In recent years, fantasy baseball has seen an explosion in popularity. Major League Baseball, with its long, storied history and the enormous quantity of data available, naturally lends itself to the modern-day recreational activity known as fantasy baseball. Fantasy baseball is a game in which participants manage an imaginary roster of real players and compete against one another using those players' real-life statistics to score points. Early forms of fantasy baseball began in the early 1960s, but beginning in the 1990s, the sport was revolutionized due to the advent of powerful computers and the Internet. The data used in this project come from an actual fantasy baseball league which uses a head-to-head, points-based scoring system. The data consist of the weekly point totals that were accumulated over the first three-fourths of the 2011 regular season by the top 110 hitters and top 70 pitchers in Major League Baseball. The purpose of this project is analyze the relative value of pitchers versus hitters in this league using hierarchical Bayesian models. Three models will be compared, one which differentiates between hitters and pitchers, another which also differentiates between starting pitchers and relief pitchers, and a third which makes no distinction whatsoever between hitters and pitchers. The models will be compared using the deviance information criterion (DIC). The best model will then be used to predict weekly point totals for the last fourth of the 2011 season. Posterior predictive densities will be compared to actual weekly scores.

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Neste trabalho investigamos os determinantes da adesão de países a dois tratados internacionais de patentes: A Convenção de Paris e o Tratado de Cooperação de Patentes (TCP). Por meio de um modelo hierárquico Bayesiano, apresentamos evidências de que fatores domésticos são importantes para predizer adesão aos tratados estudados. Porém, quais fatores são importantes dependem do tipo de tratado. Para o TCP, que é um tratado que visa reduzir custos de transação, a legislação doméstica de patentes não é relevante. Para a Convenção de Paris, que limita as opções de política na área de patente, a legislação doméstica é fator relevante. Nós mostramos também que os ganhos diretos de participar dos tratados, medido pelo número de patentes no exterior, é uma variável importante e positivamente associada à probabilidade de adesão a ambos os acordos. Apresentamos ainda evidências de que variáveis sistêmicas são importantes e que as mudanças no sistema internacional nos últimos 30 anos são fatores importantes para explicar a adesão. / In this paper we investigate the determinants of the accession of two international patent treaties: the Paris Convention and Patent Cooperation Treaty (PCT). Through a Bayesian hierarchical model, we present evidence that domestic factors are important in predicting accession to the treaties studied. However, what factors are important depends on the type of treaty. For TCP, which is a treaty aimed at reducing transaction costs, the domestic law of patents is not important. For the Paris Convention, which limits the options in the area of patent policy, domestic law is a relevant factor. We also show that the direct gains from participating in treaties, as measured by the number of patents abroad, is an important variable and positively associated with the likelihood of ratification to both agreements. We also present evidence that systemic variables are important and that changes in the international system over the past 30 years are important factors to explain the membership to the treaties.

Neste trabalho investigamos os determinantes da adesão de países a dois tratados internacionais de patentes: A Convenção de Paris e o Tratado de Cooperação de Patentes (TCP). Por meio de um modelo hierárquico Bayesiano, apresentamos evidências de que fatores domésticos são importantes para predizer adesão aos tratados estudados. Porém, quais fatores são importantes dependem do tipo de tratado. Para o TCP, que é um tratado que visa reduzir custos de transação, a legislação doméstica de patentes não é relevante. Para a Convenção de Paris, que limita as opções de política na área de patente, a legislação doméstica é fator relevante. Nós mostramos também que os ganhos diretos de participar dos tratados, medido pelo número de patentes no exterior, é uma variável importante e positivamente associada à probabilidade de adesão a ambos os acordos. Apresentamos ainda evidências de que variáveis sistêmicas são importantes e que as mudanças no sistema internacional nos últimos 30 anos são fatores importantes para explicar a adesão. / In this paper we investigate the determinants of the accession of two international patent treaties: the Paris Convention and Patent Cooperation Treaty (PCT). Through a Bayesian hierarchical model, we present evidence that domestic factors are important in predicting accession to the treaties studied. However, what factors are important depends on the type of treaty. For TCP, which is a treaty aimed at reducing transaction costs, the domestic law of patents is not important. For the Paris Convention, which limits the options in the area of patent policy, domestic law is a relevant factor. We also show that the direct gains from participating in treaties, as measured by the number of patents abroad, is an important variable and positively associated with the likelihood of ratification to both agreements. We also present evidence that systemic variables are important and that changes in the international system over the past 30 years are important factors to explain the membership to the treaties.

Many researchers have highlighted the dire prospects for biodiversity in fragmented agricultural landscapes and stressed the need for increasing the area of, and connectivity between, natural ecosystems. Some have advocated the use of naturally regenerating forest ecosystems for sequestering atmospheric carbon, with opportunities for dual restoration and carbon benefits. However, no studies have explicitly explored the feasibility of obtaining such dual benefits from a regenerating woody ecosystem. This thesis aims to provide a detailed assessment of the restoration and carbon potential of Brigalow regrowth, an extensive naturally regenerating ecosystem throughout the pastoral regions of north eastern Australia. It combines observational, experimental and modelling techniques to describe the agricultural legacy of pastoral development, identify constraints to restoration and explore methods to remove these constraints. A review of existing ecological knowledge of Brigalow ecosystems is provided in chapter 3, along with discussion of policy and socio-economic issues that are likely to influence how and to what extent regrowth is utilised for restoration and carbon purposes in the Brigalow Belt. The review found restoring regrowth is likely to have benefits for a wide range of native flora and fauna, including the endangered bridled nailtail wallaby. Knowledge gaps exist relating to the landscape ecology of Brigalow regrowth and the impacts of management and climate change on carbon and restoration potential. Also, a conflict exists between short-term carbon sequestration and long-term restoration goals. Regional demand for high biomass regrowth as a carbon offset is likely to be high but ambiguities in carbon policy threaten to diminish the use of natural regrowth for reforestation projects. A large cross-sectional study of regrowth is presented in chapter 4. Data were analysed using multi-level / hierarchical Bayesian models (HBMs). Firstly, we found that repeated attempts at clearing Brigalow regrowth increases stem densities and densities remain high over the long term, particularly in high rainfall areas and on clay soils with deep gilgais. Secondly, higher density stands have slower biomass accumulation and structural development in the long term. Spatial extrapolations of the HBMs indicated that the central and eastern parts of the study region are most environmentally suitability for biomass accumulation, however these may not correspond to the areas that historically supported the highest biomass Brigalow forests. We conclude that carbon and restoration goals are largely congruent within regions of similar climate. At the regional scale however, spatial prioritisation of restoration and carbon projects may only be aligned in areas with higher carbon potential. Given the importance of stem density in determining restoration and carbon potential, an experimental thinning trial was established in dense Brigalow regrowth in southern Queensland (chapter 5). Four treatments were applied in a randomised block design and growth and mortality of a subset of stems was monitored for two years. Data were analysed using mixed-effects models and HBMs and the latter were subsequently used to parameterise an individual-based simulation model of stand structural development and biomass accumulation over 50 years. The main findings of this study were that growth and mortality of stems is influenced by the amount of space available to each stem (a neighbourhood effect) and that thinning accelerates structural development and increases woody species diversity. The examination of neighbourhood effects is taken further by considering drought-related mortality in a Eucalyptus savanna ecosystem (chapter 6). For this work a multi-faceted approach was employed including spatial pattern analyses and statistical models of stem survival to test three competing hypotheses relating to neighbourhood effects on drought related tree mortality. The main finding of this study was that neighbour density and microsite effects both influence drought-related mortality and the observed patterns can readily be explained by an interaction between these two factors. As a whole, this thesis contributes the following scientific insights: (1) restoration and carbon goals may be aligned for naturally regenerating woody ecosystems, but the degree of goal congruence will vary across the landscape in question, (2) while some woody ecosystems retain an excellent capacity to regenerate naturally, the agricultural legacy may still have long term effects on restoration and carbon potential, (3) neighbourhood effects that operate at the stem scale strongly influence dynamics at the ecosystem scale.

Hierarchical Bayesian Models and Matrix factorization methods provide an unsupervised way to learn latent components of data from the grouped or sequence data. For example, in document data, latent component corn-responds to topic with each topic as a distribution over a note vocabulary of words. For many applications, there exist sparse relationships between the domain entities and the latent components of the data. Traditional approaches for topic modelling do not take into account these sparsity considerations. Modelling these sparse relationships helps in extracting relevant information leading to improvements in topic accuracy and scalable solution. In our thesis, we explore these sparsity relationships for di errant applications such as text segmentation, topical analysis and entity resolution in dyadic data through the Bayesian and Matrix tri-factorization approaches, propos-in scalable solutions. In our rest work, we address the problem of segmentation of a collection of sequence data such as documents using probabilistic models. Existing state-of-the-art Hierarchical Bayesian Models are connected to the notion of Complete Exchangeability or Markov Exchangeability. Bayesian Nonpareil-metric Models based on the notion of Markov Exchangeability such as HDP-HMM and Sticky HDP-HMM, allow very restricted permutations of latent variables in grouped data (topics in documents), which in turn lead to com-mutational challenges for inference. At the other extreme, models based on Complete Exchangeability such as HDP allow arbitrary permutations within each group or document, and inference is significantly more tractable as a result, but segmentation is not meaningful using such models. To over-come these problems, we explored a new notion of exchangeability called Block Exchangeability that lies between Markov Exchangeability and Com-plate Exchangeability for which segmentation is meaningful, but inference is computationally less expensive than both Markov and Complete Exchange-ability. Parametrically, Block Exchangeability contains sparser number of transition parameters, linear in number of states compared to the quadratic order for Markov Exchangeability that is still less than that for Complete Exchangeability and for which parameters are on the order of the number of documents. For this, we propose a nonparametric Block Exchangeable model (BEM) based on the new notion of Block Exchangeability, which we have shown to be a superclass of Complete Exchangeability and subclass of Markov Exchangeability. We propose a scalable inference algorithm for BEM to infer the topics for words and segment boundaries associated with topics for a document using the collapsed Gibbs Sampling procedure. Empirical results show that BEM outperforms state-of-the-art nonparametric models in terms of scalability and generalization ability and shows nearly the same segmentation quality on News dataset, Product review dataset and on a Synthetic dataset. Interestingly, we can tune the scalability by varying the block size through a parameter in our model for a small trade-o with segmentation quality. In addition to exploring the association between documents and words, we also explore the sparse relationships for dyadic data, where associations between one pair of domain entities such as (documents, words) and as-associations between another pair such as (documents, users) are completely observed. We motivate the analysis of such dyadic data introducing an additional discrete dimension, which we call topics, and explore sparse relation-ships between the domain entities and the topic, such as of user-topic and document-topic respectively. In our second work, for this problem of sparse topical analysis of dyadic data, we propose a formulation using sparse matrix tri-factorization. This formulation requires sparsity constraints, not only on the individual factor matrices, but also on the product of two of the factors. To the best of our knowledge, this problem of sparse matrix tri-factorization has not been stud-ide before. We propose a solution that introduces a surrogate for the product of factors and enforces sparsity on this surrogate as well as on the individual factors through L1-regularization. The resulting optimization problem is e - cogently solvable in an alternating minimization framework over sub-problems involving individual factors using the well-known FISTA algorithm. For the sub-problems that are constrained, we use a projected variant of the FISTA algorithm. We also show that our formulation leads to independent sub-problems towards solving a factor matrix, thereby supporting parallel implementation leading to a scalable solution. We perform experiments over bibliographic and product review data to show that the proposed framework based on sparse tri-factorization formulation results in better generalization ability and factorization accuracy compared to baselines that use sparse bi-factorization. Even though the second work performs sparse topical analysis for dyadic data, ending sparse topical associations for the users, the user references with di errant names could belong to the same entity and those with same names could belong to different entities. The problem of entity resolution is widely studied in the research community, where the goal is to identify real users associated with the user references in the documents. Finally, we focus on the problem of entity resolution in dyadic data, where associations between one pair of domain entities such as documents-words and associations between another pair such as documents-users are ob.-served, an example of which includes bibliographic data. In our nil work, for this problem of entity resolution in bibliographic data, we propose a Bayesian nonparametric `Sparse entity resolution model' (SERM) exploring the sparse relationships between the grouped data involving grouping of the documents, and the topics/author entities in the group. Further, we also exploit the sparseness between an author entity and the associated author aliases. Grouping of the documents is achieved with the stick breaking prior for the Dirichlet processes (DP). To achieve sparseness, we propose a solution that introduces separate Indian Bu et process (IBP) priors over topics and the author entities for the groups and k-NN mechanism for selecting author aliases for the author entities. We propose a scalable inference for SERM by appropriately combining partially collapsed Gibbs sampling scheme in Focussed topic model (FTM), the inference scheme used for parametric IBP prior and the k-NN mechanism. We perform experiments over bibliographic datasets, Cite seer and Rexa, to show that the proposed SERM model imp-proves the accuracy of entity resolution by ending relevant author entities through modelling sparse relationships and is scalable, when compared to the state-of-the-art baseline