Optimal Bayesian estimation of the median effective dose
type: Item
instance of: scholarly article
title: Optimal Bayesian estimation of the median effective dose
zbMATH Open document ID: 0629.62072
DOI: 10.1016/0378-3758(88)90017-1
published in: Journal of Statistical Planning and Inference
publication date: 1988-01-01T00:00:00Z
review text: This paper provides some properties of the Fisher information function arising in quantal response bioassay, attribute life testing and dilution assay models. It is shown that the Fisher information function (arising in probit, logit and extreme value models) is a totally positive function of order 2 and consequently unimodal as a function of the unknown parameter as well as a function of the design level. A method is provided for obtaining estimates of the shift parameter (median effective dose when scale parameter is known for symmetric tolerance densities) in these models from Bayesian and adaptive Bayesian points of view. We assume that the prior distribution belongs to a class containing Polya densities of order 2 defined over the real line besides the rectangular densities. Optimality is defined in terms of maximizing the expected Fisher information function. It is shown that the optimal Bayesian estimates exist and are unique under certain conditions on the model and the prior distributions. Optimal Bayesian estimates of the median effective dose for a two stage design set up for logit model are provided for some prior distributions. It is shown that the tables of optimal Bayesian estimates obtained for the uniform prior can be used for logistic prior as well.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62K99
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 4024554
zbMATH Keywords: Fisher information
zbMATH Keywords: quantal response bioassay
zbMATH Keywords: attribute life testing
zbMATH Keywords: dilution assay models
zbMATH Keywords: estimates of the shift parameter
zbMATH Keywords: median effective dose
zbMATH Keywords: adaptive Bayesian
zbMATH Keywords: Polya densities of order 2
zbMATH Keywords: rectangular densities
zbMATH Keywords: expected Fisher information
zbMATH Keywords: optimal Bayesian estimates
zbMATH Keywords: prior distributions
zbMATH Keywords: two stage design set up
zbMATH Keywords: logit model
zbMATH Keywords: tables
zbMATH Keywords: uniform prior
zbMATH Keywords: logistic prior
author: M. K. Khan
MaRDI profile type: Publication
full work available at URL: 0378-3758(88)90017-1
OpenAlex ID: W2064274850
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description: scientific article; zbMATH DE number 4024554