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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 T252027 Unclassified Security Classification of this page REPORT DOCUMENTATION PAGE UNCLASSIFIED la Report Security Classification 1b Restrictive Markings 2a Security Classification Authority 3 Distribution Availability of Report 2b Declassification/Downgrading Schedule Approved forpublic release; distribution is unlimited. 4 Performing Organization Report NumbeT(s) 5 Monitoring Organization Report Number(s) 6a Name of Performing Organization 6b Office Symbol 7a Name of Monitoring Organization Naval Postgraduate School (IfApplicable) Naval Postgraduate School EC 6c Address (city,stale, andZIPcode) 7b Address(city, state, andZIPcode) Monterey, CA 93943-5000 Monterey, CA 93943-5000 8a Name of Funding/Sponsoring Organization 8b Office Symbol 9 Procurement Instrument Identification Number (IfApplicable) !c Address (ciry, state, andZIPcode) 1 Source ofFunding Numbers Progn:m Element Number ProjectNo TukNo WorkUnitAccessionNo 1 1 Tmt(IncludeSecurityClassification) DETECTION OF ABRUPT CHANGES IN STATISTICAL MODELS A 12 Personal Authors) David viv 13a Type of Report 13b TimeCovered 14 Date ofReport (year, month,day) 15 Page Count Doctoral Dissertation From To 1991, June 251 16 Supplementary Notation The views expressed in this paper are those ofthe author and do not reflect the official 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. 20 Distribution/Availability of Abstract 21 Abstract Security Classificauon |X| unclassified/unlimited same as report DTICusers Unclassified 22a Name of Responsible Individual 22b Telephone(IncludeAreacode) 22c Office Symbol R. C. Cristi (408) 646-2223 ecvcx DDFORM 1473, 84 MAR 83 APR edition may be used until exhausted security classificauon of this page All other editions are obsolete Unclassified i 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