol 3 (2) ◽  
pp. 215
Author(s):  
Abd El-Maseh, M. P
Keyword(s):  
Bayesian Estimation ◽  
Accelerated Life Testing ◽  
Constant Stress ◽  
Type I ◽  
Life Testing ◽  
Unknown Parameters ◽  
Numerical Studies ◽  
Inverse Power Law ◽  
Accelerated Life ◽  
Power Law Function

<p>In this paper, the Bayesian estimation for the unknown parameters for the bivariate generalized exponential (BVGE) distribution under Bivariate censoring type-I samples with constant stress accelerated life testing (CSALT) are discussed. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The parameters are estimated by Bayesian approach using Markov Chain Monte Carlo (MCMC) method based on Gibbs sampling. Then, the numerical studies are introduced to illustrate the approach study using samples which have been generated from the BVGE distribution.</p>

scholarly journals Empirical Bayes Estimation of a Sparse Vector of Gene Expression Changes

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Stephen Erickson ◽  
Chiara Sabatti
Keyword(s):  
Hypothesis Testing ◽  
Bayesian Estimation ◽  
Cell Lines ◽  
Empirical Bayes ◽  
Type I Error ◽  
Bayes Estimation ◽  
Type I ◽  
Population Difference ◽  
Interesting Connection ◽  
Sparse Solutions

Gene microarray technology is often used to compare the expression of thousand of genes in two different cell lines. Typically, one does not expect measurable changes in transcription amounts for a large number of genes; furthermore, the noise level of array experiments is rather high in relation to the available number of replicates. For the purpose of statistical analysis, inference on the ``population'' difference in expression for genes across the two cell lines is often cast in the framework of hypothesis testing, with the null hypothesis being no change in expression. Given that thousands of genes are investigated at the same time, this requires some multiple comparison correction procedure to be in place. We argue that hypothesis testing, with its emphasis on type I error and family analogues, may not address the exploratory nature of most microarray experiments. We instead propose viewing the problem as one of estimation of a vector known to have a large number of zero components. In a Bayesian framework, we describe the prior knowledge on expression changes using mixture priors that incorporate a mass at zero, and we choose a loss function that favors the selection of sparse solutions. We consider two different models applicable to the microarray problem, depending on the nature of replicates available, and show how to explore the posterior distributions of the parameters using MCMC. Simulations show an interesting connection between this Bayesian estimation framework and false discovery rate (FDR) control. Finally, two empirical examples illustrate the practical advantages of this Bayesian estimation paradigm.

scholarly journals Estimation of Random Coefficient Multilevel Models in the Context of Small Numbers of Level 2 Clusters

2018 ◽  
Vol 79 (2) ◽  
pp. 217-248 ◽  
Author(s):  
Jocelyn H. Bolin ◽  
W. Holmes Finch ◽  
Rachel Stenger
Keyword(s):  
Monte Carlo ◽  
Bayesian Estimation ◽  
Multilevel Modeling ◽  
Fixed Effects ◽  
Random Coefficient ◽  
Type I ◽  
Multilevel Data ◽  
Monte Carlo Simulation Study ◽  
Industry Standard ◽  
Level 2

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the treatment of multilevel data specifically when there is random coefficient variation in small samples. The methods being compared are fixed effects modeling (the industry standard in business and managerial sciences), multilevel modeling using restricted maximum likelihood (REML) estimation (the industry standard in the social and behavioral sciences), multilevel modeling using the Kenward–Rogers correction, and Bayesian estimation using Markov Chain Monte Carlo. Results indicate that multilevel modeling does have an advantage over fixed effects modeling when Level 2 slope parameter variance exists. Bayesian estimation of multilevel effects can be advantageous over traditional multilevel modeling using REML, but only when prior probabilities are correctly specified. Results are presented in terms of Type I error, power, parameter estimation bias, empirical parameter estimate standard error, and parameter 95% coverage rates, and recommendations are presented.

Sign in / Sign up

Export Citation Format

Share Document