Boundary Crossing Probabilities and Statistical Applications.

Abstract

This paper surveys recent results involving boundary crossing probabilities and related statistical applications. The first part is concerned with problems of sequential analysis, especially repeated significance tests and their application to sequential clinical trials involving survival data. The second part develops the probability theory motivated by the problems of Part 1. A method for computing first passage distributions of Brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries. The third part is concerned with fixed sample statistical problems, especially change-point problems, which involve boundary crossing probabilities. Examples are given of problems for which methods of Part 2 appear adequate and of problems which require new methods.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1985
Accession Number
ADA151027

Entities

People

  • David Siegmund

Organizations

  • Stanford University

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Clinical Trials
  • Computations
  • Data Science
  • Distribution Functions
  • Information Science
  • Normal Distribution
  • Probability
  • Random Variables
  • Random Walk
  • Sampling
  • Sequential Analysis
  • Statistical Algorithms
  • Statistics
  • Stochastic Processes
  • Surveys
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Statistical inference.