There are very many processes in the natural and social sciences which can be represented as a set of flows of objects or people between categories of some kind. The Markov chain model has been used in the study of many of them. The basic form of the Markov chain model is, however, rarely adequate to describe social, occupational and geographical mobility processes. We shall therefore discuss a number of generalizations designed to introduce greater realism. In Chapter I we formulate and investigate a general model which results from relaxing the assumptions of sojourn-time's memorylessness and independence of origin and destination states, and of population homogeneity. The model (a mixture of semi-Markov processes) is then used in two ways. First, it provides a framework in which various special cases (which correspond to models which were used by social scientists) can be analytically compared. We pay particular attention to comparisons of rate of mobility in related versions of various models and to compatability of popular parametric forms with observed mobility patterns. Second, any result obtained for the general model can be specialized for the various cases and subcases. In Chapter II we formulate a system-model allowing interaction among individuals (components), which has been motivated by Conlisk. We define processes on this model and analyze their properties. A major effort is then devoted to establishing that when the population size becomes large, this rather complex stochastic model can be approximated by a single deterministic recursion due to Conlisk (1976). Nevertheless, we draw attention to certain aspects (particularly steady-state behavior) in which the approximation may fail. In Chapter III we address ourselves to the issue of measurement of (what we refer to as) social inheritance in intergenerational mobility processes. We distinguish between various aspects and concepts of social inheritance and outline the implications that certain "social values" may have on constructing a measure (or index). In the mathematical discussion which follows certain mechanisms for generating "families" of measures are indicated, and the properties of some particular combinations are investigated. / Business, Sauder School of / Graduate

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published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

This thesis provides a stochastic modeling tool to assist in the component selection process for Army Aviation's Condition-Based Maintenance Plus (CBM+) program. This work is in conjunction with the Operations Research Center of Excellence (ORCEN) at the United States Military Academy to assist in providing insight for the U.S. Aviation and Missile Command (AMCOM). The component selected for this thesis is the AH-64/UH-60 T701C Turbine Helicopter Engine. Data analysis of the failure data indicated that a nonhomogeneous Poisson process appropriately modeled the failure characteristics of this engine. A Microsoft Excel simulation utilizing Crystal Ball version 5.5 compares an engine monitored by CBM+ versus the traditional Legacy system of maintenance. This simulation provides information on diagnosed faults, mission aborts, repair times, false positives, and logistical implications. This simulation is generic and can be used in comparing CBM+ candidate components for future inclusion into the CBM+ program. Results suggest when considering a component for inclusion in the CBM+ program important factors to consider are even the smallest false positive rate can invalidate process, large sensor probability of detection isn't necessary for beneficial results, and by entering a component into the CBM+ the on hand component requirements can be greatly reduced. / US Army (USA) author.

by Lau Chung Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1980. / Bibliography: leaf 90.

So-Kuen Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 99-102). / Chapter Chapter One --- Preview --- p.1 / Chapter Section 1 --- Introduction --- p.1 / Chapter Section 2 --- The Life Time Distribution --- p.4 / Chapter 2.1 --- Exponential Distribution --- p.5 / Chapter 2.2 --- Gamma Distribution --- p.6 / Chapter 2.3 --- Weibull Distribution --- p.7 / Chapter 2.4 --- Lognormal Distribution --- p.10 / Chapter Section 3 --- Nonparametric Inference for Geometric Process --- p.13 / Chapter 3.1 --- Test for Geometric Process --- p.13 / Chapter 3.2 --- Nonparametric Estimation Method --- p.17 / Chapter Section 4 --- Test for Distribution --- p.20 / Chapter 4.1 --- Graphical Method --- p.20 / Chapter 4.2 --- KS-test --- p.22 / Chapter 4.3 --- x2 GOF-test --- p.27 / Chapter 4.4 --- F-test (Exponential Dist.) --- p.28 / Chapter Chapter Two --- Parametric Inference for Geometric Process --- p.29 / Chapter Chapter Three --- Simulations --- p.39 / Chapter Chapter Four --- Examples --- p.49 / Chapter Chapter Five --- Comparison and Conclusion --- p.57 / Tables and Graphs --- p.61 / References --- p.99

The thesis is devoted to non-stationary point process models as generalizations of the standard homogeneous Poisson process. The work can be divided in two parts. In the first part, we introduce a fractional non-homogeneous Poisson process (FNPP) by applying a random time change to the standard Poisson process. We characterize the FNPP by deriving its non-local governing equation. We further compute moments and covariance of the process and discuss the distribution of the arrival times. Moreover, we give both finite-dimensional and functional limit theorems for the FNPP and the corresponding fractional non-homogeneous compound Poisson process. The limit theorems are derived by using martingale methods, regular variation properties and Anscombe's theorem. Eventually, some of the limit results are verified via a Monte-Carlo simulation. In the second part, we analyze statistical point process models for durations between trades recorded in financial high-frequency trading data. We consider parameter settings for models which are non-stationary or very close to non-stationarity which is quite typical for estimated parameter sets of models fitted to financial data. Simulation, parameter estimation and in particular model selection are discussed for the following three models: a non-homogeneous normal compound Poisson process, the exponential autoregressive conditional duration model (ACD) and a Hawkes process model. In a Monte-Carlo simulation, we test the performance of the following information criteria for model selection: Akaike's information criterion, the Bayesian information criterion and the Hannan-Quinn information criterion. We are particularly interested in the relation between the rate of correct model selection and the underlying sample size. Our numerical results show that the model selection for the compound Poisson type model works best for small parameter numbers. Moreover, the results for Hawkes processes confirm the theoretical asymptotic distributions of model selection whereas for the ACD model the model selection exhibits adverse behavior in certain cases.

by Wong Yin Bun, Terence. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 99-104). / Abstract also in Chinese. / List of Figures --- p.ix / List of Tables --- p.xi / Chapter I --- Preliminary --- p.1 / Chapter 1 --- Introduction --- p.2 / Chapter 1.1 --- Thesis themes --- p.4 / Chapter 1.1.1 --- Dynamical view of landscape --- p.4 / Chapter 1.1.2 --- Bottom-up self-feedback algorithm with memory --- p.4 / Chapter 1.1.3 --- Cooperation and competition --- p.5 / Chapter 1.1.4 --- Contributions to genetic algorithms --- p.5 / Chapter 1.2 --- Thesis outline --- p.5 / Chapter 1.3 --- Contribution at a glance --- p.6 / Chapter 1.3.1 --- Problem --- p.6 / Chapter 1.3.2 --- Approach --- p.7 / Chapter 1.3.3 --- Contributions --- p.7 / Chapter 2 --- Background --- p.8 / Chapter 2.1 --- Iterative stochastic searching algorithms --- p.8 / Chapter 2.1.1 --- The algorithm --- p.8 / Chapter 2.1.2 --- Stochasticity --- p.10 / Chapter 2.2 --- Fitness landscapes and its relation to neighborhood --- p.12 / Chapter 2.2.1 --- Direct searching --- p.12 / Chapter 2.2.2 --- Exploration and exploitation --- p.12 / Chapter 2.2.3 --- Fitness landscapes --- p.13 / Chapter 2.2.4 --- Neighborhood --- p.16 / Chapter 2.3 --- Species formation methods --- p.17 / Chapter 2.3.1 --- Crowding methods --- p.17 / Chapter 2.3.2 --- Deterministic crowding --- p.18 / Chapter 2.3.3 --- Sharing method --- p.18 / Chapter 2.3.4 --- Dynamic niching --- p.19 / Chapter 2.4 --- Summary --- p.21 / Chapter II --- Probabilistic Binary Hierarchical Search --- p.22 / Chapter 3 --- The basic algorithm --- p.23 / Chapter 3.1 --- Introduction --- p.23 / Chapter 3.2 --- Search space reduction with binary hierarchy --- p.25 / Chapter 3.3 --- Search space modeling --- p.26 / Chapter 3.4 --- The information processing cycle --- p.29 / Chapter 3.4.1 --- Local searching agents --- p.29 / Chapter 3.4.2 --- Global environment --- p.30 / Chapter 3.4.3 --- Cooperative refinement and feedback --- p.33 / Chapter 3.5 --- Enhancement features --- p.34 / Chapter 3.5.1 --- Fitness scaling --- p.34 / Chapter 3.5.2 --- Elitism --- p.35 / Chapter 3.6 --- Illustration of the algorithm behavior --- p.36 / Chapter 3.6.1 --- Test problem --- p.36 / Chapter 3.6.2 --- Performance study --- p.38 / Chapter 3.6.3 --- Benchmark tests --- p.45 / Chapter 3.7 --- Discussion and analysis --- p.45 / Chapter 3.7.1 --- Hierarchy of partitions --- p.45 / Chapter 3.7.2 --- Availability of global information --- p.47 / Chapter 3.7.3 --- Adaptation --- p.47 / Chapter 3.8 --- Summary --- p.48 / Chapter III --- Cooperation and Competition --- p.50 / Chapter 4 --- High-dimensionality --- p.51 / Chapter 4.1 --- Introduction --- p.51 / Chapter 4.1.1 --- The challenge of high-dimensionality --- p.51 / Chapter 4.1.2 --- Cooperation - A solution to high-dimensionality --- p.52 / Chapter 4.2 --- Probabilistic Cooperative Binary Hierarchical Search --- p.52 / Chapter 4.2.1 --- Decoupling --- p.52 / Chapter 4.2.2 --- Cooperative fitness --- p.53 / Chapter 4.2.3 --- The cooperative model --- p.54 / Chapter 4.3 --- Empirical performance study --- p.56 / Chapter 4.3.1 --- pBHS versus pcBHS --- p.56 / Chapter 4.3.2 --- Scaling behavior of pcBHS --- p.60 / Chapter 4.3.3 --- Benchmark test --- p.62 / Chapter 4.4 --- Summary --- p.63 / Chapter 5 --- Deception --- p.65 / Chapter 5.1 --- Introduction --- p.65 / Chapter 5.1.1 --- The challenge of deceptiveness --- p.65 / Chapter 5.1.2 --- Competition: A solution to deception --- p.67 / Chapter 5.2 --- Probabilistic cooperative-competitive binary hierarchical search --- p.67 / Chapter 5.2.1 --- Overview --- p.68 / Chapter 5.2.2 --- The cooperative-competitive model --- p.68 / Chapter 5.3 --- Empirical performance study --- p.70 / Chapter 5.3.1 --- Goldberg's deceptive function --- p.70 / Chapter 5.3.2 --- "Shekel family - S5, S7, and S10" --- p.73 / Chapter 5.4 --- Summary --- p.74 / Chapter IV --- Finale --- p.78 / Chapter 6 --- A new genetic operator --- p.79 / Chapter 6.1 --- Introduction --- p.79 / Chapter 6.2 --- Variants of the integration --- p.80 / Chapter 6.2.1 --- Fixed-fraction-of-all --- p.83 / Chapter 6.2.2 --- Fixed-fraction-of-best --- p.83 / Chapter 6.2.3 --- Best-from-both --- p.84 / Chapter 6.3 --- Empricial performance study --- p.84 / Chapter 6.4 --- Summary --- p.88 / Chapter 7 --- Conclusion and Future work --- p.89 / Chapter A --- The pBHS Algorithm --- p.91 / Chapter A.1 --- Overview --- p.91 / Chapter A.2 --- Details --- p.91 / Chapter B --- Test problems --- p.96 / Bibliography --- p.99

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