分量迴歸在近幾年來的應用相當廣泛，但透過貝氏方法估計分量迴歸參數，是由Yu & Moyeed（2001）所提出，拜電腦運算發達之賜而生的新估計方法，因此在實證應用上的研究，貝氏分量迴歸仍在起步的狀態。並且應用馬可夫鍊蒙地卡羅方法的貝氏分量迴歸，在後驗分配的收斂上並沒有類似的探討文獻。因此本研究嘗試以馬可夫鍊蒙地卡羅方法的應用觀點出發，研究運用貝氏方法的分量迴歸估計是否達到馬可夫鍊所重視的收斂至穩態分配，也就是利用模擬資料，探討使用馬可夫鍊蒙地卡羅方法的貝氏分量迴歸在何種情況下，具有較好的收斂情形，以及選擇適當的提議分配。接著以台灣上市公司為例，依電子、紡織以及塑膠產業為別，利用貝氏分量迴歸，觀察民國86~90年，以及91~95年兩區間，股價報酬率在各分量下與財務比率的關連性，並依產業分別進行探討。 本論文研究結果指出，貝氏分量迴歸在使用時仍須注意馬可夫鍊的收斂情形，將馬可夫鍊的接受頻率定在約20%~30%為佳，且估計結果與Koenker & Bassett（1978）所提出的無母數方法相當一致。在實證資料的分析上，以電子、紡織以及塑膠產業各別的配適結果來看，都依產業別的不同而具有合理的解釋，但貝氏分量迴歸容易因自變數值域的問題，造成馬可夫鍊接受頻率不理想，以及收斂速度過慢的情形，因此在應用貝氏分量迴歸時，自變數值域的影響需要納入考慮，並仍須選擇適當的提議分配、馬可夫鍊重複次數，所得到的結果才會較佳。

運用傳統再保險契約移轉風險受限於承保能量的逐年波動，尤其自90年代起，全球巨災頻繁，保險人損失巨幅增加，承保能量急遽萎縮，基於巨災市場之資金需求，再保險轉向資本市場，預期將巨災風險移轉至投資人，促成保險衍生性金融商品之創新，本研究針對佔有顯著交易量的巨災風險債券進行分析，基於Cummins和Geman (1995)所建構巨災累積損失模型，引用Duffie 與Singleton (1999)於違約債券的計價模式，將折現利率表示為短期利率加上事故發生率及預期損失比例之乘積，並將債券期間延長至多年期，以符合市場承保的需求，應用市場無套利假設及平賭測度計價的方法計算合理的市場價值，巨災損失過程將分成損失發展期與損失確定期，以卜瓦松過程表示巨災發生頻率，並利用台灣巨災經驗資料建立合適之損失幅度模型，最後以蒙地卡羅方法針對三種不同型態的巨災風險債券試算合理價值，並具體結論所得的數值結果與後續之研究建議。 / Using traditional reinsurance treaties to transfer insurance risks are restrained due to the volatility of the underwriting capacity annually. Catastrophe risks have substantially increased since the early 1990s and have directly resulted significant claim losses for the insurers. Hence the insurers are pursuing the financial capacities from the capital market. Transferring the catastrophe risks to the investor have stimulated the financial innovation for the insurance industry. In this study, pricing issues for the heavily traded catastrophe risk bonds (CAT-bond) are investigated. The aggregated catastrophe loss model in Cummins and Geman (1995) are adopted. While the financial techniques in valuing the defaultable bonds in Duffie and Singleton (1999) are employed to determine the fair prices incorporating the claim hazard rates and the loss severity. The duration of the CAT-bonds is extended from single year to multiple years in order to meet the demand from the reinsurance market. Non- arbitrage theory and martingale measures are employed to determine their fair market values. The contract term of the CAT-bonds is divided into the loss period and the development period. The frequency of the catastrophe risk is modeled through the Poisson process. Taiwan catastrophe loss experiences are examined to build the plausible loss severity model. Three distant types of CAT-bonds are analyzed through Monte Carlo method for illustrations. This paper concludes with remarks regarding some pricing issues of CAT-bonds.

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.

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.