A Bayesian Approach to Bioassay.

Abstract

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)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1979
Accession Number
ADA067273

Entities

People

  • D. Basu
  • Richard Fagerstrom

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Assays
  • Asymptotic Normality
  • Bayesian Networks
  • Bioassay
  • Computations
  • Data Analysis
  • Data Science
  • Estimators
  • Information Science
  • Intervals
  • Markov Chains
  • Military Research
  • Probability
  • Random Variables
  • Random Walk
  • Statistical Inference
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.
  • Theoretical Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms