The Subjectivity of Scientists and the Bayesian Approach

Press, S. James; Tanur, Judith M.

doi:10.1002/9781118150634

Cited by 81 publications

(28 citation statements)

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“…Press [25] suggested to use very small non-negative values of the hyperparameters in this case, and it will make the priors proper. We have tried a = b = c = d = 0.0001.…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

Estimating the parameters of Lomax distribution from imprecise information

Pak¹,

Mahmoudi²

2018

JSTA

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Traditional statistical approaches for estimating the parameters of Lomax distribution have dealt with precise information. However, in real world situations, some information about an underlying system might be imprecise and are represented in the form of fuzzy information. In this paper, we consider the problem of estimating the parameters of Lomax distribution when the available observations are described by means of fuzzy information. We obtain the maximum likelihood estimate of the parameters by using the Newton-Raphson as well as the EM algorithm. We also provide an approximation namely, Tierney and Kadane's approximation, to compute the Bayes estimates of the unknown parameters. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their estimated biases and mean squared errors. Finally, analysis of one data set is provided for the purpose of illustration.

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“…Press [25] suggested to use very small non-negative values of the hyperparameters in this case, and it will make the priors proper. We have tried a = b = c = d = 0.0001.…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

Estimating the parameters of Lomax distribution from imprecise information

Pak¹,

Mahmoudi²

2018

JSTA

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“…Note that in this case the priors are non-proper also. Press (2001) suggested to use very small non-negative values of the hyper parameters in this case, and it will make the priors proper. We have tried α 1 = α 2 = β 1 = β 2 = 0.0001.…”

Section: Simulation Studymentioning

confidence: 99%

Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data

Lee¹,

Cho

2015

Journal of the Korean Data and Information Science Society

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In lifetime data analysis, it is generally known that the lifetimes of test items may not be recorded exactly. There are also situations wherein the withdrawal of items prior to failure is prearranged in order to decrease the time or cost associated with experience. Moreover, it is generally known that more than one cause or risk factor may be present at the same time. Therefore, analysis of censored competing risks data are needed. In this article, we derive the Bayes estimators for the entropy function under the exponential distribution with an unknown scale parameter based on multiply Type II censored competing risks data. The Bayes estimators of entropy function for the exponential distribution with multiply Type II censored competing risks data under the squared error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF) are provided. Lindley's approximate method is used to compute these estimators. We compare the proposed Bayes estimators in the sense of the mean squared error (MSE) for various multiply Type II censored competing risks data. Finally, a real data set has been analyzed for illustrative purposes.

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“…Lindley [20] first proposed his procedure to approximate the ratio of two integrals such as (30). Several others used this approximation; see Press [22] for details. Based on Lindley's approximation, the approximate Bayes estimates of , and for the squared error loss functions are respectively and where and For the detailed derivations, see the Appendix, part A.…”

Section: A Lindley's Approximationmentioning

confidence: 99%

Inference Based on Type-II Hybrid Censored Data From a Weibull Distribution

2008

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Abstract-A hybrid censoring scheme is a mixture of Type-I and Type-II censoring schemes. This article presents the statistical inferences on Weibull parameters when the data are Type-II hybrid censored. The maximum likelihood estimators, and the approximate maximum likelihood estimators are developed for estimating the unknown parameters. Asymptotic distributions of the maximum likelihood estimators are used to construct approximate confidence intervals. Bayes estimates, and the corresponding highest posterior density credible intervals of the unknown parameters, are obtained using suitable priors on the unknown parameters, and by using Markov Chain Monte Carlo techniques. The method of obtaining the optimum censoring scheme based on the maximum information measure is also developed. We perform Monte Carlo simulations to compare the performances of the different methods, and we analyse one data set for illustrative purposes.

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The Subjectivity of Scientists and the Bayesian Approach

Cited by 81 publications

References 0 publications

Estimating the parameters of Lomax distribution from imprecise information

Estimating the parameters of Lomax distribution from imprecise information

Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data

Inference Based on Type-II Hybrid Censored Data From a Weibull Distribution

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