Phase transition in a four-dimensional random walk with application to medical statistics

O. E. Percus, Jerome Percus

Research output: Contribution to journalArticle

Abstract

A random walk in a piecewise homogeneous medium can exhibit a variety of asymptotic behaviors. In particular, it may lodge strictly in one region or divide in probability among several. This will depend upon the parameters describing (a) the walk, (b) the interregion boundary, and (c) the initial location of the walk. We analyze from this point of view a special four-dimensional walk on an integer lattice with two homogeneous regions separated by a hyperplane of codimension 1. The walk represents a continuing sequence of clinical trials of two drugs of unknown success probabilities and the two regions represent the Bayes-derived criterion as to which drug to try next. The demarcation in the parameter space of success probabilities and initial coordinates between one- and two-region asymptotics is mapped out analytically in several special cases and supporting numerical evidence given in the general case.

Original languageEnglish (US)
Pages (from-to)755-783
Number of pages29
JournalJournal of Statistical Physics
Volume30
Issue number3
DOIs
StatePublished - Mar 1983

Fingerprint

random walk
Random walk
Phase Transition
Walk
statistics
Statistics
drugs
hyperplanes
Drugs
integers
Bayes
Hyperplane
Clinical Trials
Codimension
Divides
Parameter Space
Strictly
Asymptotic Behavior
Unknown
Integer

Keywords

  • clinical trials
  • integer lattice
  • Phase transition
  • piecewise homogeneous
  • random walk

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Phase transition in a four-dimensional random walk with application to medical statistics. / Percus, O. E.; Percus, Jerome.

In: Journal of Statistical Physics, Vol. 30, No. 3, 03.1983, p. 755-783.

Research output: Contribution to journalArticle

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