Empirical Bayes Estimation of Critical Dosages Having Smallest Predictive Risk.

Abstract

An empirical Bayes procedure is developed for the estimation of critical dosages in the linear regression case. If Y = alpha + beta x + e is the basic linear model, the critical dosage is defined as xi (eta) = (eta - alpha)/beta, for beta > 0. A new type of Bayes estimator of xi(eta) is derived under the criterion of minimizing the predictive risk E < (alpha + beta xi - eta)-squared bar F sub n >. The empirical Bayes procedure provides consistant estimators of the prior parameters when a large number of independent repetitions of the experiment is available. The methodology is developed to analyze a large set of photodynamic bioassays, for the determination of critical air concentrations of benzo-soluble organic extracts. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 15, 1979
Accession Number
ADA074376

Entities

People

  • Ora Bialik
  • Shelemyahu Zacks

Organizations

  • Case Western Reserve University

Tags

DTIC Thesaurus Topics

  • Assays
  • Bayesian Networks
  • Bioassay
  • Chemical Composition
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Mathematics
  • Models
  • Normal Distribution
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Samples
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.
  • Toxicology/Environmental Toxicology