A Note on the Construction of Highest Posterior Density Intervals

1986 ◽  
Vol 35 (1) ◽  
pp. 49 ◽  
Author(s):  
D. E. Wright
Keyword(s):  
Posterior Density ◽  
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 Efeito materno e paterno sobre as taxas de fertilização e eclosão em curimba (Prochilodus lineatus)

2012 ◽  
Vol 64 (6) ◽  
pp. 1584-1590 ◽  
Author(s):  
I.B. Allaman ◽  
R.T.F. Freitas ◽  
A.T.M. Viveiros ◽  
A.F. Nascimento ◽  
G.R. Oliveira ◽  
...  
Keyword(s):  
Posterior Density ◽  
Prochilodus Lineatus ◽  
Highest Posterior Density

Avaliou-se o quanto fêmeas e machos contribuem para a variação total das taxas de fertilização e de eclosão em curimba (Prochilodus lineatus). Utilizou-se sêmen criopreservado proveniente de cinco machos para fertilizar ovócitos de seis fêmeas em um esquema fatorial cruzado 5x6, totalizando 30 famílias. Além das características reprodutivas dos machos e fêmeas, foram avaliadas as taxas de fertilização e eclosão para cômputo dos efeitos materno e paterno. Os componentes da variância foram estimados por meio da máxima verossimilhança restrita, sendo construídos intervalos Highest Posterior Density (HPD) para cada componente. Verificou-se que as fêmeas contribuíram muito mais para a variação total em relação aos machos para as taxas de fertilização e eclosão. Para a taxa de fertilização, as fêmeas contribuíram com 26,3% da variação total e os machos com 8,9%. Em relação à taxa de eclosão, as fêmeas contribuíram com 11,9% e os machos com 1,6%. Concluiu-se que houve efeito materno sobre as taxas de fertilização e eclosão e que o efeito paterno avaliado individualmente foi pouco expressivo ou até mesmo insignificante.

scholarly journals Computation of posterior distribution in Bayesian analysis – application in an intermittently used reliability system

2002 ◽  
Vol 21 (3) ◽  
pp. 78-82
Author(s):  
V. S.S. Yadavalli ◽  
P. J. Mostert ◽  
A. Bekker ◽  
M. Botha
Keyword(s):  
Posterior Distribution ◽  
Jeffreys Prior ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Stationary Rate ◽  
Analysis Application ◽  
Definition Of ◽  
Hpd Intervals ◽  
Highest Posterior Density ◽  
Bayes Procedure

Bayesian estimation is presented for the stationary rate of disappointments, D∞, for two models (with different specifications) of intermittently used systems. The random variables in the system are considered to be independently exponentially distributed. Jeffreys’ prior is assumed for the unknown parameters in the system. Inference about D∞ is being restrained in both models by the complex and non-linear definition of D∞. Monte Carlo simulation is used to derive the posterior distribution of D∞ and subsequently the highest posterior density (HPD) intervals. A numerical example where Bayes estimates and the HPD intervals are determined illustrates these results. This illustration is extended to determine the frequentistical properties of this Bayes procedure, by calculating covering proportions for each of these HPD intervals, assuming fixed values for the parameters.

scholarly journals Reliable confidence intervals for RelTime estimates of evolutionary divergence times

2019 ◽  
Author(s):  
Qiqing Tao ◽  
Koichiro Tamura ◽  
Beatriz Mello ◽  
Sudhir Kumar
Keyword(s):  
Confidence Intervals ◽  
Divergence Time ◽  
Simulated Data ◽  
Molecular Dating ◽  
Divergence Times ◽  
Rate Variation ◽  
Evolutionary Divergence ◽  
Posterior Density ◽  
Divergence Time Estimates ◽  
Highest Posterior Density

AbstractConfidence intervals (CIs) depict the statistical uncertainty surrounding evolutionary divergence time estimates. They capture variance contributed by the finite number of sequences and sites used in the alignment, deviations of evolutionary rates from a strict molecular clock in a phylogeny, and uncertainty associated with clock calibrations. Reliable tests of biological hypotheses demand reliable CIs. However, current non-Bayesian methods may produce unreliable CIs because they do not incorporate rate variation among lineages and interactions among clock calibrations properly. Here, we present a new analytical method to calculate CIs of divergence times estimated using the RelTime method, along with an approach to utilize multiple calibration uncertainty densities in these analyses. Empirical data analyses showed that the new methods produce CIs that overlap with Bayesian highest posterior density (HPD) intervals. In the analysis of computer-simulated data, we found that RelTime CIs show excellent average coverage probabilities, i.e., the true time is contained within the CIs with a 95% probability. These developments will encourage broader use of computationally-efficient RelTime approach in molecular dating analyses and biological hypothesis testing.

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