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Typescript (photocopy). / Digitized by Kansas Correctional Industries

The first purpose of this thesis is to provide a framework for the inclusion of data from a secondary source in Bayesian decision analysis as an aid in decision making under uncertainty. A second purpose is to show that the Bayesian procedures can be implemented on a computer to obtain accurate results at little expense in computing time. The state variables of a bridge design example problem are the unknown parameters of the probability distribution of the primary data. The primary source is the annual peak flow data for the stream being spanned. Information pertinent to the choice of bridge design is contained in rainfall data from gauges on the watershed but the distribution of this secondary data cannot be directly expressed in terms of the state variables. This study shows that a linear regression equation relating the primary and secondary data provides a means of using secondary data for finding the Bayes risk and expected opportunity loss associated with any particular bridge design and single new rainfall observation. The numerical results for the example problem indicate that the information gained from the rainfall data reduces the Bayes risk and expected opportunity loss and allows for a more economical structural design. Furthermore, the careful choice of the numerical methods employed reduces the computation time for these quantities to a level acceptable to any budget.

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Humans need to rapidly select movements that achieve their goal while avoiding negative outcomes. The processes leading to these decisions have only recently been studied. In the typical paradigm used to gain insight into the decision process, participants aim to a target circle that is overlapped by a penalty circle. They receive 100 points for hitting the target, and lose points for hitting the penalty region. Previous research has shown that participants generally behave like a rational decision maker by adapting their endpoint when the distance between the target and penalty circle and the penalty value changes (although some suboptimal selection has been noted). The overall purpose of the research reported in the present thesis was to determine if there are contexts when participants’ behaviour is suboptimal in a rapid, motor decision making tasks. Taken together, the results from four studies showed that: 1) participants require experience and feedback to aim to optimal locations; 2) participants often aimed closer to target center than optimal; and, 3) probability (represented through spatial parameters) has more influence over participant’s motor decisions than does the value of the penalty. Therefore, participants’ actions do not necessarily conform to a rational model of decision making; rather, there are consistent biases arising in the selection, planning, and execution of actions in specific contexts. These findings and conclusions can lead to a more descriptive understanding of motor decision making to provide information that is in addition to prescriptive models of rational behaviour.

Humans need to rapidly select movements that achieve their goal while avoiding negative outcomes. The processes leading to these decisions have only recently been studied. In the typical paradigm used to gain insight into the decision process, participants aim to a target circle that is overlapped by a penalty circle. They receive 100 points for hitting the target, and lose points for hitting the penalty region. Previous research has shown that participants generally behave like a rational decision maker by adapting their endpoint when the distance between the target and penalty circle and the penalty value changes (although some suboptimal selection has been noted). The overall purpose of the research reported in the present thesis was to determine if there are contexts when participants’ behaviour is suboptimal in a rapid, motor decision making tasks. Taken together, the results from four studies showed that: 1) participants require experience and feedback to aim to optimal locations; 2) participants often aimed closer to target center than optimal; and, 3) probability (represented through spatial parameters) has more influence over participant’s motor decisions than does the value of the penalty. Therefore, participants’ actions do not necessarily conform to a rational model of decision making; rather, there are consistent biases arising in the selection, planning, and execution of actions in specific contexts. These findings and conclusions can lead to a more descriptive understanding of motor decision making to provide information that is in addition to prescriptive models of rational behaviour.

by Jian-Wei Chen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 84-86). / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Bayesian approach to single variable sampling plan for the exponential distribution --- p.3 / Chapter 1.3 --- Outline of the thesis --- p.7 / Chapter Chapter 2 --- Single Variable Sampling Plan With Type II Censoring / Chapter 2.1 --- Model --- p.10 / Chapter 2.2 --- Loss function and finite algorithm --- p.13 / Chapter 2.3 --- Numerical examples and sensitivity analysis --- p.17 / Chapter Chapter 3 --- Double Variable Sampling Plan With Type II Censoring / Chapter 3.1 --- Model --- p.25 / Chapter 3.2 --- Loss function and Bayes risk --- p.27 / Chapter 3.3 --- Discretization method and numerical analysis --- p.33 / Chapter Chapter 4 --- Bayesian Approach to Single Variable Sampling Plans for General Life Distribution with Type I Censoring / Chapter 4.1 --- Model --- p.42 / Chapter 4.2 --- The case of the Weibull distribution --- p.47 / Chapter 4.3 --- The case of the two-parameter exponential distribution --- p.49 / Chapter 4.4 --- The case of the gamma distribution --- p.52 / Chapter 4.5 --- Numerical examples and sensitivity analysis --- p.54 / Chapter Chapter 5 --- Discussions / Chapter 5.1 --- Comparison between Bayesian variable sampling plans and OC curve sampling plans --- p.63 / Chapter 5.2 --- Comparison between single and double sampling plans --- p.64 / Chapter 5.3 --- Comparison of both models --- p.66 / Chapter 5.4 --- Choice of parameters and coefficients --- p.66 / Appendix --- p.78 / References --- p.84

Tse Ka Ling Carol. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 72-76). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Factor Analysis Model --- p.1 / Chapter 1.2 --- Main Objectives --- p.2 / Chapter 1.2.1 --- Investigate the distribution of the estimated Factor Scores --- p.2 / Chapter 1.2.2 --- Propose an alternative method for getting the estimates of the LISREL model --- p.4 / Chapter 1.3 --- Summary --- p.4 / Chapter 2 --- Joint Bayesian Approach of the Factor Analysis Model --- p.6 / Chapter 2.1 --- Conditional Distribution --- p.7 / Chapter 2.1.1 --- Conditional distribution of Z given Y and θ --- p.7 / Chapter 2.1.2 --- Conditional distribution of θ given Y and Z --- p.7 / Chapter 2.2 --- Implementation of the Gibbs sampler for generating the random observations --- p.11 / Chapter 2.3 --- Bayesian Estimates and their Statistical Properties --- p.13 / Chapter 2.3.1 --- Estimates of unknown parameter --- p.13 / Chapter 2.3.2 --- Estimates of Factor Score --- p.14 / Chapter 3 --- Examine the distribution of the estimated factor scores --- p.15 / Chapter 3.1 --- The 1st Simulation Study --- p.15 / Chapter 3.2 --- The 2nd Simulation Study --- p.30 / Chapter 3.3 --- The 3rd Simulation Study --- p.31 / Chapter 4 --- An Alternative method for getting the parameter estimatesin the LISREL Model --- p.44 / Chapter 4.1 --- Full LISREL model --- p.44 / Chapter 4.2 --- Our proposed method --- p.46 / Chapter 4.3 --- Simulation Studies --- p.49 / Chapter 4.3.1 --- The 1st Simulation Study --- p.49 / Chapter 4.3.2 --- The 3rd Simulation Study --- p.50 / Chapter 4.4 --- Conclusion --- p.53 / Appendix --- p.56 / Bibliography --- p.72

在日常生活和科学研究中产生大量偏好数据，其反应一组被关注对象受偏好的程度。通常用排序数据或多元选择数据来记录观察结果。有时候关于两个对象的偏好没有明显强弱之分，导致排序产生节点，也就是所谓的删失排序。为了研究带有删失的排序数据，基于Thurstone的随机效用假设理论我们建立了一个对称贝叶斯probit模型。然而，参数识别是probit模型必须解决的问题，即确定一组潜在效用的位置和尺度。通常方法是选择其中一个对象为基，然后用其它对象的效用减去这个基的效用，最后我们关于这些效用差来建模。问题是，在用贝叶斯方法处理多元选择数据时，其预测结果对基的选择有敏感性，即选不同对象为基预测结果是不一样的。本文，我们虚构一个基，即一组对象偏好的平均。依靠这个基，我们为多元选择probit模型给出一个不依赖于对象标号的识别方法，即对称识别法。进一步，我们设计一种贝叶斯算法来估计这个模型。通过仿真研究和真实数据分析，我们发现这个贝叶斯probit模型被完全识别，而且消除通常识别法所存在的敏感性。接下来，我们把这个关于多元选择数据建立的probit模型推广到处理一般删失排序数据，即得到对称贝叶斯删失排序probit 模型。最后，我们用这个模型很好的分析了香港赌马数据。 / Vast amount of preference data arise from daily life or scientific research, where observations consist of preferences on a set of available objects. The observations are usually recorded by ranking data or multinomial data. Sometimes, there is not a clear preference between two objects, which will result in ranking data with ties, also called censored rank-ordered data. To study such kind of data, we develop a symmetric Bayesian probit model based on Thurstone's random utility (discriminal process) assumption. However, parameter identification is always an unavoidable problem for probit model, i.e., determining the location and scale of latent utilities. The standard identification method need to specify one of the utilities as a base, and then model the differences of the other utilities subtracted by the base. However, Bayesian predictions have been verified to be sensitive to specification of the base in the case of multinomial data. In this thesis, we set the average of the whole set of utilities as a base which is symmetric to any relabeling of objects. Based on this new base, we propose a symmetric identification approach to fully identify multinomial probit model. Furthermore, we design a Bayesian algorithm to fit that model. By simulation study and real data analysis, we find that this new probit model not only can be identifed well, but also remove sensitivities mentioned above. In what follows, we generalize this probit model to fit general censored rank-ordered data. Correspondingly, we get the symmetric Bayesian censored rank-ordered probit model. At last, we apply this model to analyze Hong Kong horse racing data successfully. / Detailed summary in vernacular field only. / Pan, Maolin. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 50-55). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.2 / Chapter 1.1.1 --- The Ranking Model --- p.2 / Chapter 1.1.2 --- Discrete Choice Model --- p.4 / Chapter 1.2 --- Methodology --- p.7 / Chapter 1.2.1 --- Data Augmentation --- p.8 / Chapter 1.2.2 --- Marginal Data Augmentation --- p.8 / Chapter 1.3 --- An Outline --- p.9 / Chapter 2 --- Bayesian Multinomial Probit Model Based On Symmetric I-denti cation --- p.11 / Chapter 2.1 --- Introduction --- p.11 / Chapter 2.2 --- The MNP Model --- p.14 / Chapter 2.3 --- Symmetric Identification and Bayesian Analysis --- p.17 / Chapter 2.3.1 --- Symmetric Identification --- p.18 / Chapter 2.3.2 --- Bayesian Analysis --- p.21 / Chapter 2.4 --- Case Studies --- p.25 / Chapter 2.4.1 --- Simulation Study --- p.25 / Chapter 2.4.2 --- Clothes Detergent Purchases Data --- p.27 / Chapter 2.5 --- Summary --- p.29 / Chapter 3 --- Symmetric Bayesian Censored Rank-Ordered Probit Model --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- Ranking Model --- p.33 / Chapter 3.2.1 --- Ranking Data --- p.33 / Chapter 3.2.2 --- Censored Rank-Ordered Probit Model --- p.35 / Chapter 3.2.3 --- Symmetrically Identified CROP Model --- p.36 / Chapter 3.3 --- Bayesian Analysis on Symmetrically Identified CROP Model --- p.37 / Chapter 3.3.1 --- Model Estimation --- p.38 / Chapter 3.4 --- Application: Hong Kong Horse Racing --- p.41 / Chapter 3.5 --- Summary --- p.44 / Chapter 4 --- Conclusion and Further Studies --- p.45 / Chapter A --- Prior for covariance matrix with trace augmented restriction --- p.47 / Chapter B --- Derivation of sampling intervals --- p.49 / Bibliography --- p.50

We propose an axiomatization of the Choquet integral model for the general case of a heterogeneous product set X = X1 Xn. Previous characterizations of the Choquet integral have been given for the particular cases X = Y n and X = Rn. However, this makes the results inapplicable to problems in many fields of decision theory, such as multicriteria decision analysis (MCDA), state-dependent utility (SD-DUU), and social choice. For example, in multicriteria decision analysis the elements of X are interpreted as alternatives, characterized by criteria taking values from the sets Xi. Obviously, the identicalness or even commensurateness of criteria cannot be assumed a priori. Despite this theoretical gap, the Choquet integral model is quite popular in the MCDA community and is widely used in applied and theoretical works. In fact, the absence of a sufficiently general axiomatic treatment of the Choquet integral has been recognized several times in the decision-theoretic literature. In our work we aim to provide missing results { we construct the axiomatization based on a novel axiomatic system and study its uniqueness properties. Also, we extend our construction to various particular cases of the Choquet integral and analyse the constraints of the earlier characterizations. Finally, we discuss in detail the implications of our results for the applications of the Choquet integral as a model of decision making.