A Bayesian Approach to Bioassay.

摘要

This article explains in general terms how some sequential bioassay methods like the stochastic approximation method or the up-and-down method are not in conformity with the likelihood principle. Irrespective of the sampling plan, the bioassay data may be analyzed in terms of the following simple prior probability model for the response probabilities. Let x'1 < x'2 < ... < x'm be the distinct dosage levels used in a bioassay experiment and let P1 < P2 < ... < pm be the corresponding unknown response probabilities. Let U1 = P1 and Ui = (Pi - P(i-1)/(1 - P(i-1), i = 2, 3, ... m. The ui's are regarded as mutually independent random variables taking values in the unit interval. The Pi's then form a Markov chain. The means and the variances of the Pi's are related to those of the ui's in a rather simple fashion. The case where ui' approx Beta(1, lambda sub i) is found to be particularly tractable for the analysis of bioassay data. (Author)