Assuming a set of variates are independent and normally distributed is commonplace in statistics. In this thesis, we consider the consequences of these assumptions as they pertain to global sensitivity analysis. We begin by illustrating how the notion of sensitivity becomes distorted in the presence of codependent model inputs. This observation motivates us to develop a new methodology which accommodates for input codependencies. Our methodology can be summarized through three points: First, a new form of sensitivity is presented which performs as well as the classical form but can be obtained at a fraction of the computational cost. Second, we define a measure which quantifies the extent of distortion caused by codependent inputs. The third point is regarding the modelling of said codependencies. The multivariate normal distribution is a natural choice for modelling codependent inputs; however, our methodology uses a copula-based approach instead. Copulas are a contemporary strategy for constructing multivariate distributions whereby the marginal and joint behaviours are treated separately. As a result, a practitioner has more flexibility when modelling inputs. / Thesis (Master, Chemical Engineering) -- Queen's University, 2013-12-05 10:16:26.81

by Man-lai Tang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Chapter PART I ： --- ANALYSIS OF DATA WITH POLYTOMOUS VARIABLES --- p.1 / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the Model with Incomplete Data --- p.5 / Chapter §2.1 --- The Model --- p.5 / Chapter §2.2 --- Two-stage Estimation Method --- p.7 / Chapter Chapter 3 --- Generalization to Several Populations --- p.16 / Chapter §3.1 --- The Model --- p.16 / Chapter §3.2 --- Two-stage Estimation Method --- p.18 / Chapter Chapter 4 --- Computation of the Estimates --- p.23 / Chapter §4.1 --- Maximum Likelihood Estimates in Stage I --- p.23 / Chapter §4.2 --- Generalized Least Squares Estimates in Stage II --- p.27 / Chapter §4.3 --- Approximation for the weight matrix W --- p.28 / Chapter Chapter 5 --- Some Illustrative Examples --- p.31 / Chapter §5.1 --- Single Population --- p.31 / Chapter §5.2 --- Multisample --- p.37 / Chapter PART II ： --- ANALYSIS OF CONTINUOUS AND POLYTOMOUS VARIABLES --- p.42 / Chapter Chapter 6 --- Introduction --- p.42 / Chapter Chapter 7 --- Several Populations Structural Equation Models with Continuous and Polytomous Variables --- p.44 / Chapter §7.1 --- The Model --- p.44 / Chapter §7.2 --- Analysis of the Model --- p.45 / Chapter Chapter 8 --- Analysis of Structural Equation Models of Polytomous and Continuous Variables with Incomplete Data by Multisample Technique --- p.54 / Chapter §8.1 --- Motivation --- p.54 / Chapter §8.2 --- The Model --- p.55 / Chapter §8.3 --- The Method --- p.56 / Chapter Chapter 9 --- Computation of the Estimates --- p.60 / Chapter §9.1 --- Optimization Procedure --- p.60 / Chapter §9.2 --- Derivatives --- p.61 / Chapter Chapter 10 --- Some Illustrative Examples --- p.65 / Chapter §10.1 --- Multisample Example --- p.65 / Chapter §10.2 --- Incomplete Data Example --- p.67 / Chapter §10.3 --- The LISREL Program --- p.69 / Chapter Chapter 11 --- Conclusion --- p.71 / Tables --- p.73 / Appendix --- p.85 / References --- p.89

by Terry Shing-fong Lew. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 40-42). / Chapter Chapter 1 --- Introduction --- p.Page1 / Chapter Chapter 2 --- Measures of Association for Polytomous Variables --- p.Page5 / Chapter §2.1 --- "Notations," --- p.5 / Chapter §2.2 --- "Pearson Product-moment Correlation Coefficient," --- p.6 / Chapter §2.3 --- "Spearman Rank Correlation Coefficient," --- p.7 / Chapter §2.4 --- "Kendall's Tau-b," --- p.9 / Chapter §2.5 --- "Polychoric Correlation Coefficient," --- p.9 / Chapter Chapter 3 --- Monte Carlo Study of Measures of Association for Polytomous Variables with Multivariate Normal Distribution --- p.Page 13 / Chapter §3.1 --- "Design," --- p.13 / Chapter §3.2 --- "Results and Findings," --- p.18 / Chapter §3.3 --- "Discussion," --- p.23 / Chapter §3.4 --- "Implications," --- p.26 / Chapter Chapter 4 --- Monte Carlo Studies for Polytomous Variables with Non-normal Distribution --- p.Page 27 / Chapter §4.1 --- "Elliptica1-t Distribution," --- p.27 / Chapter §4.2 --- "Design," --- p.28 / Chapter §4.3 --- "Results and Findings," --- p.30 / Chapter §4.4 --- "Discussion," --- p.33 / Chapter §4.5 --- "Implications," --- p.34 / Chapter Chapter 5 --- Conclusion --- p.Page36 / References --- p.Page40 / Figures --- p.Page43 / Tables --- p.Page51

by King-hong Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 110-111). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Prediction Problem of Factor Scores --- p.5 / Chapter 2.1 --- The Basic Model --- p.5 / Chapter 2.2 --- Regression Formula in Predicting Factor Scores --- p.7 / Chapter 2.3 --- The Model with Polytomous Variables --- p.9 / Chapter Chapter 3 --- Prediction Methods of Factor Scores --- p.11 / Chapter 3.1 --- Model with Continuous and Polytomous Variables --- p.11 / Chapter 3.2 --- Model with Polytomous Variables --- p.16 / Chapter Chapter 4 --- Monte-Carlo Study --- p.20 / Chapter 4.1 --- Model with Continuous and Polytomous Variables --- p.20 / Chapter 4.1.1 --- Design of the Monte-Carlo Study --- p.20 / Chapter 4.1.2 --- Results of the Monte-Carlo Study --- p.24 / Chapter 4.2 --- Model with Polytomous Variables --- p.30 / Chapter 4.2.1 --- Design of the Monte-Carlo Study --- p.30 / Chapter 4.2.2 --- Results of the Monte-Carlo Study --- p.33 / Chapter Chapter 5 --- Summary and Conclusion --- p.38 / Tables --- p.41 / Figures --- p.56 / References --- p.110

Tang Fung Chu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 79-81). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- The Multivariate Model and Bayesian Analysis of Stochastic Prior Information --- p.4 / Chapter 2.1 --- The Model --- p.4 / Chapter 2.2 --- Identification of the Model --- p.5 / Chapter 2.3 --- Bayesian Analysis of Stochastic Prior Information --- p.8 / Chapter 2.4 --- Computational Procedure --- p.10 / Chapter 2.4.1 --- Optimization Procedures --- p.11 / Chapter 2.4.2 --- Analytical Expressions --- p.12 / Chapter Chapter 3. --- Example and Simulation Study --- p.18 / Chapter 3.1 --- Example --- p.18 / Chapter 3.2 --- Simulation Study --- p.19 / Chapter 3.2.1 --- Designs --- p.20 / Chapter 3.2.2 --- Results --- p.23 / Chapter Chapter 4. --- Conclusion --- p.26 / Tables --- p.29 / References --- p.79

Chung Chi Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 80-84). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Partition Maximum Likelihood Estimation of the General Model --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Model --- p.5 / Chapter 2.3 --- The Partition Maximum Likelihood Procedure --- p.8 / Chapter 2.3.1 --- PML estimation of pa --- p.9 / Chapter 2.3.2 --- PML estimation of pab --- p.13 / Chapter 2.3.3 --- Asymptotic properties of the first-stage PML estimates --- p.15 / Chapter 3 --- Bayesian Analysis of Stochastic Prior Information --- p.19 / Chapter 3.1 --- Introduction --- p.19 / Chapter 3.2 --- Bayesian analysis of the Model --- p.20 / Chapter 3.2.1 --- "Case 1, Γ = σ2I" --- p.21 / Chapter 3.2.2 --- Case 2，Г as diagonal matrix with different diagonal el- ements --- p.24 / Chapter 3.2.3 --- "Case 3, Г as a general positive definite matrix" --- p.26 / Chapter 4 --- Simulation Design and Numerical Example --- p.29 / Chapter 4.1 --- Simulation Design --- p.29 / Chapter 4.1.1 --- Model --- p.29 / Chapter 4.1.2 --- Methods of evaluation --- p.32 / Chapter 4.1.3 --- Data analysis --- p.33 / Chapter 4.2 --- Numerical Example --- p.34 / Chapter 4.2.1 --- Model --- p.35 / Chapter 5 --- Conclusion and Discussion --- p.42 / APPENDIX I to V --- p.44-50 / TABLES 1 to 10 --- p.51-77 / FIGURES 1 to 3 --- p.78-79 / REFERENCE --- p.80-84

by Lai-seung Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 58-59). / Abstract also in Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- The Bivariate Model and Maximum Likelihood Estimation --- p.5 / Chapter 2.1 --- The Model --- p.5 / Chapter 2.2 --- Likelihood function of the model --- p.7 / Chapter 2.3 --- Derivatives of likelihood equations --- p.8 / Chapter 2.4 --- Asymptotic properties --- p.11 / Chapter 2.5 --- Optimization procedures --- p.12 / Chapter Chapter 3. --- Generalization to Multivariate Model --- p.14 / Chapter 3.1 --- The Model --- p.14 / Chapter 3.2 --- The Partition Maximum Likelihood (PML) Estimation --- p.15 / Chapter 3.3 --- Asymptotic properties of the PML estimates --- p.19 / Chapter 3.4 --- Optimization procedures --- p.21 / Chapter Chapter 4. --- Simulation Study --- p.22 / Chapter 4.1 --- Designs --- p.22 / Chapter 4.2 --- Results --- p.26 / Chapter Chapter 5. --- Conclusion --- p.30 / Tables --- p.32 / References --- p.58

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 91-93. / by Mark Joseph Durst. / Ph.D.

Lai Kim Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 55-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Likelihood Ratio Test Statistic --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Formulation --- p.6 / Chapter 2.3 --- Likelihood Ratio Type Statistic --- p.7 / Chapter 2.4 --- Dirichlet Distribution --- p.8 / Chapter 2.5 --- Edgeworth Expansion --- p.12 / Chapter 3 --- Divided Difference --- p.15 / Chapter 3.1 --- Introduction --- p.15 / Chapter 3.2 --- Definition of Divided Difference --- p.15 / Chapter 3.3 --- Theorem --- p.17 / Chapter 3.4 --- Proof of the Theorem --- p.18 / Chapter 3.5 --- Application of Theorem --- p.19 / Chapter 4 --- Computational Results --- p.22 / Chapter 4.1 --- Introduction --- p.22 / Chapter 4.2 --- Critical Values for Moderate and Large Sample Sizes --- p.22 / Chapter 4.3 --- Critical Values for Small Sample Sizes --- p.23 / Chapter 4.3.1 --- Exact Critical Values --- p.23 / Chapter 4.3.2 --- Edgeworth Expansion Results --- p.23 / Chapter 4.3.3 --- Simulation Results --- p.23 / Chapter 4.4 --- Power --- p.24 / Chapter 5 --- Illustrative Examples --- p.29 / Chapter 5.1 --- Stanford Heart Transplant Data --- p.29 / Chapter 5.1.1 --- The Data --- p.29 / Chapter 5.1.2 --- Result --- p.31 / Chapter 5.2 --- Air Conditioning Data --- p.31 / Chapter 5.2.1 --- The Data --- p.31 / Chapter 5.2.2 --- Result --- p.32 / Chapter 5.3 --- Insulating Fluid Failure Data --- p.33 / Chapter 5.3.1 --- The Data --- p.33 / Chapter 5.3.2 --- Result --- p.33 / Chapter 6 --- Conclusion and Further Research Topic --- p.35 / Chapter 6.1 --- Conclusion --- p.35 / Chapter 6.2 --- Further Research Topic --- p.38 / Appendix A --- p.39 / Appendix B --- p.46 / Bibliography --- p.55

Thesis (Ph.D.)--University of Melbourne, Dept. of Mathematics and Statistics, 2001. / Typescript (photocopy). Includes bibliographical references (leaves 126-128).