Permissible boundary prior function as a virtually proper prior density

2013 ◽  
Vol 66 (4) ◽  
pp. 789-809
Author(s):  
Takemi Yanagimoto ◽  
Toshio Ohnishi
Keyword(s):  
Prior Density

scholarly journals Density Estimation of Neonatal Mortality Rate Using Empirical Bayes Deconvolution with Poisson Distributed Surrogate in Central Java Province Indonesia

2020 ◽  
pp. 206-212
Author(s):  
Fevi Novkaniza ◽  
Khairil Anwar Notodiputro ◽  
I Wayan Mangku ◽  
Kusman Sadik
Keyword(s):  
Mortality Rate ◽  
Neonatal Mortality ◽  
Density Estimation ◽  
Poisson Distribution ◽  
Empirical Bayes ◽  
Prior Density ◽  
Neonatal Mortality Rate ◽  
Neonatal Deaths ◽  
Central Java ◽  
Central Java Province

This article is concerned with the density estimation of Neonatal Mortality Rate (NMR) in Central Java Province, Indonesia. Neonatal deaths contribute to 73% of infant deaths in Central Java Province. The number of neonatal deaths for 35 districts/municipalities in Central Java Province is considered as Poisson distributed surrogate with NMR as the rate of Poisson distribution. It is assumed that each number of neonatal deaths by district/municipality in Central Java Province were realizations of unobserved NMR, which come from unknown prior density. We applied the Empirical Bayes Deconvolution (EBD) method for estimating the unknown prior density of NMR based on Poisson distributed surrogate. We used secondary data from the Health Profiles of Central Java Province, Indonesia, in 2018. The density estimation of NMR by the EBD method showed that the resulting prior estimate is relatively close to the Gamma distribution based on Poisson surrogate. This is implying that the suitability of the obtained prior density estimation as a conjugate prior for Poisson distribution.

scholarly journals Asymptotic approximations to the Bayes posterior risk

1990 ◽  
Vol 3 (2) ◽  
pp. 99-116
Author(s):  
Toufik Zoubeidi
Keyword(s):  
Parameter Space ◽  
Exponential Family ◽  
Distribution Functions ◽  
Independent Random Variables ◽  
Asymptotic Approximations ◽  
Prior Density ◽  
Posterior Probabilities ◽  
Exponential Family Of Distributions ◽  
Family Of Distributions ◽  
Convex Subsets

Suppose that, given ω=(ω1,ω2)∈ℜ2, X1,X2,… and Y1,Y2,… are independent random variables and their respective distribution functions Gω1 and Gω2 belong to a one parameter exponential family of distributions. We derive approximations to the posterior probabilities of ω lying in closed convex subsets of the parameter space under a general prior density. Using this, we then approximate the Bayes posterior risk for testing the hypotheses H0:ω∈Ω1 versus H1:ω∈Ω2 using a zero-one loss function, where Ω1 and Ω2 are disjoint closed convex subsets of the parameter space.

scholarly journals Maximizing the Expected Duration of Owning a Relatively Best Object in a Poisson Process with Rankable Observations

2009 ◽  
Vol 46 (02) ◽  
pp. 402-414
Author(s):  
Aiko Kurushima ◽  
Katsunori Ano
Keyword(s):  
Poisson Process ◽  
Stopping Time ◽  
Fixed Time ◽  
Time Interval ◽  
Prior Density ◽  
Deterministic Equation ◽  
Fixed Time Interval ◽  
Unknown Number ◽  
Random Intensity ◽  
Time Selection

Suppose that an unknown number of objects arrive sequentially according to a Poisson process with random intensity λ on some fixed time interval [0,T]. We assume a gamma prior density G λ(r, 1/a) for λ. Furthermore, we suppose that all arriving objects can be ranked uniquely among all preceding arrivals. Exactly one object can be selected. Our aim is to find a stopping time (selection time) which maximizes the time during which the selected object will stay relatively best. Our main result is the following. It is optimal to select the ith object that is relatively best and arrives at some time s i (r) onwards. The value of s i (r) can be obtained for each r and i as the unique root of a deterministic equation.

scholarly journals Reliability of Sampling Inspection Schemes Applied to Replacement Steam Generators

2006 ◽  
Vol 129 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Guy Roussel ◽  
Leon Cizelj
Keyword(s):  
Closed Form ◽  
Steam Generator ◽  
The State ◽  
The Other ◽  
Prior Density ◽  
Steam Generators ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Sampling Inspection ◽  
Steam Generator Tubing

The basis for determining the size of the random sample of tubes to be inspected in replacement steam generators is revisited in this paper. A procedure to estimate the maximum number of defective tubes left in the steam generator after no defective tubes have been detected in the randomly selected inspection sample is proposed. A Bayesian estimation is used to obtain closed-form solutions for uniform, triangular, and binomial prior densities describing the number of failed tubes in steam generators. It is shown that the particular way of selecting the random inspection sample (e.g., one sample from both SG, one sample from each SG, etc.) does not affect the results of the inspection and also the information obtained about the state of the uninspected tubing, as long as the inspected steam generators belong to the same population. Numerical examples further demonstrate two possible states of the knowledge existing before the inspection of the tubing. First, virtually no knowledge about the state of the steam generator tubing before the inspection is modeled using uniform and triangular prior densities. It is shown that the knowledge about the uninspected part of the tubing strongly depends on the size of the sample inspected. Further, even small inspection samples may significantly improve our knowledge about the uninspected part. On the other hand, rather strong belief on the state of the tubing prior to the inspection is modeled using binomial prior density. In this case, the knowledge about the uninspected part of the tubing is virtually independent on the size of the sample. Furthermore, it is shown qualitatively and quantitatively that such inspection brings no additional knowledge on the uninspected part of the tubing.

Reliability Estimation for the Two-Parameter Exponential Family Based on Progressively Type-II Censored Data

2018 ◽  
Vol 25 (01) ◽  
pp. 1850005
Author(s):  
Wenhao Gui
Keyword(s):  
Reliability Function ◽  
Reliability Estimation ◽  
Type Ii ◽  
Prior Density ◽  
Monte Carlo Simulation Study ◽  
Censored Samples ◽  
Type Ii Censored Data ◽  
Two Parameters ◽  
Parameter Case ◽  
Two Parameter

In this paper, we deal with the problem of estimating the reliability function of the two-parameter exponential distribution. Classical Maximum likelihood and Bayes estimates for one and two parameters and the reliability function are obtained on the basis of progressively type-II censored samples. The inverted gamma conjugate prior density is assumed for the one-parameter case, whereas the joint prior density of the two-parameter case is composed of the inverted gamma and the uniform densities. A comparison between the obtained estimators is made through a Monte Carlo simulation study. A real example is used to illustrate the proposed methods.

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