by Kwan-Moon Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 77-79. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of the Model with Some Polytomous Entries Missed --- p.5 / Chapter §2.1 --- The Model --- p.5 / Chapter §2.2 --- Full Maximum Likelihood (FML) Estimation --- p.7 / Chapter Chapter 3 --- Estimation of the Model with Some Continuous and Polytomous Entries Missed --- p.13 / Chapter §3.1 --- The Model --- p.13 / Chapter §3.2 --- Pseudo Maximum Likelihood (PsML) Estimation --- p.15 / Chapter Chapter 4 --- Indirect Methods --- p.19 / Chapter §4.1 --- Listwise Deletion Method --- p.19 / Chapter §4.2 --- Mean Imputation Method --- p.19 / Chapter §4.3 --- Regression Imputation Method --- p.20 / Chapter Chapter 5 --- Computation of the Estimates --- p.23 / Chapter §5.1 --- Optimization Procedure --- p.23 / Chapter §5.2 --- Starting Value and Gradient Vector of the Model with Some Polytomous Entries Missed --- p.25 / Chapter §5.3 --- Starting Value and Gradient Vector of the Model with Some Continuous and Polytomous Entries Missed --- p.29 / Chapter Chapter 6 --- Partition Maximum Likelihood (PML) Estimation --- p.35 / Chapter §6.1 --- Motivation --- p.35 / Chapter §6.2 --- PML Procedure of the Model with Some Polytomous Entries Missed --- p.35 / Chapter §6.3 --- PML Procedure of the Model with Some Continuous and Polytomous Entries Missed --- p.37 / Chapter Chapter 7 --- Simulation Studies and Comparison --- p.39 / Chapter §7.1 --- Simulation Study I --- p.39 / Chapter §7.2 --- Simulation Study II --- p.44 / Chapter Chapter 8 --- Summary and Discussion --- p.43 / Tables / Appendix / References

by Lai Siu Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 50-52.

by Chung Sai Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 53-56). / SUMMARY / Chapter 1. --- Introduction --- p.1 / "Functional, Structural and Ultrastructural Relationships" --- p.2 / Identifiability --- p.4 / Non-normally Distributed Regressor --- p.5 / Chapter 2. --- Underlying Non-normality --- p.7 / Beta Regressor and Guassian Errors --- p.8 / Moments --- p.14 / Moment Generating Function & Characteristic Function --- p.17 / Modality --- p.18 / Distribution Portfolio --- p.21 / Chapter 3. --- Modified Maximum Likelihood Estimation --- p.24 / Consistency --- p.26 / Asymptotically Normality --- p.30 / Efficiency of the MMLE --- p.34 / Chapter 4. --- Monte Carlo Simulation Studies --- p.36 / The Use of MMLE --- p.36 / Third Order Moment Estimator with Asymptotically Minimal Variance --- p.42 / Robustness --- p.46 / Chapter 5. --- Discussions and Conclusions --- p.48 / Other Alternatives --- p.48 / Semiparametric and Nonparametric Maximum Likelihood Estimation --- p.51 / References --- p.53

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

Wong Kwan-to. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 50-52). / Abstracts in English and Chinese. / ACKNOWLEDGMENT --- p.iii / CHAPTER / Chapter ONE --- INTRODUCTION AND LITERATURE REVIEW --- p.1 / Chapter TWO --- THE MODEL --- p.3 / Chapter THREE --- ASYMPTOTIC BEHAVIOR OF THE LEAST SQUARES ESTIMATORS --- p.6 / Chapter FOUR --- EIGHT SPECIAL CASES --- p.12 / Chapter FIVE --- MONTE CARLO EXPERIMENTS --- p.36 / Chapter SIX --- CONCLUSION --- p.40 / APPENDIX --- p.41 / BIBLIOGRAPHY --- p.50

by Mannon Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 42-47). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Maximum Likelihood Estimations of Polyserial Correlations --- p.7 / Chapter 3 --- Normal Curvature and the Conformal Normal Curvature of Lo- cal Influence --- p.12 / Chapter 3.1 --- Normal Curvature --- p.14 / Chapter 3.2 --- Conformal Normal Curvature as an Influential Measure --- p.16 / Chapter 4 --- Influential Observations in the Estimations of Polyserial Corre- lations and the Thresholds --- p.18 / Chapter 4.1 --- Case-weights perturbation --- p.18 / Chapter 4.2 --- "Observations Influencing the Estimates of = (μ, Σ, ε，T)" --- p.20 / Chapter 4.3 --- "Observations Influencing the Estimates of θ1 = （(μ, Σ)" --- p.25 / Chapter 4.4 --- Observations Influencing the Estimates of θ2 = （(ε，T) --- p.27 / Chapter 5 --- Examples --- p.28 / Chapter 5.1 --- Cox's Data --- p.28 / Chapter 5.2 --- Aids Data --- p.32 / Chapter 5.3 --- Simulation Data --- p.35 / Chapter 6 --- Discussion --- p.38 / Chapter 7 --- References --- p.42 / Chapter A --- Appendix I --- p.48 / Chapter B --- Appendix II --- p.50 / Chapter C --- Appendix III --- p.73

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

by Chun-Wai Sit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 91-92). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Ridge Regression --- p.3 / Chapter 1.2 --- Generalized Ridge Regression and Present Work --- p.11 / Chapter Chapter 2 --- Shrinkage Estimation of Regression Coefficients --- p.14 / Chapter 2.1 --- Introduction --- p.15 / Chapter 2.2 --- Dominance over the Least Squares Estimator --- p.17 / Chapter 2.3 --- Dominance over the Ridge Estimator --- p.26 / Chapter 2.4 --- Bayesian Motivation --- p.31 / Chapter 2.5 --- Choosing the Shrinkage Factor --- p.33 / Chapter 2.5.1 --- Generalized Cross-Validation (GCV) --- p.34 / Chapter 2.5.2 --- RIDGM --- p.35 / Chapter 2.5.3 --- Iterative method for selecting the optimum parameter (IA) --- p.38 / Chapter 2.5.4 --- Empirical Bayes Approach --- p.45 / Chapter Chapter 3 --- Simulation Study --- p.47 / Chapter 3.1 --- Simulation Plan --- p.48 / Chapter 3.2 --- Simulation Result --- p.54 / Chapter 3.2.1 --- β = βL --- p.55 / Chapter 3.2.2 --- β = βs --- p.61 / Chapter 3.3 --- Average k and a --- p.67 / Chapter 3.3.1 --- Shrinkage Estimator --- p.67 / Chapter 3.3.2 --- Ridge Estimator --- p.78 / Chapter 3.4 --- Conclusion --- p.88 / References --- p.91

This thesis is concerned with the solutions to several issues, including the problems of joint localisation, motion de-noising/smoothing, and soft tissue artefacts correction, in skeletal motion reconstruction for motion analysis, using marker-based optical motion capture technologies. We propose a very efficient joint localisation method, which only needs to optimise over three parameters, regardless of the total numbers of markers and frames. A framework powered by this joint localisation solution is also developed, which can automatically find all the joints in an articulated body structure, and significantly reduce the total number of markers needed in a typical motion capture session, by implementing a solvability propagation process. This framework is also configured to operate in a hybrid scheme, which can automatically switch between the primary joint estimator and a slower solution having fewer conditions regarding the required number of markers on a given body segment. This makes the framework workable even for extreme scenarios in which there are fewer than three markers on any body segment. A non-linear optimisation method for 3D trajectory smoothing is also proposed for de-noising the estimated joint paths. By immobilising a series of characteristic points in the trajectory, this method is able to effectively preserve detailed information for vigorous motion sequences. Various other smoothing techniques in the literature are also discussed and compared, concluding that a size-3 weighted average filter implemented in an automatic manner is a good real-time solution for low intensity activities. The effects of skin deformation on marker position data, known as soft tissue artefacts, are learned via a behavioural study on the human upper-body, with specific emphasis on combined limb actions. Based on the experimental findings, mathematical models are proposed to characterise the development of different types of artefacts, including translational, rotational, and transverse. We also theoretically demonstrate the feasibility of using a Kalman filter to correct the soft tissue artefacts, using the mathematical models.

This thesis presents several aspects of simulation-based point estimation in the context of Bayesian decision theory. The first part of the thesis (Chapters 4 - 5) concerns the estimation-then-minimisation (ETM) method as an efficient computational approach to compute simulation-based Bayes estimates. We are interested in applying the ETM method to compute Bayes estimates under some non-standard loss functions. However, for some loss functions, the ETM method cannot be implemented straightforwardly. We examine the ETM method via Taylor approximations and cubic spline interpolations for Bayes estimates in one dimension. In two dimensions, we implement the ETM method via bicubic interpolation. The second part of the thesis (Chapter 6) concentrates on the analysis of a mixture posterior distribution with a known number of components using the Markov chain Monte Carlo (MCMC) output. We aim for Bayesian point estimation related to a label invariant loss function which allows us to estimate the parameters in the mixture posterior distribution without dealing with label switching. We also investigate uncertainty of the point estimates which is presented by the uncertainty bound and the crude uncertainty bound of the expected loss evaluated at the point estimates based on MCMC samples. The crude uncertainty bound is relatively cheap, but it seems to be unreliable. On the other hand, the uncertainty bound which is approximated a 95% confidence interval seems to be reliable, but are very computationally expensive. The third part of the thesis (Chapter 7), we propose a possible alternative way to present the uncertainty for Bayesian point estimates. We adopt the idea of leaving out observations from the jackknife method to compute jackknife-Bayes estimates. We then use the jackknife-Bayes estimates to visualise the uncertainty of Bayes estimates. Further investigation is required to improve the method and some suggestions are made to maximise the efficiency of this approach.