Bayes estimates as an approximation to maximum likelihood estimates

2015 ◽  
Vol 58 (1) ◽  
pp. 45-52 ◽  
Author(s):  
Kohji Yamamura
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimates ◽  
Bayes Estimates

scholarly journals Estimation of the Inverse Weibull Distribution Parameters under Type-I Hybrid Censoring

2021 ◽  
Vol 50 (5) ◽  
pp. 38-51
Author(s):  
Mohammad Kazemi ◽  
Mina Azizpoor
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Unknown Parameters ◽  
Bayes Estimates ◽  
Hybrid Censoring ◽  
Inverse Weibull Distribution ◽  
Distribution Parameters ◽  
Highest Posterior Density

The hybrid censoring is a mixture of type-I and type-II censoring schemes. This paper presents the statistical inferences of the inverse Weibull distribution parameters when the data are type-I hybrid censored. First, we consider the maximum likelihood estimates of the unknown parameters. It is observed that the maximum likelihood estimates can not be obtained in closed form. We further obtain the Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimates using Lindley's approximation technique. The performance of the Bayes estimates have been compared with maximum likelihood estimates through the Monte Carlo Markov chain techniques. Finally, a real data set have been analysed for illustration purpose.

scholarly journals Classical and Bayesian Estimation of Two-Parameter Power Function Distribution

2021 ◽  
Author(s):  
Xuechen Liu ◽  
Muhammad Arslan ◽  
Majid Khan ◽  
Syed Masroor Anwar ◽  
Zahid Rasheed
Keyword(s):  
Maximum Likelihood ◽  
Power Function ◽  
Real Life ◽  
Maximum Likelihood Estimates ◽  
Time Model ◽  
Data Set ◽  
Bayes Estimates ◽  
Function Distribution ◽  
Power Function Distribution ◽  
Two Parameter

The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

scholarly journals Risk Efficiencies of Empirical Bayes and Generalized Maximum Likelihood Estimates for Rayleigh Model under Censored Data

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Dinesh Barot ◽  
Manhar Patel
Keyword(s):  
Maximum Likelihood ◽  
Loss Function ◽  
Empirical Bayes ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Comparison Method ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Bayes Estimates ◽  
Generalized Maximum Likelihood

The comparison of empirical Bayes and generalized maximum likelihood estimates of reliability performances is made in terms of risk efficiencies when the data are progressively Type II censored from Rayleigh distribution. The empirical Bayes estimates are obtained using an asymmetric loss function. The risk functions of the estimates and risk efficiencies are obtained under this loss function. A real data set is presented to illustrate the proposed comparison method, and the performance of the estimates is examined and compared in terms of risk efficiencies by means of Monte Carlo simulations. The simulation results indicate that the proposed empirical Bayes estimates are more preferable than the generalized maximum likelihood estimates.

Estimation of Reliability in a Multicomponent Stress–Strength Model Based on Power Transformed Half-Logistic Distribution

2020 ◽  
pp. 2150009 ◽  
Author(s):  
Thomas Xavier ◽  
Joby K. Jose
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Strength Model ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Bayes Estimates ◽  
Squared Error ◽  
Proposed Model

This paper deals with the study of the reliability of multicomponent stress–strength model assuming that the strength components are independently and identically distributed as power transformed half-logistic (PHL) distribution. The strength components which are subject to a common stress are assumed to be independent with either Weibull distribution or PHL distribution. The maximum likelihood estimates of the multicomponent stress–strength reliability and its asymptotic confidence interval under the above said conditions are obtained. The Bayes estimates of the multicomponent stress–strength reliability are also obtained under squared error loss function and using gamma priors for the parameters. To evaluate the performance of the procedure, a simulation study is considered. For illustration purpose of the proposed model, two real life examples are given.

scholarly journals Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

scholarly journals An Integrated Framework for the Inference of Viral Population History From Reconstructed Genealogies

Genetics ◽  
2000 ◽  
Vol 155 (3) ◽  
pp. 1429-1437
Author(s):  
Oliver G Pybus ◽  
Andrew Rambaut ◽  
Paul H Harvey
Keyword(s):  
Maximum Likelihood ◽  
Sequence Data ◽  
Demographic History ◽  
Population History ◽  
Maximum Likelihood Estimates ◽  
Viral Population ◽  
True Parameter ◽  
Subtype B ◽  
Exponential Growth Model ◽  
Parameter Values

Abstract We describe a unified set of methods for the inference of demographic history using genealogies reconstructed from gene sequence data. We introduce the skyline plot, a graphical, nonparametric estimate of demographic history. We discuss both maximum-likelihood parameter estimation and demographic hypothesis testing. Simulations are carried out to investigate the statistical properties of maximum-likelihood estimates of demographic parameters. The simulations reveal that (i) the performance of exponential growth model estimates is determined by a simple function of the true parameter values and (ii) under some conditions, estimates from reconstructed trees perform as well as estimates from perfect trees. We apply our methods to HIV-1 sequence data and find strong evidence that subtypes A and B have different demographic histories. We also provide the first (albeit tentative) genetic evidence for a recent decrease in the growth rate of subtype B.

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