Award Date

May 2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Chih-Hsiang Ho

Second Committee Member

Amei Amei

Third Committee Member

Malwane Ananda

Fourth Committee Member

Kaushik Ghosh

Fifth Committee Member

Guogen Shan

Number of Pages

271

Abstract

Point processes often serve as a natural language to chronicle an event's temporal evolution, and significant changes in the flow, synonymous with non-stationarity, are usually triggered by assignable and frequently preventable causes, often heralding devastating ramifications. Examples include amplified restlessness of a volcano, increased frequencies of airplane crashes, hurricanes, mining mishaps, among others. Guessing these time points of changes, therefore, merits utmost care. Switching the way time traditionally propagates, we posit a new genre of bidirectional tests which, despite a frugal construct, prove to be exceedingly efficient in culling out non-stationarity under a wide spectrum of environments. A journey surveying a lavish class of intensities, ranging from the tralatitious power laws to the deucedly germane rough steps, tracks the established unidirectional forward and backward test's evolution into a p-value induced dual bidirectional test, the best member of the proffered category. Niched within a hospitable Poissonian framework, this dissertation, through a prudent harnessing of the bidirectional category's classification prowess, incites a refreshing alternative to estimating changes plaguing a soporific flow, by conducting a sequence of tests. Validation tools, predominantly graphical, rid the structure of forbidding technicalities, aggrandizing the swath of applicability. Extensive simulations, conducted especially under hostile premises of hard non-stationarity detection, document minimal estimation error and reveal the algorithm's obstinate versatility at its most unerring.

Keywords

bi-directional tests; change point identification; empirical recurrence rates and ratios; point processes; repairable systems; step intensities

Disciplines

Industrial Engineering | Industrial Technology | Mathematics | Statistics and Probability

Language

English


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