過去國內之抵押貸款提前清償與逾期還款之相關研究，在實證研究上最主要利用邏輯斯迴歸或是比例轉機模型( Proportional hazard model )分析影響一般住宅抵押貸款人提前清償與逾期還款之因素，並估計一般住宅抵押貸款人提前清償之機率。本文選擇採用研究抵押貸款時，國內未曾使用之卜瓦松迴歸( Poisson regression model )來估計比例轉機模型假設下影響提前清償與違約變數之參數，以研究影響抵押貸款借款人之提前償還與違約因素。 本研究結合比例轉機模型與卜瓦松迴歸模型，目的在結合兩模型之優點，在處理時間相依之共變數效率提高，並且在處理多重時間尺度的方程式較偏最大概似估計法直接，以得到較佳的研究成果。另外，過去國內提前清償與違約之文獻中並未加入利率走勢之變數，本研究加入再融資利率對31∼90天期商業本票利率之比率與再融資利率波動性兩變數，以考慮利率走勢對貸款者提前清償及違約行為之影響。 模型中的解釋變數包括地區、季節、抵押貸款年齡、貸款成數、貸款人年齡、性別、婚姻狀況、教育程度、職業、屋齡、房屋坪數、所得、貸款金額、月付額對薪資比、再融資利率/31∼90天期商業本票利率、再融資利率波動性等十六項。實證結果在提前清償部份，顯著正向之變數有貸款年齡、屋齡、房屋坪數、所得、月付額與薪資比，顯著負向之變數包括季節、再融資利率對31∼90天期商業本票利率之比率、貸款金額。在違約部份，顯著正向之變數包括貸款年齡、貸款成數、年齡、所得、月付額與薪資比、再融資利率對31∼90天期商業本票利率之比率；顯著負向之變數包括季節、教育程度及貸款金額。

The mechanisms that control growth processes in biology tissues have attracted continuous research interest despite their complexity. With the emergence of big data experimental approaches there is an urgent need to develop statistical and computational models to fit the experimental data and that can be used to make predictions to guide future research. In this work we apply statistical methods on growth process of different biological tissues, focusing on development of neuron dendrites and tumor cells. We first examine the neuron cell growth process, which has implications in neural tissue regenerations, by using a computational model with uniform branching probability and a maximum overall length constraint. One crucial outcome is that we can relate the parameter fits from our model to real data from our experimental collaborators, in order to examine the usefulness of our model under different biological conditions. Our methods can now directly compare branching probabilities of different experimental conditions and provide confidence intervals for these population-level measures. In addition, we have obtained analytical results that show that the underlying probability distribution for this process follows a geometrical progression increase at nearby distances and an approximately geometrical series decrease for far away regions, which can be used to estimate the spatial location of the maximum of the probability distribution. This result is important, since we would expect maximum number of dendrites in this region; this estimate is related to the probability of success for finding a neural target at that distance during a blind search. We then examined tumor growth processes which have similar evolutional evolution in the sense that they have an initial rapid growth that eventually becomes limited by the resource constraint. For the tumor cells evolution, we found an exponential growth model best describes the experimental data, based on the accuracy and robustness of models. Furthermore, we incorporated this growth rate model into logistic regression models that predict the growth rate of each patient with biomarkers; this formulation can be very useful for clinical trials. Overall, this study aimed to assess the molecular and clinic pathological determinants of breast cancer (BC) growth rate in vivo.

Selection of signi?cant genes via expression patterns is important in a microarray problem. Owing to small sample size and large number of variables (genes), the selection process can be unstable. This research proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables in a regression setting and use a Bayesian mixture prior to perform the variable selection. Due to the binary nature of the data, the posterior distributions of the parameters are not in explicit form, and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the posterior distributions. The Bayesian model is ?exible enough to identify the signi?cant genes as well as to perform future predictions. The method is applied to cancer classi?cation via cDNA microarrays. In particular, the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify the set of signi?cant genes to classify BRCA1 and others. Microarray data can also be applied to survival models. We address the issue of how to reduce the dimension in building model by selecting signi?cant genes as well as assessing the estimated survival curves. Additionally, we consider the wellknown Weibull regression and semiparametric proportional hazards (PH) models for survival analysis. With microarray data, we need to consider the case where the number of covariates p exceeds the number of samples n. Speci?cally, for a given vector of response values, which are times to event (death or censored times) and p gene expressions (covariates), we address the issue of how to reduce the dimension by selecting the responsible genes, which are controlling the survival time. This approach enables us to estimate the survival curve when n << p. In our approach, rather than ?xing the number of selected genes, we will assign a prior distribution to this number. The approach creates additional ?exibility by allowing the imposition of constraints, such as bounding the dimension via a prior, which in e?ect works as a penalty. To implement our methodology, we use a Markov Chain Monte Carlo (MCMC) method. We demonstrate the use of the methodology with (a) di?use large B??cell lymphoma (DLBCL) complementary DNA (cDNA) data and (b) Breast Carcinoma data. Lastly, we propose a mixture of Dirichlet process models using discrete wavelet transform for a curve clustering. In order to characterize these time??course gene expresssions, we consider them as trajectory functions of time and gene??speci?c parameters and obtain their wavelet coe?cients by a discrete wavelet transform. We then build cluster curves using a mixture of Dirichlet process priors.

Selection of signi?cant genes via expression patterns is important in a microarray problem. Owing to small sample size and large number of variables (genes), the selection process can be unstable. This research proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables in a regression setting and use a Bayesian mixture prior to perform the variable selection. Due to the binary nature of the data, the posterior distributions of the parameters are not in explicit form, and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the posterior distributions. The Bayesian model is ?exible enough to identify the signi?cant genes as well as to perform future predictions. The method is applied to cancer classi?cation via cDNA microarrays. In particular, the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify the set of signi?cant genes to classify BRCA1 and others. Microarray data can also be applied to survival models. We address the issue of how to reduce the dimension in building model by selecting signi?cant genes as well as assessing the estimated survival curves. Additionally, we consider the wellknown Weibull regression and semiparametric proportional hazards (PH) models for survival analysis. With microarray data, we need to consider the case where the number of covariates p exceeds the number of samples n. Speci?cally, for a given vector of response values, which are times to event (death or censored times) and p gene expressions (covariates), we address the issue of how to reduce the dimension by selecting the responsible genes, which are controlling the survival time. This approach enables us to estimate the survival curve when n << p. In our approach, rather than ?xing the number of selected genes, we will assign a prior distribution to this number. The approach creates additional ?exibility by allowing the imposition of constraints, such as bounding the dimension via a prior, which in e?ect works as a penalty. To implement our methodology, we use a Markov Chain Monte Carlo (MCMC) method. We demonstrate the use of the methodology with (a) di?use large B??cell lymphoma (DLBCL) complementary DNA (cDNA) data and (b) Breast Carcinoma data. Lastly, we propose a mixture of Dirichlet process models using discrete wavelet transform for a curve clustering. In order to characterize these time??course gene expresssions, we consider them as trajectory functions of time and gene??speci?c parameters and obtain their wavelet coe?cients by a discrete wavelet transform. We then build cluster curves using a mixture of Dirichlet process priors.

The input collected from warranty claims data links customer feedback with product quality. Results from warranty claim analysis can potentially improve product quality, customer relationships and positively affect business. However working on warranty claims data holds many challenges that requires a significant share of time devoted to data cleaning and data processing. The purpose of warranty claims analysis is to get the comprehensive overview of the reliability, costs and quality of household appliances produced by ASKO. While there are different ways to approach this problem, we will focus on non-parametric and semi-parametric methods, by using Kaplan-Meier estimators and Cox proportional hazard model respectively. These kinds of models are time dependent and therefore used for prediction of household appliance reliability. Even though non-parametric models are quite informative they cannot handle additional characteristics about observable product hence the semi-parametric Cox proportional hazard model was proposed. Apart from the reliability analysis, we will also predict warranty costs with probit model and observe inequality in household appliances part failures as a part of quality control analysis. Described methods were selected due to the fact that the warranty claims analysis will be practiced in future by ASKO’s quality department and therefore straight forward methods with very informative results are needed.

Cox proportional hazard model is often used to estimate the effect of covariates on hazard for censored event times. In this thesis we study the semiparametric models of additive risk for censored data. In this model the hazard is given as a sum of unknown baseline hazard function and a product of covariates and coefficients. Further the general additive-multiplicative model is assumed. In this model the effect of a covariate can be either multiplicative, additive or both at the same time. We focuse on determining the effect of a covariate in the general model. This model can be used to test for the multiplicative or addtive effect of a covariate on the hazard.

<p>  </p> <p>During the construction of a bridge, more specifically a concrete bridge deck, there are sometimes defects in materials or workmanship, resulting in what is called a construction defect. These defects can have a large impact on the lifecycle performance of the bridge deck, potentially leading to more preventative and reactive maintenance actions over time and thus a larger monetary investment by the bridge owner. Bridge asset managers utilize prediction software to inform their annual budgetary needs, however this prediction software traditionally relies only on historical condition rating data for its predictions. When attempting to understand how deterioration of a bridge deck changes with the influence of construction defects, utilizing the current prediction software is not appropriate as there is not enough historical data available to ensure accuracy of the prediction. There are numerical modeling approaches available that capture the internal physical and chemical deterioration processes, and these models can account for the change in deterioration when construction defects are present. There are also numerical models available that capture the effect of external factors that may be affecting the deterioration patterns of the bridge deck, in parallel to the internal processes. The goal of this study is to combine a mechanistic model capturing the internal physical and chemical processes associated with deterioration of a concrete bridge deck, with a model that is built strictly from historical condition rating data, in order to predict the changes in condition rating prediction of a bridge deck for a standard construction case versus a substandard construction case. Being able to measure the change in prediction of deterioration when construction defects are present then allows for quantifying the additional cost that would be required to maintain the defective bridge deck which is also presented. </p>

This thesis surveys the method of extending Cox proportional hazard models (1972) and the general class of semiparametric model (2004) in the upgrades or downgrades of credit ratings by S&P. The two kinds of models can be used to modify the relationship of covariates to a recurrent event data of upgrades or downgrades. The benchmark credit-scoring model with a quintet of financial ratios which is inspired by the Z-Score model is employed. These financial ratios include measures of short-term liquidity, leverage, sales efficiency, historical profitability and productivity. The evidences of empirical results show that the financial ratios of historical profitability, leverage, and sales efficiency are significant factors on the rating transitions of upgrades. For the downgrades data setting, the financial ratios of short-term liquidity, productivity, and leverage are significant factors in the extending Cox models, whereas only the historical profitability is significant in the general class of semiparametric model. The empirical analysis of S&P credit ratings provide evidence supporting that the transitions of credit ratings are related to some determined financial ratios under these new econometrics methods.

本研究主要以Cox 迴歸模型為主軸，以1995年7月1日至1999年5月7日公務人員退撫基金成員:公務人員及教育人員為研究對象，分析影響基金成員各項脫退的個別變數，並量化所擇取之變數的影響，以估計各個基金成員的脫退率。同時針對現有基金成員，評估退撫基金短期現金支出並分析之。實證結果發現：藉由Cox迴歸模型之分析可知，相異的脫退因素，被不同的迴歸變數所影響著，且各個變數對各項脫退的影響程度亦存在著差異。短期現金支出的評估結果顯示，各項給付支出，以退休給付的支出佔最大的比例，次為資遣、死亡及離職給付。而人數比例較少的教育人員，其脫退給付支出金額，高於公務人員之給付支出。 略 / Cox regression model is proposed in this study to investigate the demographic factors (i.e., gender, age, seniority, salary scale and the entry date) that influence the turnover pattern of the plan members. This research has focused on the government employees and public school teachers in Taiwan Public Employees Retirement System (Tai-PERS). Quantitative analyses on turnover are performed through monitoring and selecting the significant factors in Cox regression model. Finally based on the current members in Tai-PERS, the short-term cash outflow is projected. Based on the empirical results, different causes of turnover (i.e., death, withdrawal, layoff and retirernent) are influenced by the selected factors. Significant differences have been found within the various causes of decrements. Result from the short-term cash outflow shows that the payment due to retirement has the largest proportion. Then follows the payment amount due to payoff, death and withdrawal if we rank them in order. In additions, the total payments of the public school teachers are larger than those of the government employees, while the plan members of the public school teachers are comparatively less.

In this thesis, we develop some inferential results for one-shot device testing data analysis. These extend and generalize existing methods in the literature. First, a competing-risk model is introduced for one-shot testing data under accelerated life-tests. One-shot devices are products which will be destroyed immediately after use. Therefore, we can observe only a binary status as data, success or failure, of such products instead of its lifetime. Many one-shot devices contain multiple components and failure of any one of them will lead to the failure of the device. Failed devices are inspected to identify the specific cause of failure. Since the exact lifetime is not observed, EM algorithm becomes a natural tool to obtain the maximum likelihood estimates of the model parameters. Here, we develop the EM algorithm for competing exponential and Weibull cases. Second, a semi-parametric approach is developed for simple one-shot device testing data. Semi-parametric estimation is a model that consists of parametric and non-parametric components. For this purpose, we only assume the hazards at different stress levels are proportional to each other, but no distributional assumption is made on the lifetimes. This provides a greater flexibility in model fitting and enables us to examine the relationship between the reliability of devices and the stress factors. Third, Bayesian inference is developed for one-shot device testing data under exponential distribution and Weibull distribution with non-constant shape parameters for competing risks. Bayesian framework provides statistical inference from another perspective. It assumes the model parameters to be random and then improves the inference by incorporating expert's experience as prior information. This method is shown to be very useful if we have limited failure observation wherein the maximum likelihood estimator may not exist. The thesis proceeds as follows. In Chapter 2, we assume the one-shot devices to have two components with lifetimes having exponential distributions with multiple stress factors. We then develop an EM algorithm for developing likelihood inference for the model parameters as well as some useful reliability characteristics. In Chapter 3, we generalize to the situation when lifetimes follow a Weibull distribution with non-constant shape parameters. In Chapter 4, we propose a semi-parametric model for simple one-shot device test data based on proportional hazards model and develop associated inferential results. In Chapter 5, we consider the competing risk model with exponential lifetimes and develop inference by adopting the Bayesian approach. In Chapter 6, we generalize these results on Bayesian inference to the situation when the lifetimes have a Weibull distribution. Finally, we provide some concluding remarks and indicate some future research directions in Chapter 7. / Thesis / Doctor of Philosophy (PhD)