scholarly journals Bayesian Approaches for Poisson Distribution Parameter Estimation

2021 ◽  
Vol 5 (5) ◽  
pp. 755-774
Author(s):  
Yadpirun Supharakonsakun
Keyword(s):  
Parameter Estimation ◽  
Empirical Bayes ◽  
Random Variable ◽  
Credible Interval ◽  
Point Estimation ◽  
Quadratic Loss ◽  
Bayesian Approaches ◽  
True Parameter ◽  
Coverage Probabilities ◽  
Distribution Parameter Estimation

The Bayesian approach, a non-classical estimation technique, is very widely used in statistical inference for real world situations. The parameter is considered to be a random variable, and knowledge of the prior distribution is used to update the parameter estimation. Herein, two Bayesian approaches for Poisson parameter estimation by deriving the posterior distribution under the squared error loss or quadratic loss functions are proposed. Their performances were compared with frequentist (maximum likelihood estimator) and Empirical Bayes approaches through Monte Carlo simulations. The mean square error was used as the test criterion for comparing the methods for point estimation; the smallest value indicates the best performing method with the estimated parameter value closest to the true parameter value. Coverage Probabilities (CPs) and average lengths (ALs) were obtained to evaluate the performances of the methods for constructing confidence intervals. The results reveal that the Bayesian approaches were excellent for point estimation when the true parameter value was small (0.5, 1 and 2). In the credible interval comparison, these methods obtained CP values close to the nominal 0.95 confidence level and the smallest ALs for large sample sizes (50 and 100), when the true parameter value was small (0.5, 1 and 2). Doi: 10.28991/esj-2021-01310 Full Text: PDF

Bayesian and frequentist approaches to assessing reliability and precision of health-care provider quality measures

2015 ◽  
Vol 26 (3) ◽  
pp. 1341-1349 ◽  
Author(s):  
Vincent S Staggs ◽  
Byron J Gajewski
Keyword(s):  
Health Care ◽  
Empirical Bayes ◽  
High Reliability ◽  
Credible Interval ◽  
Quality Measures ◽  
Care Quality ◽  
Interval Length ◽  
Bayesian Approaches ◽  
Reliability Estimates ◽  
Fall Rates

Our purpose was to compare frequentist, empirical Bayes, and Bayesian hierarchical model approaches to estimating reliability of health care quality measures, including construction of credible intervals to quantify uncertainty in reliability estimates, using data on inpatient fall rates on hospital nursing units. Precision of reliability estimates and Bayesian approaches to estimating reliability are not well studied. We analyzed falls data from 2372 medical units; the rate of unassisted falls per 1000 inpatient days was the measure of interest. The Bayesian methods “shrunk” the observed fall rates and frequentist reliability estimates toward their posterior means. We examined the association between reliability and precision in fall rate rankings by plotting the length of a 90% credible interval for each unit’s percentile rank against the unit’s estimated reliability. Precision of rank estimates tended to increase as reliability increased but was limited even at higher reliability levels: Among units with reliability >0.8, only 5.5% had credible interval length <20; among units with reliability >0.9, only 31.9% had credible interval length <20. Thus, a high reliability estimate may not be sufficient to ensure precise differentiation among providers. Bayesian approaches allow for assessment of this precision.

scholarly journals Association between Migraine and the Risk of Stroke: A Bayesian Meta-Analysis

2021 ◽  
Vol 13 (7) ◽  
pp. 3759
Author(s):  
Kim-Ngan Ta-Thi ◽  
Kai-Jen Chuang ◽  
Chyi-Huey Bai
Keyword(s):  
Ischemic Stroke ◽  
Hemorrhagic Stroke ◽  
Stroke Risk ◽  
Meta Analysis ◽  
Credible Interval ◽  
Fixed Effect Model ◽  
Bayesian Approaches ◽  
Effect Model ◽  
Newcastle Ottawa Scale ◽  
Form Quality

There are still inconsistent results about association between migraine and stroke risk in studies. This paper was to review findings on the association between migraine (with or without aura) and stroke risk. We searched articles in the Embase and PubMed up to January 2021. Two independent reviewers extracted basic data from individual studies using a standardized form. Quality of studies was also assessed using the Newcastle–Ottawa Scale. We conducted a meta-analysis, both classical and Bayesian approaches. We identified 17 eligible studies with a sample size more than 2,788,000 participants. In the fixed effect model, the results demonstrated that migraine was positively associated with the risk of total stroke, hemorrhagic stroke, and ischemic stroke. Nevertheless, migraine was associated with only total stroke in the random effects model (risk ratio (RR) 1.31, 95%CI: 1.06–1.62). The probability that migraine increased total stroke risk was 0.978 (RR 1.31; 95% credible interval (CrI): 1.01–1.72). All types of migraine were not associated with ischemic stroke and hemorrhagic stroke. Under three prior distributions, there was no association between migraine and the risk of ischemic stroke or hemorrhagic stroke. Under the non-informative prior and enthusiastic prior, there was a high probability that migraine was associated with total stroke risk.

The Application of Statistic Inference in the SMS Package Model

2013 ◽  
Vol 380-384 ◽  
pp. 1129-1132
Author(s):  
Miao Chao Chen ◽  
Ting Zhou
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Hypothesis Testing ◽  
Poisson Distribution ◽  
Distribution Parameter ◽  
Research Results ◽  
Distribution Parameter Estimation

Hypothesis testing is one of the most important aspects in statistic inference. In this paper, we consider the SMS package problem of hypothesis testing. Firstly, we establish a mathematical model for SMS package problem. Secondly, we use the knowledge of Poisson distribution, parameter estimation and hypothesis testing to analyze this model, and the research results have proved the validity of the method.

scholarly journals Empirical Bayes estimation of farm prevalence adjusting for multistage sampling and uncertainty in test performance: a Brucella cross-sectional serostudy in southern Kazakhstan

2016 ◽  
Vol 144 (16) ◽  
pp. 3531-3539 ◽  
Author(s):  
W. BEAUVAIS ◽  
M. ORYNBAYEV ◽  
J. GUITIAN
Keyword(s):  
Confidence Interval ◽  
Test Performance ◽  
Empirical Bayes ◽  
Small Ruminants ◽  
Credible Interval ◽  
Bayes Estimation ◽  
Test Accuracy ◽  
Endemic Region ◽  
Cross Sectional ◽  
Seropositive Animal

SUMMARYEstimation of farm prevalence is common in veterinary research. Typically, not all animals within the farm are sampled, and imperfect tests are used. Often, assumptions about herd sizes and sampling proportions are made, which may be invalid in smallholder settings. We propose an alternative method for estimating farm prevalence in the context of Brucella seroprevalence estimation in an endemic region of Kazakhstan. We collected 210 milk samples from Otar district, with a population of about 1000 cattle and 16 000 small ruminants, and tested them using an indirect ELISA. Individual-level prevalence and 95% confidence intervals were estimated using Taylor series linearization. A model was developed to estimate the smallholding prevalence, taking into account variable sampling proportions and uncertainty in the test accuracy. We estimate that 73% of households that we sampled had at least one Brucella-seropositive animal (95% credible interval 68–82). We estimate that 58% (95% confidence interval 40–76) of lactating small ruminants and 14% (95% confidence interval 1–28) of lactating cows were seropositive. Our results suggest that brucellosis is highly endemic in the area and conflict with those of the official brucellosis-testing programme, which found that in 2013 0% of cows and 1·7% of small ruminants were seropositive.

Estimating the potential of wind energy resources using Weibull parameters: A case study of the coastline region of Dar es Salaam, Tanzania

2021 ◽  
Vol 11 (1) ◽  
pp. 1093-1104
Author(s):  
Enock Michael ◽  
Dominicus Danardono Dwi Prija Tjahjana ◽  
Aditya Rio Prabowo
Keyword(s):  
Parameter Estimation ◽  
Wind Energy ◽  
Wind Turbine ◽  
Cost Effective ◽  
Dar Es Salaam ◽  
Capacity Factor ◽  
Energy Potential ◽  
Weibull Parameters ◽  
Distribution Parameter Estimation ◽  
Annual Capacity

Abstract This study aimed to compare the graphical method (GM) and standard deviation method (SDM), based on analyses and efficient Weibull parameters by estimating future wind energy potential in the coastline region of Dar es Salaam, Tanzania. Hence, the conclusion from the numerical method comparisons will also determine suitable wind turbines that are cost-effective for the study location. The wind speed data for this study were collected by the Tanzania Meteorological Authority Dar es Salaam station over the period of 2017 to 2019. The two numerical methods introduced in this study were both found to be appropriate for Weibull distribution parameter estimation in the study area. However, the SDM gave a higher value of the Weibull parameter estimation than the GM. Furthermore, the five selected commercial wind turbine models that were simulated in terms of performance were based on a capacity factor using the SDM and were both over 25% the recommended capacity factor value. The Polaris P50-500 commercial wind turbine is recommend as a suitable wind turbine to be installed in the study area due to its maximum annual capacity factor value over 3 years.

Empirical Bayes point estimation

2018 ◽  
pp. 64-106
Author(s):  
J.S. Maritz ◽  
T. Lwin
Keyword(s):  
Empirical Bayes ◽  
Point Estimation

scholarly journals Bayesian Inference of δ=P(X

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 794 ◽  
Author(s):  
Jessie Marie Byrnes ◽  
Yu-Jau Lin ◽  
Tzong-Ru Tsai ◽  
Yuhlong Lio
Keyword(s):  
Empirical Distribution ◽  
Credible Interval ◽  
Absolute Error ◽  
Maximum Likelihood Estimates ◽  
Strength Parameter ◽  
Bayes Estimates ◽  
Censored Samples ◽  
Coverage Probabilities ◽  
Censored Sample ◽  
Burr Type Xii

Let X and Y follow two independent Burr type XII distributions and δ = P ( X < Y ) . If X is the stress that is applied to a certain component and Y is the strength to sustain the stress, then δ is called the stress–strength parameter. In this study, The Bayes estimator of δ is investigated based on a progressively first failure-censored sample. Because of computation complexity and no closed form for the estimator as well as posterior distributions, the Markov Chain Monte Carlo procedure using the Metropolis–Hastings algorithm via Gibbs sampling is built to collect a random sample of δ via the joint distribution of the progressively first failure-censored sample and random parameters and the empirical distribution of this collected sample is used to estimate the posterior distribution of δ . Then, the Bayes estimates of δ using the square error, absolute error, and linear exponential error loss functions are obtained and the credible interval of δ is constructed using the empirical distribution. An intensive simulation study is conducted to investigate the performance of these three types of Bayes estimates and the coverage probabilities and average lengths of the credible interval of δ . Moreover, the performance of the Bayes estimates is compared with the maximum likelihood estimates. The Internet of Things and a numerical example about the miles-to-failure of vehicle components for reliability evaluation are provided for application purposes.

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