Bayes Sequential Search of an Optimal Dosage: The Case When Both the Slope and the Intercept of the Regression Line are Unknown.

Abstract

The problem of determining the optimal dosage is studied for the case of normal distribution of toxicity, with a linear dosage-toxicity relationship. Both the slope and the intercept of the regression line are unknown. The sequential procedure is derived within a Bayesian framework, assigning the unknown intercept, A, and slope, B, a prior bivariate normal distribution. Most of the paper is devoted to the problem of proving the consistency of this Bayes search procedure. It is proven that a discrete version of the procedure is strongly consistent. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1972
Accession Number
AD0751083

Entities

People

  • B. H. Eichhorn
  • Shelemyahu Zacks

Organizations

  • Case Western Reserve University

Tags

DTIC Thesaurus Topics

  • Bayesian Networks
  • Consistency
  • Distribution Functions
  • Functions (Mathematics)
  • Mathematical Models
  • Mathematics
  • Normal Distribution
  • Toxicity

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • Statistical inference.

Technology Areas

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