scholarly journals A Bayesian approach to construct confidence intervals for comparing the rainfall dispersion in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e8502 ◽  
Author(s):  
Patcharee Maneerat ◽  
Sa-aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Drainage Basin ◽  
Average Length ◽  
Small Sample ◽  
Posterior Density ◽  
Natural Rainfall ◽  
Credible Intervals ◽  
Small Sample Sizes ◽  
Variance Estimates ◽  
Highest Posterior Density ◽  
Normal Gamma Prior

Natural disasters such as drought and flooding are the consequence of severe rainfall fluctuation, and rainfall amount data often contain both zero and positive observations, thus making them fit a delta-lognormal distribution. By way of comparison, rainfall dispersion may not be similar in enclosed regions if the topography and the drainage basin are different, so it can be evaluated by the ratio of variances. To estimate this, credible intervals using the highest posterior density based on the normal-gamma prior (HPD-NG) and the method of variance estimates recovery (MOVER) for the ratio of delta-lognormal variances are proposed. Monte Carlo simulation was used to assess the performance of the proposed methods in terms of coverage probability and relative average length. The results of the study reveal that HPD-NG performed very well and was able to meet the requirements in various situations, even with a large difference between the proportions of zeros. However, MOVER is the recommended method for equal small sample sizes. Natural rainfall datasets for the northern and northeastern regions of Thailand are used to illustrate the practical use of the proposed credible intervals.

scholarly journals Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials

2021 ◽  
Vol 18 (2) ◽  
pp. 595
Author(s):  
Fulvio De Santis ◽  
Stefania Gubbiotti
Keyword(s):  
Clinical Trials ◽  
Posterior Probability ◽  
Interval Estimation ◽  
Small Sample ◽  
Sample Sizes ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Credible Intervals ◽  
Small Sample Sizes ◽  
Highest Posterior Density

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds.

scholarly journals The Bayesian Confidence Interval for Coefficient of Variation of Zero-inflated Poisson Distribution with Application to Daily COVID-19 Deaths in Thailand

2021 ◽  
Vol 5 ◽  
pp. 62-76
Author(s):  
Sunisa Junnumtuam ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
Average Length ◽  
Simulated Data ◽  
Posterior Density ◽  
The World ◽  
Bayesian Confidence Interval ◽  
Percentile Bootstrap ◽  
Highest Posterior Density ◽  
Better Than

Coronavirus disease 2019 (COVID-19) has spread rapidly throughout the world and has caused millions of deaths. However, the number of daily COVID-19 deaths in Thailand has been low with most daily records showing zero deaths, thereby making them fit a Zero-Inflated Poisson (ZIP) distribution. Herein, confidence intervals for the Coefficient Of Variation (CV) of a ZIP distribution are derived using four methods: the standard bootstrap (SB), percentile bootstrap (PB), Markov Chain Monte Carlo (MCMC), and the Bayesian-based highest posterior density (HPD), for which using the variance of the CV is unnecessary. We applied the methods to both simulated data and data on the number of daily COVID-19 deaths in Thailand. Both sets of results show that the SB, MCMC, and HPD methods performed better than PB for most cases in terms of coverage probability and average length. Overall, the HPD method is recommended for constructing the confidence interval for the CV of a ZIP distribution. Doi: 10.28991/esj-2021-SPER-05 Full Text: PDF

scholarly journals Bayesian Nonparametric Inference of Population Size Changes from Sequential Genealogies

2015 ◽  
Author(s):  
Julia A Palacios ◽  
John Wakeley ◽  
Sohini Ramachandran
Keyword(s):  
Population Size ◽  
Broad Class ◽  
Likelihood Estimation ◽  
Small Sample ◽  
Bayesian Nonparametric ◽  
Coalescent Model ◽  
Credible Intervals ◽  
Population Sizes ◽  
Small Sample Sizes ◽  
Over Time

Sophisticated inferential tools coupled with the coalescent model have recently emerged for estimating past population sizes from genomic data. Accurate methods are available for data from a single locus or from independent loci. Recent methods that model recombination require small sample sizes, make constraining assumptions about population size changes, and do not report measures of uncertainty for estimates. Here, we develop a Gaussian process-based Bayesian nonparametric method coupled with a sequentially Markov coalescent model which allows accurate inference of population sizes over time from a set of genealogies. In contrast to current methods, our approach considers a broad class of recombination events, including those that do not change local genealogies. We show that our method outperforms recent likelihood-based methods that rely on discretization of the parameter space. We illustrate the application of our method to multiple demographic histories, including population bottlenecks and exponential growth. In simulation, our Bayesian approach produces point estimates four times more accurate than maximum likelihood estimation (based on the sum of absolute differences between the truth and the estimated values). Further, our method's credible intervals for population size as a function of time cover 90 percent of true values across multiple demographic scenarios, enabling formal hypothesis testing about population size differences over time. Using genealogies estimated with ARGweaver, we apply our method to European and Yoruban samples from the 1000 Genomes Project and confirm key known aspects of population size history over the past 150,000 years.

Comparing Medical Care Costs using Bayesian Credible Intervals for the Ratio of Means of Delta-Lognormal Distributions

2020 ◽  
Vol 28 (Supp01) ◽  
pp. 51-68 ◽  
Author(s):  
Patcharee Maneerat ◽  
Sa-Aat Niwitpong
Keyword(s):  
Medical Care ◽  
Average Length ◽  
Credible Interval ◽  
Error Rates ◽  
Lognormal Distributions ◽  
Medical Care Costs ◽  
Bayesian Credible Interval ◽  
Credible Intervals ◽  
Variance Estimates ◽  
Care Costs

When considering the medical care costs data with a high proportion of zero items of two inpatient groups, comparing them can be estimated using confidence intervals for the ratio of the means of two delta-lognormal distributions. The Bayesian credible interval-based uniform-beta prior (BCIh-UB) is proposed and compared with the generalized confidence interval (GCI), fiducial GCI (FGCI), the method of variance estimates recovery (MOVER), BCIh based on Jeffreys’ rule prior (BCIh-JR), and BCIh based on the normal-gamma prior (BCIh-NG). The coverage probability (CP), average length (AL), and lower and upper error rates were the performance measures applied for assessing the methods through a Monte Carlo simulation. A numerical evaluation showed that BCIh-UB had much better CP and AL than the others even with a large difference between the variances and with a high proportion of zero. Finally, to illustrate the efficacy of BCIh-UB, the methods were applied to two sets of medical care costs data.

EXACT BAYESIAN ESTIMATION OF SYSTEM RELIABILITY WITH POTENTIAL MISCLASSIFICATIONS IN SAMPLING

2004 ◽  
Vol 11 (03) ◽  
pp. 223-241
Author(s):  
N. TURKKAN ◽  
T. PHAM-GIA
Keyword(s):  
Bayesian Estimation ◽  
Bayesian Approach ◽  
Posterior Distribution ◽  
System Reliability ◽  
Exact Expression ◽  
System Level ◽  
Posterior Density ◽  
Approximate Methods ◽  
Credible Intervals ◽  
Highest Posterior Density

We provide the exact expression of the reliability of a system under a Bayesian approach, using beta distributions as both native and induced priors at the system level, and allowing uncertainties in sampling, expressed under the form of misclassifications, or noises, that can affect the final posterior distribution. Exact 100(1-α)% highest posterior density credible intervals, for system reliability, are computed, and comparisons are made with results from approximate methods proposed in the literature.

Revisit to progressively Type-II censored competing risks data from Lomax distributions

2021 ◽  
pp. 1748006X2098397
Author(s):  
Rui Hua ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Competing Risks ◽  
Maximum Likelihood Estimates ◽  
Type Ii ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Linex Loss ◽  
Credible Intervals ◽  
Competing Risks Data ◽  
Highest Posterior Density

In survival analysis, more than one factor typically contributes to individual failure. In addition, censoring is inevitable in lifespan tests or reliability studies due to external causes or experimental purposes. In this article, the competing risks model is considered and investigated under progressively Type-II censoring where data is from Lomax distributions. Assumptions are further made that these competitive factors are independently distributed, and the latent lifetimes of these factors follow Lomax distributions where both scale parameters and shape parameters are different. For all unknown parameters, maximum likelihood estimates have been attained by Newton-Raphson (NR) method as well as expectation maximization (EM) method, and then the approximate confidence intervals are acquired, in addition to bootstrap confidence intervals. Furthermore, under square error and LINEX loss functions, Bayes estimates and corresponding highest posterior density credible intervals are successively constructed. Finally, simulation experiments are implemented to access performance of several proposed methods in this article, and laboratory dataset is presented and analyzed for illustrative purposes.

scholarly journals Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2130
Author(s):  
Wisunee Puggard ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Simulation Study ◽  
Average Length ◽  
Credible Interval ◽  
Posterior Density ◽  
Concentration Data ◽  
Monte Carlo Simulation Study ◽  
The Difference ◽  
Highest Posterior Density ◽  
Hpd Interval

The Birnbaum–Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an important descriptive statistic for explaining variation within a dataset, has not previously been used for statistical inference on a BS distribution. The aim of this study is to present four methods for constructing confidence intervals for the CV, and the difference between the CVs of BS distributions. The proposed methods are based on the generalized confidence interval (GCI), a bootstrapped confidence interval (BCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval. A Monte Carlo simulation study was conducted to evaluate their performances in terms of coverage probability and average length. The results indicate that the HPD interval was the best-performing method overall. PM 2.5 concentration data for Chiang Mai, Thailand, collected in March and April 2019, were used to illustrate the efficacies of the proposed methods, the results of which were in good agreement with the simulation study findings.

scholarly journals Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

2018 ◽  
Vol 47 (3) ◽  
pp. 40-62 ◽  
Author(s):  
Ankita Chaturvedi ◽  
Sanjay Kumar Singh ◽  
Umesh Singh
Keyword(s):  
Real Data ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Type Ii ◽  
Posterior Density ◽  
Numerical Illustration ◽  
Data Set ◽  
Bayesian Procedures ◽  
Credible Intervals ◽  
Highest Posterior Density

This article presents the procedures for the estimation of the parameter of Rayleighdistribution based on Type-II progressive hybrid censored fuzzy lifetime data. Classicalas well as the Bayesian procedures for the estimation of unknown model parameters has been developed. The estimators obtained here are Maximum likelihood (ML) estimator, Method of moments (MM) estimator, Computational approach (CA) estimator and Bayes estimator. Highest posterior density (HPD) credible intervals of the unknown parameter are obtained by using Markov Chain Monte Carlo (MCMC) technique. For numerical illustration, a real data set has been considered.

scholarly journals Estimating the average daily rainfall in Thailand using confidence intervals for the common mean of several delta-lognormal distributions

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e10758
Author(s):  
Patcharee Maneerat ◽  
Sa-Aat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Average Length ◽  
Daily Rainfall ◽  
Parametric Bootstrap ◽  
Posterior Density ◽  
Lognormal Distributions ◽  
Common Mean ◽  
The Common ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

The daily average natural rainfall amounts in the five regions of Thailand can be estimated using the confidence intervals for the common mean of several delta-lognormal distributions based on the fiducial generalized confidence interval (FGCI), large sample (LS), method of variance estimates recovery (MOVER), parametric bootstrap (PB), and highest posterior density intervals based on Jeffreys’ rule (HPD-JR) and normal-gamma-beta (HPD-NGB) priors. Monte Carlo simulation was conducted to assess the performance in terms of the coverage probability and average length of the proposed methods. The numerical results indicate that MOVER and PB provided better performances than the other methods in a variety of situations, even when the sample case was large. The efficacies of the proposed methods were illustrated by applying them to real rainfall datasets from the five regions of Thailand.

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