當造成失敗的原因不只一種時，若各對象同一時間最多只經歷一種失敗原因，則這些失敗原因稱為競爭風險。然而，有些個體不會失敗或者經過治療之後已痊癒，我們稱這部分的群體為治癒群。本文考慮同時處理競爭風險及治癒率的混合模式，即競爭風險的治癒率模式，亦將解釋變數結合到治癒率、競爭風險的條件失敗機率，或未治癒下競爭風險的條件存活函數中，並以建立在完整資料上之擴充的概似函數為貝氏分析的架構。對於右設限對象則以插補方式決定是否會治癒或會因何種風險而失敗，並推導各參數的完全條件後驗分配及其性質。由於邊際後驗分配的數學形式無法明確呈現，再加上需對右設限者判斷其狀態，所以採用屬於馬可夫鏈蒙地卡羅法的Gibbs抽樣法及適應性拒絕抽樣法(adaptive rejection sampling) ，執行參數之模擬抽樣及設算右設限者之治癒或失敗狀態。實證部分，我們分析Klein and Moeschberger (1997)書中骨髓移植後的血癌病患的資料，並用不同模式之下的參數模擬值計算各對象之條件預測指標(CPO)，換算成各模式的對數擬邊際概似函數值(LPML)，比較不同模式的優劣。 / In case that there are more than one possible failure types, if each subject experiences at most one failure type at one time, then these failure types are called competing risks. Moreover, some subjects have been cured or are immune so they never fail, then they are called the cured ones. This dissertation discusses several mixture models containing competing risks and cure rate. Furthermore, covariates are associated with cure rate, conditional failure rate of each risk, or conditional survival function of each risk, and we propose the Bayesian procedure based on the augmented likelihood function of complete data. For right censored subjects, we make use of imputation to determine whether they were cured or failed by which risk and derive full conditional posterior distributions. Since all marginal posterior distributions don’t have closed forms and right censored subjects need to be identified their statuses, we take Gibbs sampling and adaptive rejection sampling of Markov chain Monte Carlo method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the bone marrow transplant data from the book written by Klein and Moeschberger (1997). To do model selection, we compute the conditional predictive ordinate(CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudo marginal likelihood (LMPL) of each model.

為瞭解臺灣地區男女自殺死亡率的差異，本文採用Held and Riebler (2010)所建議的多元年齡-年代-世代模型，同時探討男女性自殺死亡率在年齡、年代及世代三種效應上的差異，我們同時使用非條件概似函數法（或稱對數線性模型法）及條件概似函數法（或稱多項式邏輯模型法）對台灣地區男女自殺死亡資料來配適模型。結果發現在假設世代效應與性別無關的前提下，年齡方面， 女性的自殺死亡率在10歲到24歲時顯著比男性高，在15到19歲這個年齡層差異達到最大，20歲之後差異開始變小，到了25至34歲，兩性則已無顯著差異，35歲之後男性的自殺死亡率開始顯著大於女性，並且隨著年齡增長兩性的差異越大，直到60歲之後差異才開始減小，到70歲時兩性無顯著差異。年代方面，男女的自殺死亡率在1959年到1973年間沒有顯著的差異，在1974到1988年女性的自殺死亡率顯著大於男性並於1979年到1983年來到最低點，也就是差異最大，之後差異開始變小，到了1989年時兩性已無顯著差異，從1994年開始男性的自殺死亡率反而開始顯著大於女性，而且隨著年代增加差異越大，並於2004到2008這個年代層差異達到最大。 / To understand the differences in suicide mortality between men and women in Taiwan, this study uses the Multivariate Age-Period-Cohort model proposed by Held and Riebler (2010), and explores the differences in suicide mortality between men and women on age, period and cohort effects adjusted for the other two. We use both unconditional likelihood function method (or log-linear model) and conditional likelihood function method (or multinomial logit model) to fit the model. Assuming that the cohort effect is independent of the gender, female suicide mortality in the age of 10 to 24 years old appears significantly higher than that of male, and the maximum age difference appears at the age of 15 to 19 years old. The difference is getting smaller after the age of 20, and gender difference is no longer significant between age of 25 to 34. After 35-year-old, male suicide death rate starts to exceed that of female, and the difference increases until the age of 60. After 60 years old, the difference starts to decrease till age of 70 at which there is no significant gender differences. There is no significant gender-specific suicide mortality difference between years 1959 and 1973. From 1974 to 1988 female suicide mortality rate is significantly greater than male. The difference reaches the peak in1979 to 1983. After that, the difference is getting smaller, and gender difference is no longer significant between 1989 and 1993. From 1994, suicide mortality for men begins to be significantly greater than women, and the difference increases with period. This difference reaches the maximum level in 2004 to 2008.

臺灣的連鎖式便利商店密度居世界之冠，為數眾多的門市使得便利商店與臺灣人 民的生活息息相關，就直覺來說，便利商店門市的數量也影響了廠商設立新門市 的決策。本研究建構了一離散選擇的動態賽局，分析臺北市各個行政區便利商店 門市數量對不同廠商設立新門市的影響。實證結果顯示當競爭對手門市數量剛開 始增加時，門市數量對便利商店的利潤有正向的影響，但是當對手門市數量太多 時，此數量的增加對便利商店的利潤產生負向影響。這結果表示一開始門市之間 的互補效果大於替代效果，但是門市數量太多造成過度競爭，此時門市之間的替 代效果大於互補效果。而同品牌的門市數量對於廠商的總利潤也有類似的影響。 另外，本研究也估計便利商店歷年來在臺北市各行政區展店的機率，其中大安區 和中山區是便利商店廠商最想展店的行政區，相對而言，南港區、大同區和萬華 區則是展店機率較低的行政區。 / The density of convenience stores (CVS) in Taiwan is ranked as number one in the world. The highly concentrated market of convenience stores has dramatically changed the lifestyle of Taiwanese people. The number of existing outlets in a region is also an important factor in regard to the entry decisions of new outlets. In this study, we construct a model of the dynamic discrete game, and examine the influence of the rival outlet number on CVS entry decisions in Taipei, Taiwan. The empirical evidence we find is that the CVS profits first rise and then decline as the own or rival outlet number increases. This result implies that the complement and substitution effects vary with the number of the CVS outlets in a specific region. Furthermore, we estimate the probabilities that the CVS companies will set up additional outlets in any district of Taipei during the data period. The results show that it is most likely for the companies to enter the Da’an and Zhongshan districts, while Nangang, Datong and Wanhua are districts with low entry probabilities.

本文所探討的中心為貝氏模型運用於加速壽命試驗，並且假設受測項目之壽命服從Weibull分配。加速實驗環境有三種，其中第二種環境代表正常狀態，採用加速壽命試驗的方式涵蓋了三種：固定應力、漸進之逐步應力和變量曲線之逐步應力。對於先驗參數，並不是直接給予特定的值，而是透過專家評估，給定各種環境之下的產品可靠度之中位數或百分位數，再利用這些資訊經過數值運算解出先驗參數。資料的型態分成兩種，一為區間資料，另一為型一設限資料，透過蒙地卡羅法模擬出後驗分配，並且估計正常環境狀態的可靠度。 / This article develops a Bayes inference model for accelerated life testing assuming failure times at each stress level are Weibull distributed. Using the approach, there are three stressed to be used, and the three testing scenarios to be adapted are as follows：fixed-stress, progressive step-stress and profile step-stress. Prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known Markov Chain Monte Carlo methods to derive posterior approximations.

近來地理資訊系統(GIS)之資料庫受到不同領域的統計學家廣泛的研究，以期建立及分析可描述空間聚集效應及變異之模型，而描述空間相關存活資料之統計模式為公共衛生及流行病學上新興的研究議題。本文擬建立多維度半參數的貝氏階層模型，並結合空間及非空間隨機效應以描述存活資料中的空間變異。此模式將利用多變量條件自回歸(MCAR)模型以檢驗在不同地理區域中是否存有空間聚集效應。而基準風險函數之生成為分析貝氏半參數階層模型的重要步驟，本研究將利用混合Polya樹之方式生成基準風險函數。美國國家癌症研究院之「流行病監測及最終結果」(Surveillance Epidemiology and End Results, SEER)資料庫為目前美國最完整的癌症病人長期追蹤資料，包含癌症病人存活狀況、多重癌症史、居住地區及其他分析所需之個人資料。本文將自此資料庫擷取美國愛荷華州之癌症病人資料為例作實證分析，並以貝氏統計分析中常用之模型比較標準如條件預測指標(CPO)、平均對數擬邊際概似函數值(ALMPL)、離差訊息準則(DIC)分別測試其可靠度。 / The databases of Geographic Information System (GIS) have gained attention among different fields of statisticians to develop and analyze models which account for spatial clustering and variation. There is an emerging interest in modeling spatially correlated survival data in public health and epidemiologic studies. In this article, we develop Bayesian multivariate semiparametric hierarchical models to incorporate both spatially correlated and uncorrelated frailties to answer the question of spatial variation in the survival patterns, and we use multivariate conditionally autoregressive (MCAR) model to detect that whether there exists the spatial cluster across different areas. The baseline hazard function will be modeled semiparametrically using mixtures of finite Polya trees. The SEER (Surveillance Epidemiology and End Results) database from the National Cancer Institute (NCI) provides comprehensive cancer data about patient’s survival time, regional information, and others demographic information. We implement our Bayesian hierarchical spatial models on Iowa cancer data extracted from SEER database. We illustrate how to compute the conditional predictive ordinate (CPO), the average log-marginal pseudo-likelihood (ALMPL), and deviance information criterion (DIC), which are Bayesian criterions for model checking and comparison among competing models.

當母體中有部份對象因被治癒或免疫而不會失敗時，需考慮這群對象所佔的比率，即存活分率。本文主要在探討如何以貝氏方法對含存活分率之治癒率模式進行分析，並特別針對兩種含存活分率的迴歸模式，分別是Weibull迴歸模式以及對數邏輯斯迴歸模式，導出概似函數與各參數之完全條件後驗分配及其性質。由於聯合後驗分配相當複雜，各參數之邊際後驗分配之解析形式很難表達出。所以，我們採用了馬可夫鏈蒙地卡羅方法（MCMC）中的Gibbs抽樣法及Metropolis法，模擬產生參數值，以進行貝氏分析。實證部份，我們分析了黑色素皮膚癌的資料，這是由美國Eastern Cooperative Oncology Group所進行的第三階段臨床試驗研究。有關模式選取的部份，我們先分別求出各對象在每個模式之下的條件預測指標（CPO），再據以算出各模式的對數擬邊際概似函數值（LPML），以比較各模式之適合性。 / When we face the problem that part of subjects have been cured or are immune so they never fail, we need to consider the fraction of this group among the whole population, which is the so called survival fraction. This article discuss that how to analyze cure rate models containing survival fraction based on Bayesian method. Two cure rate models containing survival fraction are focused; one is based on the Weibull regression model and the other is based on the log-logistic regression model. Then, we derive likelihood functions and full conditional posterior distributions under these two models. Since joint posterior distributions are both complicated, and marginal posterior distributions don’t have closed form, we take Gibbs sampling and Metropolis sampling of Markov Monte Carlo chain method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the data from a melanoma clinical trial in the third stage conducted by Eastern Cooperative Oncology Group. To do model selection, we compute the conditional predictive ordinate (CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudomarginal likelihood (LPML) of each model.