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Experimental Design for Bayesian Estimations in the Linear Regression Model Taking Costs into Account
Author(s) -
Tuchscherer A.
Publication year - 1983
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.19830250602
Subject(s) - optimal design , proper linear model , a priori and a posteriori , mathematics , bayesian probability , mathematical optimization , linear regression , linear model , regression analysis , regression , function (biology) , simple (philosophy) , bayesian linear regression , statistics , computer science , algorithm , polynomial regression , bayesian inference , philosophy , epistemology , evolutionary biology , biology
It is assumed that a known, correct, linear regression model (model I) is given. Let the problem be based on a Bayesian estimation of the regression parameter so that any available a priori information regarding this parameter can be used. This Bayesian estimation is, squared loss, an optimal strategy for the overall problem, which is divided into an estimation and a design problem. For practical reasons, the effort involved in performing the experiment will be taken into account as costs. In other words, the experimental design must result in the greatest possible accuracy for a given total cost (restriction of the sample size n ). The linear cost function k ( x ) = 1 + c ( x ‐ a )/( b ‐ a ) is used to construct costoptimal experimental designs for simple linear regression by means of V = H = [ a, b ] in a way similar to that used for classical optimality criteria. The complicated structures of these designs and the difficulty in determining them by a direct approach have made it appear advisable to describe an iterative procedure for the construction of cost‐optimal designs.