Muitas são as características quantitativas que são, significativamente, influenciadas por fatores genéticos, em geral, existem vários genes que colaboram para a variação de uma ou mais características quantitativas. As informações ausentes a respeito dos genótipos nos marcadores moleculares é um problema comum em estudo de mapeamento genético e, por conseguinte, no mapeamento dos locus que controlam estas características fenotípicas (QTL). Os dados que não foram observados ocorrem, principalmente, devido a erros de genotipagem e de marcadores não informativos. Para solucionar este problema foi utilizado o método do modelo oculto de Markov para inferir estes dados. Os métodos de acurácias evidenciaram o sucesso da aplicação desta técnica de imputa- ção. Uma vez imputado, na inferência bayesiana estes dados não serão mais tratados como uma variável aleatória resultando assim, numa redução no espaço paramétrico do modelo. Outra grande dificuldade no mapeamento de QTL se deve ao fato de que não se conhece ao certo a quantidade destes que influenciam uma dada característica, fazendo com que surjam diversos problemas, um deles é a dimensão do espaço paramétrico e, consequentemente, a obtenção da amostra a posteriori. Assim, com o objetivo de contornar este problema foi proposta a utilização do método Monte Carlo via cadeia de Markov com Saltos Reversíveis, uma vez que este permite flutuar, entre cada iteração, modelos com diferentes quantidades de parâmetros. A utilização da abordagem bayesiana permitiu detectar cinco QTL para a característica estudada. Todas as análises foram implementadas no programa estatístico R. / There are many quantitative characteristics which are significantly influenced by genetic factors, in general, there are several genes that contribute to the variation of one or more quantitative trait. The missing information about the genotypes in molecular markers is a common problem in studying genetic mapping and therefore the mapping of loci that control these phenotypic traits (QTL). The data were not observed occur mainly due to errors in genotyping and uninformative markers. To solve this problem the method of occult Markov model to infer this information was used. Techniques accuracies demonstrated the successful application of this technique of imputation. Once allocated, in the Bayesian inference this data will no longer be treated as a random variable thus resulting in a reduction in the parameter space of the model. Another great difficulty in mapping QTL is due to the fact that no one knows exactly the amount of these which influence a given characteristic, so that several problems arise, one of them is dimension of the parameter space and, consequently, obtaining the sample a posterior. Thus, in order to solve this problem using the method via Monte Carlo Markov chain Reversible Jump was proposed, since this allows fluctuate between each iteration, models with different numbers of parameters. The use of the Bayesian approach allowed five QTL detected for the studied trait. All analyzes were implemented in the statistical software R.

Uma das informações mais importantes no mercado financeiro é a variabilidade de um ativo. Diversos modelos foram propostos na literatura com o intuito de avaliar este fenômeno. Dentre eles podemos destacar os modelos GARCH. Este trabalho propõe o uso do método Monte Carlo Hamiltoniano (HMC) para a estimação dos parâmetros do modelo GARCH univariado e multivariado. Estudos de simulação são realizados e as estimativas comparadas com o método de estimação Metropolis-Hastings presente no pacote BayesDccGarch. Além disso, compara-se os resultados do método HMC com a metodologia adotada no pacote rstan. Por fim, é realizado uma aplicação a dados reais utilizando o DCC-GARCH bivariado e os métodos de estimação HMC e Metropolis-Hastings. / One of the most important informations in financial market is variability of an asset. Several models have been proposed in literature with a view of to evaluate this phenomenon. Among them we have the GARCH models. This paper use Hamiltonian Monte Carlo (HMC) methods for estimation of parameters univariate and multivariate GARCH models. Simulation studies are performed and the estimatives compared with Metropolis-Hastings methods of the BayesDcc- Garch package. Also, we compared the results of HMC method with the methodology present in rstan package. Finally, a application with real data is performed using bivariate DCC-GARCH and the methods of estimation HMC and Metropolis-Hastings.

Muitas são as características quantitativas que são, significativamente, influenciadas por fatores genéticos, em geral, existem vários genes que colaboram para a variação de uma ou mais características quantitativas. As informações ausentes a respeito dos genótipos nos marcadores moleculares é um problema comum em estudo de mapeamento genético e, por conseguinte, no mapeamento dos locus que controlam estas características fenotípicas (QTL). Os dados que não foram observados ocorrem, principalmente, devido a erros de genotipagem e de marcadores não informativos. Para solucionar este problema foi utilizado o método do modelo oculto de Markov para inferir estes dados. Os métodos de acurácias evidenciaram o sucesso da aplicação desta técnica de imputa- ção. Uma vez imputado, na inferência bayesiana estes dados não serão mais tratados como uma variável aleatória resultando assim, numa redução no espaço paramétrico do modelo. Outra grande dificuldade no mapeamento de QTL se deve ao fato de que não se conhece ao certo a quantidade destes que influenciam uma dada característica, fazendo com que surjam diversos problemas, um deles é a dimensão do espaço paramétrico e, consequentemente, a obtenção da amostra a posteriori. Assim, com o objetivo de contornar este problema foi proposta a utilização do método Monte Carlo via cadeia de Markov com Saltos Reversíveis, uma vez que este permite flutuar, entre cada iteração, modelos com diferentes quantidades de parâmetros. A utilização da abordagem bayesiana permitiu detectar cinco QTL para a característica estudada. Todas as análises foram implementadas no programa estatístico R. / There are many quantitative characteristics which are significantly influenced by genetic factors, in general, there are several genes that contribute to the variation of one or more quantitative trait. The missing information about the genotypes in molecular markers is a common problem in studying genetic mapping and therefore the mapping of loci that control these phenotypic traits (QTL). The data were not observed occur mainly due to errors in genotyping and uninformative markers. To solve this problem the method of occult Markov model to infer this information was used. Techniques accuracies demonstrated the successful application of this technique of imputation. Once allocated, in the Bayesian inference this data will no longer be treated as a random variable thus resulting in a reduction in the parameter space of the model. Another great difficulty in mapping QTL is due to the fact that no one knows exactly the amount of these which influence a given characteristic, so that several problems arise, one of them is dimension of the parameter space and, consequently, obtaining the sample a posterior. Thus, in order to solve this problem using the method via Monte Carlo Markov chain Reversible Jump was proposed, since this allows fluctuate between each iteration, models with different numbers of parameters. The use of the Bayesian approach allowed five QTL detected for the studied trait. All analyzes were implemented in the statistical software R.

Orientador: Verónica Andrea González-Lopez / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T10:24:16Z (GMT). No. of bitstreams: 1 Schultz_JoseAdolfodeAlmeida_M.pdf: 781903 bytes, checksum: 6f13c49a1d8a278498ea105b9b9a7a31 (MD5) Previous issue date: 2011 / Resumo: O resumo poderá ser visualizado no texto completo da tese digital / Abstract: The abstract is available with the full electronic digital document / Mestrado / Inferencia Bayesiana / Mestre em Estatística

Neste trabalho analisa-se a relevância de saltos no apreçamento de derivativos de commodities através da comparação de dois modelos. O primeiro leva em consideração um convenience yield com reversão à média, enquanto o segundo é uma generalização do primeiro com saltos no preço à vista. Ambos os modelos são estimados por meio de uma abordagem Bayesiana, sendo as distribuições a posteriori simuladas com o uso de técnincas da família MCMC. Dados de petróleo, trigo e cobre são utilizados para fins de estimação. A análise econométrica indica significância estatística para saltos, mas não encontrou-se evidência significativa de que saltos melhoram o apreçamento de derivativos. / In this work we analyze the relevance of jumps in the pricing of commodity contingent claims by comparing two models. The first takes into account mean-reverting convenience yields, and the second is a generalization of the first with jumps in spot prices. Both models were estimated using a Bayesian approach, and posterior distributions where simulated using MCMC techniques. Oil, copper and wheat data where used for estimation proposes. Econometric analysis indicates statistical significance for jumps, but we found no strong evidence that jumps improve derivative pricing.

A assimetria de informação no sistema de saúde é um tema que ultrapassa o interesse apenas das empresas operadoras de seguro de saúde, de políticas públicas e de pesquisa acadêmica. O presente estudo analisa como os contratos de cosseguro influenciam os fenômenos do risco moral e da seleção adversa presentes nos planos de saúde e sua relação com a demanda de serviços médicos. Neste contexto, analisar a assimetria de informação no sistema de saúde se torna relevante por oferecer uma resposta consistente, que poderá embasar tanto as políticas públicas, quanto a forma de comercialização dos planos pelas empresas. Esse trabalho, a partir da Pesquisa Nacional por Amostra de Domicílios - PNAD 2003, procura observar a eficiência do contrato cosseguro como um mecanismo de mitigação de assimetria de informação, ou seja, excluídos os efeitos dos riscos associados ao indivíduo, se a diferença de contrato altera o comportamento dos agentes. Para atingir esse resultado foi proposto um método para testar a assimetria de informação utilizando o método de Monte Carlo. Os resultados sugerem que os contratos de cosseguros foram eficientes nos planos individuais, enquanto nos planos coletivos sua influência pode ser descartada. Por fim, o trabalho aponta que é mais eficiente, pelo bemestar social, a utilização de cosseguro para os contratos individuais, enquanto para os contratos coletivos são mais eficiente os contratos sem cosseguro. / Asymmetric information in the health care system is a topic of interest for medical insurance, policy makers and scholars. This research analyses how the contracts of coinsurance motivate the moral hazard and adverse selection phenomenon and consequences in medical services demand. In this context, the analysis of asymmetric information in the health care system provides support for the design of public policy and insurance plans. This research aims to estimate a structural model of health insurance and health care choices, using the 2003 National Household Sample Survey PNAD. It tested whether coinsurance contracts can work as efficient mechanisms to reduce risks related to asymmetric information. A methodological procedure using the Monte Carlo method was proposed to test for asymmetric information issues. The research suggests that coinsurance contracts were beneficial for individual plans, from a social welfare perspective. For the group plans, the benefit was not supported

Neste trabalho está sendo proposto uma abordagem bayesiana para resolver o problema de inferência com restrição nos parâmetros para os modelos de Petterson, Prodan, Stofel e Curtis, utilizados para representar a relação hipsométrica em clones de Eucalyptus sp. Consideramos quatro diferentes densidades de probabilidade a priori, entre as quais, a densidade a priori não informativa de Jeffreys, a densidade a priori vaga normal flat, uma densidade a priori construída empiricamente e a densidade a priori potência. As estimativas bayesianas foram calculadas com a técnica de simulação de Monte Carlo em Cadeia de Markov (MCMC). Os métodos propostos foram aplicados em vários conjuntos de dados reais e os resultados foram comparados aos obtidos com os estimadores de máxima verossimilhança. Os resultados obtidos com as densidades a priori não informativa e vaga foram semelhantes aos resultados encontrados com os estimadores de máxima verossimilhança, porém, para vários conjuntos de dados, as estimativas não apresentaram coerência biológica. Por sua vez, as densidades a priori informativas empírica e a priori potência sempre produziram resultados coerentes biologicamente, independentemente do comportamento dos dados na parcela, destacando a superioridade desta abordagem / In this work we propose a Bayesian approach to solve the inference problem with restriction on parameters for the models of Petterson, Prodan, Stofel and Curtis used to represent the hypsometric relationship in clones of Eucalyptus sp. We consider four different prior probability densities, the non informative Jeffreys prior, a vague prior with flat normal probability density, a prior constructed empirically and a power prior density. The Bayesian estimates were calculated using the Monte Carlo Markov Chain (MCMC) simulation technique. The proposed methods were applied to several real data sets and the results were compared to those obtained with the maximum likelihood estimators. The results obtained with a non informative prior and prior vague showed similar results to those found with the maximum likelihood estimators, but, for various data sets, the estimates did not show biological coherence. In turn, the methods a prior empirical informative and a prior power, always produce biologically consistent results, regardless of the behavior of the data in the plot, highlighting the superiority of this approach

The history of populations or species is of fundamental importance in a variety of areas. Gaining details about demographic, cultural, climatic or political aspects of the past may provide insights that improve the understanding of how populations have evolved over time and how they may evolve in future. Different types of resources can be informative about different periods of time. One especially important resource is genetic data, either from a single individual or a group of organisms. Environmental conditions and circumstances can directly affect the existence and success of a group of individuals. Since genetic material gets passed on from generation to generation, traces of past events can still be detected in today\''s genetic data. For many decades scientists have tried to understand the principles of how external influences can directly affect the appearance and features of populations, leading to theoretical models that can interpret modern day genetic variation in the light of past events. Among other influencing factors like migration, natural selection etc., population size changes can have a great impact on the genetic diversity of a group of organisms. For example, in the field of conservation biology, gaining insights into how the size of a population evolves may assist in detecting past or ongoing temporal reductions of population size. This seems crucial since the reduction in size also correlates with a reduction in genetic diversity which in turn might negatively affect the evolutionary potential of a population. Using computational and population genetics methods, sequences from whole genomes can be scanned for traces of such events and therefore assist in new interpretations of historical details of populations or groups of interest. This thesis focuses on the detection and interpretation of past population size changes. Two approaches to infer particular parameters from underlying demographic models are described. The first part of this thesis introduces two summary statistics which were designed to detect fluctuations in size from genome-wide Single Nucleotide Polymorphism (SNP) data. Demographic inferences from such data are inherently complicated due to recombination and ascertainment bias. Hence, two new statistics are introduced: allele frequency-identity by descent (AF-IBD) and allele frequency-identity by state (AF-IBS). Both make use of linkage disequilibrium information and exhibit defined relationships to the time of the underlying mathematical process. A fast and efficient Approximate Bayesian Computation framework based on AF-IBD and AF-IBS is constructed that can accurately estimate demographic parameters. These two statistics were tested for the biasing effects of hidden recombination events, ascertainment bias and phasing errors. The statistics were found to be robust to a variety of these tested biases. The inference approach was then applied to genome-wide SNP data to infer the demographic histories of two human populations: (i) Yoruba from Africa and (ii) French from Europe. Results suggest, that AF-IBD and AF-IBS are able to capture sufficient amounts of information from underlying data sets in order to accurately infer parameters of interest, such as the beginning, end and strength of periods of varying size. Additionally the results from empirical data suggest a rather stable ancestral population size with a mild recent expansion for Yoruba, whereas the French apparently experienced a rather long-lasting strong bottleneck followed by a drastic population growth. The second part of this thesis introduces a new way of summarizing information from the site frequency spectrum. Commonly applied site frequency spectrum based inference methods make use of allele frequency information from individual segregating sites. Our newly developed method, the 2 point spectrum, summarizes allele frequency information from all possible pairs of segregating sites, thereby increasing the number of potentially informative values from the same underlying data set. These additional information are then incorporated into a Markov Chain Monte Carlo framework. This allows for a high degree of flexibility and implements an efficient method to infer population size trajectories over time. We tested the method on a variety of different simulated data sets from underlying demographic models. Furthermore, we compared the performance and accuracy of our method to already established methods like PSMC and diCal. Results indicate that this non-parametric 2 point spectrum method can accurately infer the extent and times of past population size changes and therefore correctly estimates the history of temporal size fluctuations. Furthermore, the initial results suggest that the amount of required data and the accuracy of the final results are comparable with other publicly available non-parametric methods. An easy to use command line program was implemented and will be made publicly available. In summary, we introduced three highly sensitive summary statistics and proposed different approaches to infer parameters from demographic models of interest. Both methods provide powerful frameworks for accurate parameter inference from genome-wide genetic data. They were tested for a variety of demographic models and provide highly accurate results. They may be used in the settings as described above or incorporated into already existing inference frameworks. Nevertheless, the statistics should prove useful for new insights into populations, especially those with complex demographic histories.

Feature selection is demanded in many modern scientific research problems that use high-dimensional data. A typical example is to find the genes that are most related to a certain disease (e.g., cancer) from high-dimensional gene expression profiles. There are tremendous difficulties in eliminating a large number of useless or redundant features. The expression levels of genes have structure; for example, a group of co-regulated genes that have similar biological functions tend to have similar mRNA expression levels. Many statistical methods have been proposed to take the grouping structure into consideration in feature selection and regression, including Group LASSO, Supervised Group LASSO, and regression on group representatives. In this thesis, we propose to use a sophisticated Markov chain Monte Carlo method (Hamiltonian Monte Carlo with restricted Gibbs sampling) to fit T-probit regression with heavy-tailed priors to make selection in the features with grouping structure. We will refer to this method as fully Bayesian T-probit. The main feature of fully Bayesian T-probit is that it can make feature selection within groups automatically without a pre-specification of the grouping structure and more efficiently discard noise features than LASSO (Least Absolute Shrinkage and Selection Operator). Therefore, the feature subsets selected by fully Bayesian T-probit are significantly more sparse than subsets selected by many other methods in the literature. Such succinct feature subsets are much easier to interpret or understand based on existing biological knowledge and further experimental investigations. In this thesis, we use simulated and real datasets to demonstrate that the predictive performances of the more sparse feature subsets selected by fully Bayesian T-probit are comparable with the much larger feature subsets selected by plain LASSO, Group LASSO, Supervised Group LASSO, random forest, penalized logistic regression and t-test. In addition, we demonstrate that the succinct feature subsets selected by fully Bayesian T-probit have significantly better predictive power than the feature subsets of the same size taken from the top features selected by the aforementioned methods.

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