Credit risk of derivative securities includes the risk of underlying company and the risk of seller's nonfulfilment of contracts. Take bonds for example, we regard Treasury bills as default-free bonds, and corporate bonds as risky bonds. When the liability of property of derivative securities underlying company is less than 1, we regard the company is of bankruptcy. And then the seller of derivative securities will break the contract. The essay extends two period risky bonds pricing valuation of Jarrow and Turnbull(1995) to multiperiod situation, and derive arbitrage-free condition. Furthermore, we derive formulae of risky bonds prices by assuming the logarithm of the odds ratio of an underlying company's bankruptcy probability satisfies an AR(1) or MA(1) processes. Empirical data of Rebar, Chinarebar, Ceon are studied, time series models are established for logarithm of odds ratios. In most cases, we find that the log odds ratios can be well fitted by AR(1) models.

Although forest properties are known to influence snowpack accumulation and spring runoff, the processes underlying the impacts of forest canopy cover on the input of snowmelt to the catchment remain poorly characterized. In this study I show that throughfall and canopy shading can combine to result in maximal snowpacks in forests of moderate canopy density. Snow depth and density data taken shortly before spring melt in the Jemez Mountains of New Mexico show strong correlation between forest canopy density and snow water equivalent, with maximal snow accumulation in forests with density between 25 and 45%. Forest edges are also shown to be highly influential on local snow depth variability, with shaded open areas holding significantly deeper snow than either unshaded open or deep forest areas. These results are broadly applicable in improving estimates of water resource availability, predicting the ecohydrological implications of vegetation change, and informing integrated water resources management.

<p>MicroRNAs (miRNAs) are a class of small non-coding RNAs that control gene expression by targeting mRNAs and triggering either translation repression or RNA degradation. Several groups pointed out that miRNAs play a major role in several diseases, including cancer. This is assumed since the expression level of several miRNAs differs between normal and cancerous cells. Further, it has been shown that miRNAs are involved in cell proliferation and cell death.</p><p>Because of this role it is suspected that miRNAs could serve as biomarkers to improve tumor classification, therapy selection, or prediction of survival. In this context, it is questioned, among other things, whether miRNA deregulations in cancer cells occur according to some pattern or in a rather random order. With this work we contribute to answering this question by adapting two approaches (Beerenwinkel et al. (J Comput Biol, 2005) and Höglund et al. (Gene Chromosome Canc, 2001)), developed to derive graph models of oncogenesis for chromosomal imbalances, to miRNA expression data and applying them to a breast cancer data set. Further, we evaluated the results by comparing them to results derived from randomly altered versions of the used data set.</p><p>We could show that miRNA deregulations most likely follow a rough temporal order, i.e. some deregulations occur early and some occur late in cancer progression. Thus, it seems to be possible that the expression level of some miRNAs can be used as indicator for the stage of a tumor. Further, our results suggest that the over expression of mir-21 as well as mir-102 are initial events in breast cancer oncogenesis.</p><p>Additionally, we identified a set of miRNAs showing a cluster-like behavior, i.e. their deregulations often occur together in a tumor, but other deregulations are less frequently present. These miRNAs are let-7d, mir-10b, mir-125a, mir-125b, mir-145, mir-206, and mir-210.</p><p>Further, we could confirm the strong relationship between the expression of mir-125a and mir-125b.</p>

MicroRNAs (miRNAs) are a class of small non-coding RNAs that control gene expression by targeting mRNAs and triggering either translation repression or RNA degradation. Several groups pointed out that miRNAs play a major role in several diseases, including cancer. This is assumed since the expression level of several miRNAs differs between normal and cancerous cells. Further, it has been shown that miRNAs are involved in cell proliferation and cell death. Because of this role it is suspected that miRNAs could serve as biomarkers to improve tumor classification, therapy selection, or prediction of survival. In this context, it is questioned, among other things, whether miRNA deregulations in cancer cells occur according to some pattern or in a rather random order. With this work we contribute to answering this question by adapting two approaches (Beerenwinkel et al. (J Comput Biol, 2005) and Höglund et al. (Gene Chromosome Canc, 2001)), developed to derive graph models of oncogenesis for chromosomal imbalances, to miRNA expression data and applying them to a breast cancer data set. Further, we evaluated the results by comparing them to results derived from randomly altered versions of the used data set. We could show that miRNA deregulations most likely follow a rough temporal order, i.e. some deregulations occur early and some occur late in cancer progression. Thus, it seems to be possible that the expression level of some miRNAs can be used as indicator for the stage of a tumor. Further, our results suggest that the over expression of mir-21 as well as mir-102 are initial events in breast cancer oncogenesis. Additionally, we identified a set of miRNAs showing a cluster-like behavior, i.e. their deregulations often occur together in a tumor, but other deregulations are less frequently present. These miRNAs are let-7d, mir-10b, mir-125a, mir-125b, mir-145, mir-206, and mir-210. Further, we could confirm the strong relationship between the expression of mir-125a and mir-125b.

<div>Model-based clustering, with its flexibility and solid statistical foundations, is an important tool for unsupervised learning, and has numerous applications in a variety of fields. This dissertation focuses on nonparametric Bayesian approaches to model-based clustering under structural restrictions. These are additional constraints on the model that embody prior knowledge, either to regularize the model structure to encourage interpretability and parsimony or to encourage statistical sharing through underlying tree or network structure.</div><div><br></div><div>The first part in the dissertation focuses on the most commonly used model-based clustering models, mixture models. Current approaches typically model the parameters of the mixture components as independent variables, which can lead to overfitting that produces poorly separated clusters, and can also be sensitive to model misspecification. To address this problem, we propose a novel Bayesian mixture model with the structural restriction being that the clusters repel each other.The repulsion is induced by the generalized Matérn type-III repulsive point process. We derive an efficient Markov chain Monte Carlo (MCMC) algorithm for posterior inference, and demonstrate its utility on a number of synthetic and real-world problems. <br></div><div><br></div><div>The second part of the dissertation focuses on clustering populations with a hierarchical dependency structure that can be described by a tree. A classic example of such problems, which is also the focus of our work, is the phylogenetic tree with nodes often representing biological species. The structure of this problem refers to the hierarchical structure of the populations. Clustering of the populations in this problem is equivalent to identify branches in the tree where the populations at the parent and child node have significantly different distributions. We construct a nonparametric Bayesian model based on hierarchical Pitman-Yor and Poisson processes to exploit this, and develop an efficient particle MCMC algorithm to address this problem. We illustrate the efficacy of our proposed approach on both synthetic and real-world problems.</div>

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Les modèles virtuels de plantes sont visuellement de plus en plus réalistes dans les applications infographiques. Cependant, dans le contexte de la biologie et l'agronomie, l'acquisition de modèles précis de plantes réelles reste un problème majeur pour la construction de modèles quantitatifs du développement des plantes.Récemment, des scanners laser 3D permettent d'acquérir des images 3D avec pour chaque pixel une profondeur correspondant à la distance entre le scanner et la surface de l'objet visé. Cependant, une plante est généralement un ensemble important de petites surfaces sur lesquelles les méthodes classiques de reconstruction échouent. Dans cette thèse, nous présentons une méthode pour reconstruire des modèles virtuels de plantes à partir de scans laser. Mesurer des plantes avec un scanner laser produit des données avec différents niveaux de précision. Les scans sont généralement denses sur la surface des branches principales mais recouvrent avec peu de points les branches fines. Le cœur de notre méthode est de créer itérativement un squelette de la structure de la plante en fonction de la densité locale de points. Pour cela, une méthode localement adaptative a été développée qui combine une phase de contraction et un algorithme de suivi de points.Nous présentons également une procédure d'évaluation quantitative pour comparer nos reconstructions avec des structures reconstruites par des experts de plantes réelles. Pour cela, nous explorons d'abord l'utilisation d'une distance d'édition entre arborescence. Finalement, nous formalisons la comparaison sous forme d'un problème d'assignation pour trouver le meilleur appariement entre deux structures et quantifier leurs différences. / In the last decade, very realistic rendering of plant architectures have been produced in computer graphics applications. However, in the context of biology and agronomy, acquisition of accurate models of real plants is still a tedious task and a major bottleneck for the construction of quantitative models of plant development. Recently, 3D laser scanners made it possible to acquire 3D images on which each pixel has an associate depth corresponding to the distance between the scanner and the pinpointed surface of the object. Standard geometrical reconstructions fail on plants structures as they usually contain a complex set of discontinuous or branching surfaces distributed in space with varying orientations. In this thesis, we present a method for reconstructing virtual models of plants from laser scanning of real-world vegetation. Measuring plants with laser scanners produces data with different levels of precision. Points set are usually dense on the surface of the main branches, but only sparsely cover thin branches. The core of our method is to iteratively create the skeletal structure of the plant according to local density of point set. This is achieved thanks to a method that locally adapts to the levels of precision of the data by combining a contraction phase and a local point tracking algorithm. In addition, we present a quantitative evaluation procedure to compare our reconstructions against expertised structures of real plants. For this, we first explore the use of an edit distance between tree graphs. Alternatively, we formalize the comparison as an assignment problem to find the best matching between the two structures and quantify their differences.

自1980年代後期Hull & White、Wiggins、Johnson & Shanno等人相繼發表關於隨機波動度模型的文獻後，就有諸多的文獻對於在選擇權定價中考慮隨機波動度作更深入的分析與模型探討，然而關於隨機波動度的研究，在早期大多採用蒙地卡羅模擬法來分析選擇權的價格行為，但蒙地卡羅模擬法受限於運算效率不高與缺乏彈性，故在評價新奇選擇權，如美式選擇權、障礙選擇權時，並無法應用。故本文以Leisen（2000）的二元樹狀模型出發，探討在不同相關係數及參數設定下之各類選擇權的定價、避險參數及隱含波動度曲面模擬計算等主題。 最後我們得到下面幾點結論： 1.在收斂速度與運算效率方面，我們可以發現二元樹狀模型在分割期數n大於20時，計算價格與收斂價格的差距就非常微小，而若我們計算不同切割期數的最大價格差異也會發現其實都不到百分之一，因此整體而言，收斂速度是令人非常滿意的。 2.當期初波動度提高時，會縮小價外選擇權與B-S價格之間的價格誤差。當到期期限增加時，隱含波動度曲線會有整體提高的趨勢。 3.若提高波動係數σ為2.5時，則不論相關係數的正負情形，價內外的程度，皆會大幅提高選擇權的隱含波動度。而在相關係數為-0.5的時候，可以發現實證中常觀察到的隱含波動度微笑曲線，這可能代表著市場上的波動係數比我們預期中的都還來的高。 4.在進行不同相關係數及不同價內外程度下二元樹狀與單元樹狀模型的美式選擇權價格比較時，我們可以發現，若以二元樹狀模型為正確價格，當相關係數為負的時候，在價外的時候，單元樹狀模型有價格低估的現象，在價內的時候，則有價格高估的現象，而在相關係數為正的時候，則反之。 5.Leisen二元樹狀與封閉解的歐式向上出局賣權價格比較，在特定的參數設定之下，Leisen二元樹狀模型在評價歐式向上出局賣權的時候，當相關係數為負的時候，在價外的時候，模型價格會高於封閉解，在價內的時候，模型價格則會低於封閉解，而在相關係數為正的時候，則反之。

We consider the N step binomial tree model of stocks. Call options and put options of European and American type are computed explicitly. With appropriate scaling in time and jumps,  convergence of the stock prices and the option prices are obtained as N-&gt; infinite. The obtained convergence is the Black-Scholes model and, for the particular case of European call option, the Black-Scholes formula is obtained. Furthermore, the Black-Scholes partial differential equation is obtained as a limit from the N step binomial tree model. Pricing of American put option under the Black-Scholes model is obtained as a limit from the N step binomial tree model. With this thesis, option pricing under the Black-Scholes model is achieved not by advanced stochastic analysis but by elementary, easily understandable probability computation. Results which in elementary books on finance are mentioned briefly are here derived in more details. Some important Java codes for N step binomial tree option prices are constructed by the author of the thesis.