Abstract/Details

Statistical monitoring and cluster detection under naturally occurring heterogeneous dichotomous events


2011 2011

Other formats: Order a copy

Abstract (summary)

Many processes produce a count statistic that is a sum of multiple non-homogeneous dichotomous random variables, that is, with different values of the Bernoulli parameter p. The probability distribution of this count statistic is the convolution of J non-identical binomial distributions and can significantly differ from its binomial and normal counterparts. In such cases the homogeneity assumption can result in incorrect probability calculations and conclusions from statistical procedures such as control charts, sequential probability ratio tests, and cluster detection via scan statistics. Use of the exact (J-binomial) distribution, however, can require prohibitively exhausting calculations as the number (J) of non-identical binomial random variables in the convolution increases.

Following the above motivations, this dissertation has three foci: The first is testing and monitoring heterogeneous processes over time. Risk-adjusted sequential probability ratio tests (SPRTs) and resetting SPRT charts are derived, their accuracy and detection performances (average run lengths and operating characteristic curves) are compared to those assuming homogeneity, and shown to be significantly better in some applications.

The second focus area is detection of geographical clusters via scan statistics in the presence of natural heterogeneity. Two risk-adjusted models of Kulldorff's Bernoulli scan statistic, based on the product of risk-adjusted probabilities (J-Bernoulli model) and the distribution of heterogeneity (J-binomial model) are developed and their comparative performance versus the conventional method is explored.

Monte Carlo performance analyses show that the risk-adjusted models lead to better inferences, detection times, and probabilities over a variety of scenarios provide insights for the selection and use of correct methodologies under the occurrence of heterogeneous dichotomous events.

The third problem addresses computation issues of J-binomial distributions. Computing these probabilities is important in many applications, especially since the above mentioned methods each require tens to thousands of J-binomial probability calculations. The accuracy of J-binomial probability estimations via a cumulant based expansion that use orthogonal polynomials and saddle point approximations is explored by comparison to both exact and Monte Carlo estimations (MCE) of probabilities. A normalized Gram-Charlier expansion (NGCE) and saddle point approximations are shown to produce the most accurate results and to be more time-efficient than computing the exact probabilities or the MCE. The NGCE algorithm is practical, known to produce an estimate under all scenarios, and of great value to analysts since it easily can be integrated into computer codes.

Indexing (details)


Subject
Statistics;
Industrial engineering
Classification
0463: Statistics
0546: Industrial engineering
Identifier / keyword
Applied sciences; Pure sciences; Cluster detection; Dichotomous events; Naturally occurring events; Statistical monitoring
Title
Statistical monitoring and cluster detection under naturally occurring heterogeneous dichotomous events
Author
Taseli, Aysun
Number of pages
155
Publication year
2011
Degree date
2011
School code
0160
Source
DAI-B 72/04, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781124497150
Advisor
Benneyan, James
Committee member
Fard, Nasser; Gutmann, Samuel
University/institution
Northeastern University
Department
Mechanical and Industrial Engineering
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3443837
ProQuest document ID
856123571
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/856123571
Access the complete full text

You can get the full text of this document if it is part of your institution's ProQuest subscription.

Try one of the following:

  • Connect to ProQuest through your library network and search for the document from there.
  • Request the document from your library.
  • Go to the ProQuest login page and enter a ProQuest or My Research username / password.