This thesis addresses the problem of combining the prior density functions, f[sub=1],…,f[subn], of n individuals. In the first of two parts, various systems of axioms are developed which characterize successively the linear opinion pool, A(f[sub=1],...,f[sub=n]) = Σ[sup=n; sub= i=1] w[sub=i] f[sub=i] , and the logarithmic opinion pool, G(f[sub=1],…,f[sub=n]) = π[sup=n; sub= i=1] f[sup=α(i); sub=i] / ʃ π[sup=n; sub= i=1] dμ. It is first shown that A is the only pooling operator, T(f[sub=1],…,f[sub=n]), which is expressible as T(f[sub=1],…,f[sub=n]) (θ) = H(f[sub=1](θ),...,f[sub=n](θ), θ) for some function H which is continuous in its first n variables and satisfies H(0,...,0,θ) = 0 for μ- almost all θ. The regularity condition on H may be dispensed with if H does not depend on θ. This result leads to an impossibility theorem involving Madansky's axiom of External Bayesianity. Other consequences of this axiom of group rationality are also examined in some detail and yield a characterization of G as the only Externally Bayesian pooling operator of the form T(f[sub=1],…,f[sub=n])(θ) = H(f[sub=1],(θ),...,f[sub=n](θ))/ ʃH(f[sub=1],…,f[sub=n])dμ for some H:(0, ∞) —>(0, ∞). To prove this n result, it is necessary to introduce a "richness" condition on the underlying space of events, (θ,μ). Next, each opinion f[sub=i] is regarded as containing some "information" about θ and we look for a pooling operator whose expected information content is a maximum. The operator so obtained depends on the definition which is chosen; for example, Kullback-Leibler's definition entails the linear opinion pool, A. In the second part of the dissertation, it is argued that the domain of pooling operators should extend beyond densities. The notion of propensity function is introduced and examples are given which motivate this generalization; these include the well-known problem of combining P-values. A theorem of Aczel is adapted to derive a large class of pooling formulas which encompasses both A and G. A final characterization of G is given via the interpretation of betting odds, and the parallel between our approach and Nash's solution to the "bargaining problem" is discussed. / Science, Faculty of / Mathematics, Department of / Graduate

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Survey is time-consuming and expensive. Therefore, it needs to be both effective and efficient. Some archaeologists have argued that current survey techniques are not effective (Shott 1985, 1989), but most archaeologists continue to employ these methods and therefore must believe they are effective. If our survey techniques are effective, why do simulations suggest otherwise? If they are ineffective, can we improve them? The answers to these practical questions depend on the topological characteristics of archaeological site distributions. In this study I analyze archaeological site distributions in the Valley of Oaxaca, Mexico, using lacunarity and fractal dimension. Fractal dimension is a parameter of fractal patterns, which are complex, space-filling designs exhibiting self-similarity and power-law scaling. Lacunarity is a statistical measure that describes the texture of a spatial dispersion. It is useful in understanding how archaeological tests should be spaced during surveys. Between these two measures, I accurately describe the regional topology and suggest new considerations for archaeological survey design. / Includes bibliography. / Thesis (M.A.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

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A new approach to structural equation modeling based on so-called extended redundancy analysis (ERA) is proposed. In ERA, latent variables are obtained as exact linear combinations of observed variables, and model parameters are estimated by consistently minimizing a single criterion. As a result, the method can avoid limitations of covariance structure analysis (e.g., stringent distributional assumptions, improper solutions, and factor score indeterminacy) in addition to those of partial least squares (e.g., the lack of a global optimization procedure). The method is simple yet versatile enough to fit more complex models; e.g., those with higher-order latent variables and direct effects of observed variables. It can also fit a model to more than one sample simultaneously. Other relevant topics are also discussed, including data transformations, missing data, metric matrices, robust estimation, and efficient estimation. Examples are given to illustrate the proposed method.

Xin-Yuan Song. / "December 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 128-142). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Wang, Chang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 139-145). / Abstracts in English and Chinese. / ABSTRACT --- p.3 / CHINESE ABSTRACT --- p.5 / ACKNOWLEDGMENTS --- p.6 / TABLE OF CONTENTS --- p.7 / LIST OF TABLES --- p.9 / LIST OF FIGURES --- p.10 / INTRODUCTION --- p.11 / Chapter 1.1 --- ISSUE OF MODEL FIT IN SEM --- p.11 / Chapter 1.2 --- CLASSIFICATION AND DEVELOPMENT OF FIT INDICES --- p.13 / Chapter 1.3 --- ORGANIZATION OF THIS THESIS --- p.18 / Chapter CHAPTER 2 --- ISSUES OF FIT INDICES IN ASSESSING MODEL FIT --- p.19 / Chapter 2.1 --- SENSITIVITY OF FIS TO MODL PARAMETER --- p.19 / Chapter 2.1.1 --- Sample size --- p.20 / Chapter 2.1.2 --- Model complexity --- p.21 / Chapter 2.1.3 --- Misspecification --- p.23 / Chapter 2.2 --- MEASUREMENT ERROR --- p.26 / Chapter 2.3 --- PERFECT FIT VS. APPROXIMATE FIT --- p.26 / Chapter 2.4 --- Minimum Fit Function chi-square vs. Normal-theory Weighted Least chi-square --- p.29 / Chapter 2.5 --- RULE OF THUMB --- p.30 / Chapter 2.6 --- FIVE RESEARCH QUESTIONS --- p.37 / Chapter CHAPTER 3 --- SIMULATION --- p.39 / Chapter 3.1 --- FIT INDICES --- p.39 / Chapter 3.2 --- DESIGN OF MONTE CARLO SIMULATIONS --- p.38 / Chapter 3.3 --- MODEL COMPLEXITY AND MODEL SPECIFICATION --- p.39 / Chapter 3.4 --- SIMULATION PROCEDURE --- p.41 / Chapter CHAPTER 4 --- RESULTS --- p.45 / Chapter 4.1 --- MEASUREMENT ERROR AND CRONBACH´ةS ALPHA --- p.45 / Chapter 4.2 --- ANSWER TO Q1 --- p.45 / Chapter 4.3 --- ANSWER TO Q2 --- p.53 / Chapter 4.4 --- ANSWER TO Q3 --- p.56 / Chapter 4.5 --- ANSWER TO Q4 --- p.60 / Chapter 4.6 --- ANSWER TO Q5 --- p.62 / Chapter CHAPTER 5 --- DUSCUSSION --- p.77 / Chapter 5.1 --- DUSCUSSION TO Q1 --- p.77 / Chapter 5.2 --- DUSCUSSION TO Q2 --- p.83 / Chapter 5.3 --- DUSCUSSION TO Q3 --- p.85 / Chapter 5.4 --- DUSCUSSION TO Q4 --- p.88 / Chapter 5.5 --- DUSCUSSION TO Q5 --- p.89 / Chapter CHAPTER 6 --- LIMITATION --- p.99 / Chapter CHAPTER 7 --- CONCLUSION --- p.101 / PREFERENCE --- p.139

The present work uses statistical mechanics tools to investigate the dynamics of markets, prices, trades and wealth distribution. We studied the evolution of market dynamics in different stages of historical development by analyzing commodity prices from two distinct periods : ancient Babylon, and medieval and early modern England. We find that the first-digit distributrions of both Babylon and England commodity prices follow Benford's Law, indicating that the data represent empirical observations typically arising from a free market. Further, we find that the normalized prices of both Babylon and England agricultural commodities are characterized by stretched exponential distributions, and exhibit persistent correlations of a power law type over long periods of up to several centuries, in contrast to contemporary markets. Our findings suggest that similar market interactions may underlie the dynamics of ancient agricultural commodity prices, and that these interactions may remain stable across centuries. To further investigate the dynamics of markets, we present the analogy between transfers of money between individuals and the transfer of energy through particle collisions by means of the kinetic theory of gases. We introduce a theoretical framework of how micro rules of trading lead to the emergence of income and wealth distribution. Particularly, we study the effects of different types of distribution of savings/investments among individuals in a society and different welfare/subsidies redistribution policies. Results show that while considering savings propensities, the models approach empirical distributions of wealth quite well. The effect of redistribution better captures specific features of the distributions which earlier models failed to do. Moreover, the models still preserve the exponential decay observed in empirical income distributions reported by tax data and surveys. / by Natalia E. Romero. / Vita. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2012. Mode of access: World Wide Web.

In this thesis we consider two comparative statics questions of changes in risk. The first question concerns situations where an individual faces some risk and has no control over the uncertain environment. In these situations we ask what kind of changes in risk will cause the individual's expected utility to increase. The second comparative statics question concerns situations where an individual faces some risk and has some control over the uncertain environment. In particular, we consider situations where the individual maximizes her expected utility with respect to some control parameter. Here we ask what kind of changes in risk will cause the individual's optimal value of the control parameter to increase. The existing literature has answered these questions for a class of individuals (for example, the class of risk averse individuals). This thesis differs from existing literature as it focuses on a given individual, and thus reveals some of the person-specific factors that affect individual?s responses to changes in risk. The aim of the thesis is to show how an order on distributions, termed single crossing likelihood ratio (SCLR) order, can intuitively answer both questions for a given individual. The main contributions of the thesis are as follows. First, the thesis presents the SCLR order and its main properties. Second, the thesis shows that the SCLR order can answer the above comparative statics questions in an intuitive way. In particular, the thesis shows that the answer to the above questions, with the use of the SCLR order, depends on a risk reference point which can be interpreted as a "certainty equivalent" point. Thus it is demonstrated that individual's responses to changes in risk are affected by her "certainty equivalent" point. Lastly, the results of the thesis can be used to provide an intuitive explanation of related existing results that were obtained for a class of individuals.

In this thesis we consider two comparative statics questions of changes in risk. The first question concerns situations where an individual faces some risk and has no control over the uncertain environment. In these situations we ask what kind of changes in risk will cause the individual's expected utility to increase. The second comparative statics question concerns situations where an individual faces some risk and has some control over the uncertain environment. In particular, we consider situations where the individual maximizes her expected utility with respect to some control parameter. Here we ask what kind of changes in risk will cause the individual's optimal value of the control parameter to increase. The existing literature has answered these questions for a class of individuals (for example, the class of risk averse individuals). This thesis differs from existing literature as it focuses on a given individual, and thus reveals some of the person-specific factors that affect individual?s responses to changes in risk. The aim of the thesis is to show how an order on distributions, termed single crossing likelihood ratio (SCLR) order, can intuitively answer both questions for a given individual. The main contributions of the thesis are as follows. First, the thesis presents the SCLR order and its main properties. Second, the thesis shows that the SCLR order can answer the above comparative statics questions in an intuitive way. In particular, the thesis shows that the answer to the above questions, with the use of the SCLR order, depends on a risk reference point which can be interpreted as a "certainty equivalent" point. Thus it is demonstrated that individual's responses to changes in risk are affected by her "certainty equivalent" point. Lastly, the results of the thesis can be used to provide an intuitive explanation of related existing results that were obtained for a class of individuals.