Detection of abrupt changes in statistical models.

260 Pages·3.9 MB·en_US

by  Aviv, David.;Therrien, Charles W.;Cristi, Roberto.

NAVAL POSTGRADUATE SCHOOL
Monterey, California
DISSERTATION
5
TtfESI
DETECTION OF ABRUPT CHANGES IN STATISTICAL MODELS
by
David ^viy,
June, 1991
Dissertation Supervisors: R. Cristi
C. W. Therrien
Approved for public release; distribution is unlimited
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12 Personal Authors) David viv
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Doctoral Dissertation From To 1991, June 251
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policy orposition of the Department ofDefense or the U.S. Government.
17 Cosati Codes 18 SubjectTerms (continue on reverse ifnecessary and identify by block number)
Field Group Subgroup Sequential tests; disorder, abruptchanges; cumulative sum tests (cumsum);
Page; Lorden; Wald; diffusion processes
19 Abstract (continue on reverse ifnecessary and identify by block number
This dissertation investigates different types ofdisorder problems by using sequential procedures foron-line
implementation. The problem is considered within the framework ofdetecting abrupt changes in an observed
random process when the disorder can occur at unknown times. The focus of this work is on quickest detection
methods for cumsum procedures implemented fordifferent parametric and nonparametric nonlinearities and their
performance evaluation. Both the non-Bayesian (Maximum-Likelihood) and the Bayesian frameworks are
presented but the focus is mainly on non-Bayesian methods for which detailed analysis is provided. The use of
Brownian motion approximations is also included and provides an additional viewpoint ofanalyzing the
performance for both the non-Bayesian and Bayesian methods.
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Approved forpublic release; distribution is unlimited
Detection of Abrupt Changes in Statistical Models
by
David Aviv
Major, Israeli Air Force
B.S., Ben Gurion University, 1981
M.S., Tel-Aviv University, 1987
Submitted in partial fulfillmentofthe
requirements for the degree of
DOCTOR OF PHILOSOPHY IN ELECTRICALENGINEERING
From the
NAVALPOSTGRADUATE SCHOOL
June 1991
ABSTRACT
This dissertation investigates different types of disorder problems by
using sequential procedures for on-line implementation. The problem is
considered within the framework of detecting abrupt changes in an observed
random process when the disorder can occur at unknown times. The focus of
this work is on quickest detection methods for cumsum procedures
implemented for different parametric and nonparametric nonlinearities and
their performance evaluation. Both the non-Bayesian (Maximum-
Likelihood) and the Bayesian frameworks are presented but the focus is
mainly on non-Bayesian methods for which detailed analysis is provided.
The use of Brownian motion approximations is also included and provides
an additional viewpoint of analyzing the performance for both the non-
Bayesian and Bayesian methods.
in
AW
CI-
TABLE OF CONTENTS
THE DISORDER AND CHANGE DETECTION PROBLEM
L
FORMULATION—AN OVERVIEW
1
INTRODUCTION
A. 1
B. THE DISORDER PROBLEM FORMULATION 3
1. The General Disorder Problem 3
2. Solution Methods 6
3. Performance Evaluation 13
C MODEL BASED METHODS
13
1. Generating the Change Indication Signals (Residuals) 15
2. Statistical Testing (stopping rules) 18
D. ORGANIZATION OF THE DISSERTATION 24
SEQUENTIAL METHODS FOR QUICKEST DETECTION OF
IL
CHANGES IN PROBABILITY: THE NON-BAYESIAN
FRAMEWORK
26
INTRODUCTION
A. 26
1. Off-line versus On-line Viewpoints 27
2. Composite Testing 28
3. Parametric versus Non-parametric Methods 28
B. ORGANIZATION OF THIS CHAPTER 29
C. SEQUENTIAL TESTS 30
1. The Fundamental Identity (Wald's Identity) of the
Sequential Analysis 33
2. Applications of Wald's Identity 34
IV