本篇論文以Regime Switching Stochastic Volatility（RSV）作為外匯選擇權市場的波動度模型，採用馬可夫鏈蒙地卡羅法（Markov Chain Monte Carlo）中的GibbS Sampling演算法估計RSV模型的參數，並預測外匯選擇權在RSV模型下的價格。 數值結果方面首先對GibbS Sampling參數估計的結果做討論，再對預測出的選擇權價格與Black and Scholes作比較，最後並提出笑狀波幅與隱含波動度平面的結果。 本研究所得到之結論： 1. RSV模型與MCMC模擬法的組合，具備產生笑狀波幅的能力，提供足夠證據顯示，RSV模型與MCMC演算法所計算出來的選擇權價格，確實反應且捕捉到了市場上選擇權價格所應具備的特色。 2. 本模型能有效解釋期限結構 （Term Stucture of Volatility）、笑狀波幅（Volatility Smile）的現象。 關鍵字：馬可夫鏈蒙地卡羅法、外匯選擇權、貝氏選擇權評價、MCMC、Regime switching Regine change、Gibbs Sampling、currency option、Markov Chain Montec Carlo

單變量c-特徵函數已被證明可處理一些難以使用傳統特徵函數解決的問題， 在本文中，我們首先提出其反演公式，透過此反演公式，我們獲得（1）Dirichlet隨機向量之線性組合的機率密度函數；（2）以一些有趣測度為參數之Ferguson-Dirichlet過程其隨機動差的機率密度函數；（3）Ferguson-Dirichlet過程之隨機泛函的Lebesgue積分表示式。 本文給予對稱分配之多變量c-特徵函數的新性質，透過這些性質，我們證明在任何$n$維球面上之Ferguson-Dirichlet過程其隨機均值是一對稱分配，並且我們亦獲得其確切的機率密度函數，此外，我們將這些結果推廣至任何n維橢球面上。 我們亦探討條件分配相容性的問題，這個問題在機率理論與貝式計算上有其重要性，我們提出其充要條件。當給定相容的條件分配時，我們不但解決相關聯合分配唯一性的問題，而且也提供方法去獲得所有可能的相關聯合分配，我們亦給予檢驗相容性、唯一性及建構機率密度函數的演算法。 透過相容性的相關理論，我們提出完整且清楚地統合性貝氏反演公式理論，並建構可應用於一般測度空間的廣義貝氏反演公式。此外，我們使用廣義貝氏反演公式提供一個配適機率密度函數的演算法，此演算法沒有疊代演算法（如Gibbs取樣法）的收斂問題。 / The univariate c-characteristic function has been shown to be important in cases that are hard to manage using the traditional characteristic function. In this thesis, we first give its inversion formulas. We then use them to obtain (1) the probability density functions (PDFs) of a linear combination of the components of a Dirichlet random vector; (2) the PDFs of random functionals of a Ferguson-Dirichlet process with some interesting parameter measures; (3) a Lebesgue integral expression of any random functional of the Ferguson-Dirichlet process. New properties of the multivariate c-characteristic function with a spherical distribution are given in this thesis. With them, we show that the random mean of a Ferguson-Dirichlet process over a spherical surface in n dimensions has a spherical distribution on the n-dimensional ball. Moreover, we derive its exact PDF. Furthermore, we generalize this result to any ellipsoidal surface in n-space. We also study the issue of compatibility for specified conditional distributions. This issue is important in probability theory and Bayesian computations. Several necessary and sufficient conditions for the compatibility are provided. We also address the problem of uniqueness of the associated joint distribution when the given conditionals are compatible. In addition, we provide a method to obtain all possible joint distributions that have the given compatible conditionals. Algorithms for checking the compatibility and the uniqueness, and for constructing all associated densities are also given. Through the related compatibility theorems, we provide a fully and cleanly unified theory of inverse Bayes formula (IBF) and construct a generalized IBF (GIBF) that is applicable in the more general measurable space. In addition, using the GIBF, we provide a marginal density fitting algorithm, which avoids the problems of convergence in iterative algorithm such as the Gibbs sampler.

行人偵測為物件偵測領域中一個極具挑戰性的議題。其主要問題在於人體姿勢以及衣著服飾的多變性，加之以光源照射狀況迥異，大幅增加了辨識的困難度。吾人在本論文中提出利用共變異矩陣描述子及結合單純貝氏分類器與級聯支持向量機的線上學習辨識器，以增進行人辨識之正確率與重現率。 實驗結果顯示，本論文所提出之線上學習策略在某些辨識狀況較差之資料集中能有效提升正確率與重現率達百分之十四。此外，即便於相同之初始訓練條件下，在USC Pedestrian Detection Test Set、 INRIA Person dataset 及 Penn-Fudan Database for Pedestrian Detection and Segmentation三個資料集中，本研究之正確率與重現率亦較HOG搭配AdaBoost之行人辨識方式為優。 / Pedestrian detection is an important yet challenging problem in object classification due to flexible body pose, loose clothing and ever-changing illumination. In this thesis, we employ covariance feature and propose an on-line learning classifier which combines naïve Bayes classifier and cascade support vector machine (SVM) to improve the precision and recall rate of pedestrian detection in a still image. Experimental results show that our on-line learning strategy can improve precision and recall rate about 14% in some difficult situations. Furthermore, even under the same initial training condition, our method outperforms HOG + AdaBoost in USC Pedestrian Detection Test Set, INRIA Person dataset and Penn-Fudan Database for Pedestrian Detection and Segmentation.

本研究利用元大台灣50 ETF作為樣本資料，檢測2006年至2016年實證期間風險基礎指數和市值加權指數所分別建構的投資組合，其績效表現、風險表現、分散性表現的優劣性；其中Choueifaty, Froidure, and Reynier (2011) 所建構的最佳風險分散投資組合 (most diversified portfolio) 為近年來新起的風險基礎指數投資組合，我們將證實在獲得良好的投資組合分散性同時，如同其他的風險基礎指數投資組合的目標，同時也能獲得超越以追蹤市值加權指數為標的的投資組合績效。 本研究以夏普比率、信息比率、阿爾法作為衡量績效的指標；以標準差、貝他作為風險衡量的指摽；另以Choueifaty and Coignard (2008) 提出的分散性比率作為分散性衡量的指標。實證結果顯示，在整體實證期間，最佳風險分散投資組合在績效、風險、分散性的指標上皆有超越市值加權指數投資組合的能力，再以年為單位的個別期間，其績效衡量上大致優於市值加權指數投資組合，風險和分散性衡量上則優於市值加權指數投資組合的表現，但論以其整體表現，並非為本研究所提出的風險基礎指數投資組合中最佳者，因此投資人在選擇該類投資組合策略時，建議從該投資組合過去表現中判斷，選擇符合自己投資習慣者為之。 / This article examines the performance, risks and diversification of different types of portfolio strategies such as risk-based indexes and cap-weighted index during 2006- 2016. We introduce the recent most diversified portfolio (MDP), which was proposed by Choueifaty, Froidure, and Reynier (2011) and find the result that like the goal of other risk-based portfolios, which is to improve the risk-return profile of cap-weighted portfolio, MDP surpasses overall performance, risks and diversification compared to cap-weighted portfolio while achieving diversification. We use Sharpe ratio, information ratio and alpha as the performance indicators, use standard deviation, beta as the risk indicators, and adopt diversification ratio (DR), which was proposed by Choueifaty and Coignard (2008), as the diversification indicator in our analysis. The results of this study show that MDP surpasses overall performance, risks and diversification compared to cap-weighted portfolio in the full empirical period. In addition, MDP is generally superior to cap-weighted portfolios in terms of performance in many single years of the whole period, and completely beat cap-weighted portfolios in terms of risks and diversification in every single year of the whole period. Although the ability of exceeding cap-weighted portfolio, MDP do not win first place of mentioned risk-based portfolios in our research. As a result, we suggest investors choose their portfolio strategies refer to its past performance, risks and diversification, and select the best according to their investment preference.

過去處理勞資雙方工資談判的文獻，多數假設勞資雙方的訊息是對稱的， 或採合作談判解，或採非合作談判解，他們得到結果多為工資協議往往非 常順利，不會有不合議的事件發生。但事實上勞資雙方談判時，公司的經 營能力或策略、工人之生產力往往是談判雙方互不了解的，也就是現實工 資談判中普遍存有訊息不對稱的情況。本文擬在訊息不對稱的情形下，假 設談判的一方訊息不完全--工會不了解公司的經營能力，設定一個兩期工 資談判模型，僅由工會提議工資，公司之反提議僅為接受或拒絕工會之提 議工資。探討模型之承諾均衡與完全貝氏均衡，並對影響完全貝氏均衡之 因素做進一步之探討。

在線性迴歸分析中，資料的不適當，常導致研究者選擇了不當的模式，為避免此缺失，在分析資料前須先做好診斷工作。本文中將從貝氏觀點提出一些不同的診斷方法以供參考。首先推導出均數移動參數a=(a₁,…,a_k)'的事後分配，並利用a'a/k的事後均數診斷出不當資料點。接著，考慮在個別模式下以β事後分配之總變異及廣義變異為標準，診斷出離群值及具有潛在影響力之觀測值。最後，分別利用(i)β的事後分配(ii)σ²的事後分配(iii)(β,σ²)的聯合事後分配，推導出對應的對稱均方差以做為診斷標準。 / In this thesis, some different diagnostic methodologies for outliers and influential observations from Bayesian point of view are proposed. We firstly derive the marginal posterior distribution of the mean-shift parameter a=(a₁,a_k)¹, then use the posterior mean of a¹a/k to detect the spurious data items. Secondly, we use the posterior total variance and generalized variance of β as diagnostic criterions for outliers and influential observations. Finally, we utilize (i) the posterior distribution of β, (ii) the posterior distribution of σ², and (iii) the joint posterior distribution of β, σ² to find their corresponding symmetric mean square differences , which can be used as diagnostic criterions.

在工業、農業、或醫藥界的實驗中，經常必須拿數個不同的試驗處理 (test treatments)和一個已使用過的對照處理(control treatment)比較 。所謂的試驗處理可能是數組新的儀器、不同配方的新藥、或不同成份的 肥料等。以實驗新藥為例，研藥者想決定是否能以新藥取代原來所使用的 藥，故對v種新藥與原藥做比較，評估其藥效之差異。為了降低實驗中不 必要的誤差以增加其準確性，集區設計成為實驗者常用的設計方法之一； 又因A式最適設計是我們欲估計的對照處理效果(effect)與試驗處理效果 之差異之估計值最小的設計，基於此良好的統計特性，我們選擇A式最適 性為評判根據。古典的A式最適性並未將對照處理與試驗處理所具備的先 前資訊(prior information)加以考慮，以上例而言，我們不可能對原來 使用的藥一無所知，經由過去的實驗或臨床的反應，研藥者必已對其藥性 有某種程度的了解，直觀上，這種過去經驗的累積，影響到實驗配置上， 可能使對照處理的實驗次數減少，相對地可對試驗處理多做實驗，設計遂 更具意義。因而本文考慮在k>v的情形下之貝式最適集區設計，對先前分 配施以某種限制，依據準確設計理論(exact design theory)，推導單項 異種消除模型(one- way elimination of heterogeneity model)之下的 貝氏A式最適設計與Γ- minimax最適設計，使Majumdar(1992)的結果能適 用於完全集區設計。此種設計對先前分配具有強韌性，即當先前分配有所 偏誤，且其誤差在某一範圍內時，此設計仍為最適設計或仍可維持所謂的 高效度(high efficiency)。本文將列舉許多實例以說明此一特性。 We consider the problem of comparing a set of v test treatments simultaneously with a control treatment when k>v. Following the work of Majumdar(1992), we use exact design theory to derive Bayes A-optimal designs and optimal Γ-minimax designs for the one-way elimination of heterogeneity model. These designs have the same properties as of Bayes A-optimal incomplete block designs. We also provide several examples of robust optimal designs and highly efficient designs.

在解釋變數含測量誤差的簡單線性迴歸模式中，欲使第t+1期之產出Y達到某一目標值Y^*，則必需控制第t+1期投入變數Z，若參數α，β為以知時，可以將其設定為θ=(Y^*-α)/β。但當參數α，β為未知時，我們利用LSCE控制法則的設定方法，得到第t+1期設定的控制值Z_t+1，而且在機率為1下，Z_t+1 收斂至θ=(Y^*-α)/β。而貝氏最佳控制法則部份則是由第t+1期的預測期望損失，找出使其為最小的Z值即是所應設定的第t+1期控制值Z_t+1，並利用模擬結果來說明。

國際研究中雖有針對國家級的銀行脆弱性作分析，卻並未定義或預測台灣系統性危機，本研究在這樣的背景下，決定建構台灣本土的銀行業預警系統，建立銀行危機的領先指標，希望不只順應國際潮流，更能發展適合台灣特殊性的模型。本研究利用貝氏網路模型的特殊性: (1)事後值(2)機率特性，以個體化資料著手，建構一總體性模型。故研究者能確切了解個別銀行財務狀況，對個別銀行發出預警。事後值的特性使研究者能同時考慮多項財務比率。另外，利用機率特性，可幫助研究者了解危機的程度，且能做總體的延伸運用。 本研究發展出兩種方法建構總體模型。第一種為百分比法，以危機銀行佔總銀行個數的比率為基礎；第二種為加權平均法，讓機率值高者有較大權數，機率小者有較小權數去建立一加權平均機率值。 將本研究的推論結果和「台灣金融服務業聯合總會委託計畫-台灣金融危機領先指標之研究」比較，顯示本模型的兩種方法皆與危機之發生有相同趨勢，而考慮危機訊號的設定後，方法二加權平均法顯然具備較佳的預測結果。此外相較總體面衝擊產生的危機，本模型在預測能力上，對來自銀行個體面造成的危機預測明顯較優異。 / International organizations defined and predicted country bank crises events without Taiwan, but they happened in Taiwan in the past twenty years. We construct the early warning system for banking crises in Taiwan and develop the specific model suited to our country. Using Bayesian Model’s specialities: (1) posterior value; (2) probability, we build a systematic model based on microeconomic data. So researcher can understand all financial conditions and predict the financial distresses of individual banks. The concept of posteriority lets researchers can consider a lot of financial ratio at the same time. The characteristic of probability makes researcher to extend the model to macroeconomic. We develop two methods to build systematic model. One is Percentage method which is based on the percentage of financial distress banks to all banks. The other one is weighted average method which used large weight in financial distress bank and small weight in financial sound banks. Comparing our results with the report that Taiwan Financial Services Roundtable issued in 2009, our methods have distress trends which link with crisis directly. But weighted average method has a better predict power than percentage method after considering the signals of distress we specify. Besides, our model has a stronger predictive power in crises from individual effect than crises from macroeconomic shocks.

在植被覆蓋的山區中，由於空載雷射掃描可穿透植被間縫隙的特性，有較高機會收集到植被下的地面資訊，因此適合作為製作植被覆蓋地區數值高程模型的資料來源，而在過濾過程中，一般僅利用點雲間的三維位置關係進行幾何過濾，而全波形空載雷射掃描可另外提供點位的波形寬、振幅值、散射截面積以及散射截面積數等波形資料，本研究將透過波形資料分析進行點雲過濾。 首先經最低點採樣後，本研究利用貝氏定理自動分析並計算得到地面點的波形資料的特徵區間範圍，採用振幅值、散射截面積以及散射截面積係數得到的特徵區間範圍開始第一階段的波形資料過濾，完成後再以第二階段的一般幾何過濾濾除剩餘之非地面點，最後的成果將與航測以及只採用幾何過濾時的成果比較。 由研究成果中顯示，不同的植被覆蓋間的單一回波波形資料的差異較明顯，最後回波類似。同一植被覆蓋下的單一回波及最後回波反應不同。而在成果的比較中，本實驗的成果與不採用波形資料輔助的成果大致相同本研究的成果在部分植被覆蓋的區域成果稍差，但透過波形過濾，可將幾何過濾所需計算的點雲數減少許多，可以增進整理過濾的效率。本研究的成果與航測相比時，在植被覆蓋區域較航測成果貼近實際的地面起伏，數值高程模型成果較為正確。 / In mountain areas covered with vegetation, discrete airborne laser scanning is an appropriate technique to produce DEMs for its laser signal is able to reach the ground beneath the vegetation. Once the scanned data was derived, point cloud filtering was performed based on the geometry relationship between the points at the processing stage. With the development of the advanced full-waveform laser scanning system, the additional waveform data has been proved useful for improving the performance of point cloud filtering. This research therefore focused on using the waveform data to extract DEM over vegetation covered area. The amplitude, backscatter cross-section and backscatter cross-section coefficient were the waveform parameters used to do the filtering. After initial waveform analysis was accomplished, an automated method to determine threshold range of each parameter representing ground points was proposed. By applying the thresholds, the original point cloud was filtered. Geometric filtering method was then used to eliminate the remained non-ground points. As a result, the DEM over the target vegetated area was derived. With the comparison against photogrammetric DEM and DEM derived from traditional filtering method, it was demonstrated that the quality of the resultant DEM was improved.