Sample Size Calculations for Binomial Proportions via Highest Posterior Density Intervals

1995 ◽  
Vol 44 (2) ◽  
pp. 143 ◽  
Author(s):  
Lawrence Joseph ◽  
David B. Wolfson ◽  
Roxane Du Berger
Keyword(s):  
Sample Size ◽  
Posterior Density ◽  
Binomial Proportions ◽  
Sample Size Calculations ◽  
Highest Posterior Density Intervals ◽  
Highest Posterior Density

scholarly journals Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

2021 ◽  
Author(s):  
Hiba Zeyada Muhammed ◽  
Essam Abd Elsalam Muhammed
Keyword(s):  
Monte Carlo ◽  
Real Data ◽  
Posterior Density ◽  
Data Set ◽  
Bayes Estimates ◽  
Squared Error ◽  
Distribution Shape ◽  
Highest Posterior Density Intervals ◽  
Metropolis Hasting Algorithm ◽  
Highest Posterior Density

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

scholarly journals Quantifying partial migration with sex-ratio balancing

2019 ◽  
Vol 97 (4) ◽  
pp. 352-361 ◽  
Author(s):  
Haley A. Ohms ◽  
Alix I. Gitelman ◽  
Chris E. Jordan ◽  
Dave A. Lytle
Keyword(s):  
Sex Ratio ◽  
Oncorhynchus Tshawytscha ◽  
Population Based ◽  
Partial Migration ◽  
Ecosystem Dynamics ◽  
Posterior Density ◽  
Data Set ◽  
Animal Populations ◽  
Highest Posterior Density Intervals ◽  
Highest Posterior Density

Partial migration, the phenomenon in which animal populations are composed of both migratory and nonmigratory individuals, is widespread among migrating animals. The proportion of migrants in these populations has direct influences on population genetics and dynamics, ecosystem dynamics, mating systems, evolution, and responses to environmental change, yet there are very few studies that measure the proportion of migrants. This is because existing methods to estimate the proportion of migrants are time-consuming and expensive. In this paper, we demonstrate a new method for estimating the proportion of migrants in a population based on sex ratio measurements. Many partially migratory taxa exhibit sex-biased migration or residency, and in these cases, the sex ratios of migrants and nonmigrants are fundamentally related to the proportion of migrants in the population. We define this relationship quantitatively and show how it can be used to infer the proportion of migrants in a population through a process we term “sex-ratio balancing”. We obtain Bayesian estimates of proportion of migrants and quantify the uncertainty in these estimates with highest posterior density intervals. Lastly, we validate the sex-ratio balancing approach with a Chinook salmon (Oncorhynchus tshawytscha Walbaum in Artedi, 1792) data set. Sex-ratio balancing holds promise as a tool for quantifying partial migration and filling a key data gap about partially migratory taxa.

BAYESIAN STUDY OF A TWO-COMPONENT SYSTEM WITH COMMON-CAUSE SHOCK FAILURES

2005 ◽  
Vol 22 (01) ◽  
pp. 105-119 ◽  
Author(s):  
V. S. S. YADAVALLI ◽  
A. BEKKER ◽  
J. PAUW
Keyword(s):  
Steady State ◽  
Posterior Density ◽  
Two Component System ◽  
Unknown Parameters ◽  
Component System ◽  
Common Cause ◽  
Two Component ◽  
Highest Posterior Density Intervals ◽  
In Series ◽  
Highest Posterior Density

The steady-state availability of a two-component system in series and parallel subject to individual failures (I-failures) and common-cause shock (CCS) failures is studied from a Bayesian viewpoint with different types of priors assumed for the unknown parameters in the system. Monte Carlo simulation is used to derive the posterior distribution for the steady-state availability and subsequently the highest posterior density intervals. A numerical example illustrates the results.

scholarly journals Estimation and Prediction for Gompertz Distribution under General Progressive Censoring

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 858
Author(s):  
Yuxuan Wang ◽  
Wenhao Gui
Keyword(s):  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Maximum Likelihood Estimates ◽  
Posterior Density ◽  
Gompertz Distribution ◽  
Bayesian Estimates ◽  
Asymptotic Confidence Intervals ◽  
Mh Algorithm ◽  
Highest Posterior Density Intervals ◽  
Highest Posterior Density

In this article, we discuss the estimation of the parameters for Gompertz distribution and prediction using general progressive Type-II censoring. Based on the Expectation–Maximization algorithm, we calculate the maximum likelihood estimates. Bayesian estimates are considered under different loss functions, which are symmetrical, asymmetrical and balanced, respectively. An approximate method—Tierney and Kadane—is used to derive the estimates. Besides, the Metropolis-Hasting (MH) algorithm is applied to get the Bayesian estimates as well. According to Fisher information matrix, we acquire asymptotic confidence intervals. Bootstrap intervals are also established. Furthermore, we build the highest posterior density intervals through the sample generated by the MH algorithm. Then, Bayesian predictive intervals and estimates for future samples are provided. Finally, for evaluating the quality of the approaches, a numerical simulation study is implemented. In addition, we analyze two real datasets.

scholarly journals Virtual reality-based relaxation for enhancement of perioperative well-being and quality of life: protocol for a randomised pilot trial

BMJ Open ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. e044193
Author(s):  
Matthias Christian Schrempf ◽  
Julian Quirin Petzold ◽  
Hugo Vachon ◽  
Morten Aagaard Petersen ◽  
Johanna Gutschon ◽  
...  
Keyword(s):  
Quality Of Life ◽  
Virtual Reality ◽  
Sample Size ◽  
Stress Reduction ◽  
Pilot Trial ◽  
Well Being ◽  
Coping Resources ◽  
Patients With Cancer ◽  
Sample Size Calculations

IntroductionPatients with cancer undergoing surgery often suffer from reduced quality of life and various forms of distress. Untreated distress can negatively affect coping resources as well as surgical and oncological outcomes. A virtual reality-based stress reduction intervention may increase quality of life and well-being and reduce distress in the perioperative phase for patients with cancer. This pilot trial aims to explore the feasibility of the proposed intervention, assess patient acceptability and obtain estimates of effect to provide data for sample size calculations.Methods and analysisPatients with colorectal cancer and liver metastasis undergoing elective surgery will be recruited for this single-centre, randomised pilot trial with a three-arm design. A total of 54 participants will be randomised at 1:1:1 ratio to one of two intervention groups or a control receiving standard treatment. Those randomised to an intervention group will either receive perioperative virtual reality-based stress reduction exercises twice daily or listen to classical music twice daily. Primary feasibility outcomes are number and proportions of participants recruited, screened, consented and randomised. Furthermore, adherence to the intervention, compliance with the completion of the quality of life questionnaires and feasibility of implementing the trial procedures will be assessed. Secondary clinical outcomes are measurements of the effectiveness of the interventions to inform sample size calculations.Ethics and disseminationThe study protocol, the patient information and the informed consent form have been approved by the ethics committee of the Ludwigs-Maximilians-University, Munich, Germany (Reference Number: 19–915). Study findings will be submitted for publication in peer-reviewed journals.Trial registration numberDRKS00020909.

scholarly journals Intra-cluster correlations from the CLustered OUtcome Dataset bank to inform the design of longitudinal cluster trials

2021 ◽  
pp. 174077452110208
Author(s):  
Elizabeth Korevaar ◽  
Jessica Kasza ◽  
Monica Taljaard ◽  
Karla Hemming ◽  
Terry Haines ◽  
...  
Keyword(s):  
Sample Size ◽  
Discrete Time ◽  
Correlation Coefficients ◽  
Time Decay ◽  
Randomised Trials ◽  
Cluster Randomised Trials ◽  
Cluster Randomised ◽  
Sample Size Calculations ◽  
Correlation Structures ◽  
Cluster Correlation

Background: Sample size calculations for longitudinal cluster randomised trials, such as crossover and stepped-wedge trials, require estimates of the assumed correlation structure. This includes both within-period intra-cluster correlations, which importantly differ from conventional intra-cluster correlations by their dependence on period, and also cluster autocorrelation coefficients to model correlation decay. There are limited resources to inform these estimates. In this article, we provide a repository of correlation estimates from a bank of real-world clustered datasets. These are provided under several assumed correlation structures, namely exchangeable, block-exchangeable and discrete-time decay correlation structures. Methods: Longitudinal studies with clustered outcomes were collected to form the CLustered OUtcome Dataset bank. Forty-four available continuous outcomes from 29 datasets were obtained and analysed using each correlation structure. Patterns of within-period intra-cluster correlation coefficient and cluster autocorrelation coefficients were explored by study characteristics. Results: The median within-period intra-cluster correlation coefficient for the discrete-time decay model was 0.05 (interquartile range: 0.02–0.09) with a median cluster autocorrelation of 0.73 (interquartile range: 0.19–0.91). The within-period intra-cluster correlation coefficients were similar for the exchangeable, block-exchangeable and discrete-time decay correlation structures. Within-period intra-cluster correlation coefficients and cluster autocorrelations were found to vary with the number of participants per cluster-period, the period-length, type of cluster (primary care, secondary care, community or school) and country income status (high-income country or low- and middle-income country). The within-period intra-cluster correlation coefficients tended to decrease with increasing period-length and slightly decrease with increasing cluster-period sizes, while the cluster autocorrelations tended to move closer to 1 with increasing cluster-period size. Using the CLustered OUtcome Dataset bank, an RShiny app has been developed for determining plausible values of correlation coefficients for use in sample size calculations. Discussion: This study provides a repository of intra-cluster correlations and cluster autocorrelations for longitudinal cluster trials. This can help inform sample size calculations for future longitudinal cluster randomised trials.

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