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

Orientador: Henrique Nunes Gonçalves / Resumo: Foi utilizada uma análise de segregação com o uso da inferência Bayesiana para se verificar a presença de genes de efeito principal (GEP) afetando duas características de carcaça: gordura intramuscular em % (GIM) e espessura de toucinho em mm (ET); e uma de crescimento, ganho de peso (g/dia) no período entre 25 a 90 kg de peso vivo (GP). Para este estudo foram usadas informações de 1.257 animais provenientes de um experimento de cruzamento de suínos machos da raça Meishan (raça chinesa) e fêmeas de linhagens holandesas de Large White e Landrace. No melhoramento genético animal, Modelos Poligênicos Finitos (MPF) podem ser uma alternativa a Modelos Poligênicos Infinitesimais (MPI) para avaliação genética de características quantitativas usando pedigris complexos. MPI, MPF e MPI combinado com MPF, foram empiricamente testados para estimar componentes de variâncias e número de genes no MPF. Para a estimação de médias marginais a posteriori de componentes de variância e parâmetros foi usado uma metodologia Bayesiana, através do uso da Cadeia de Markov, algoritmos de Monte Carlo (MCMC), via Amostrador de Gibbs e "Reversible Jump Sampler (Metropolis-Hastings)". Em função dos resultados obtidos, pode-se evidenciar quatro GEP, isto é, dois para GIM e dois para ET. Para ET, o GEP explicou a maior parte da variação genética, enquanto para GIM, o GEP reduziu significativamente a variação poligênica. Para a variação do GP não foi possível determinar a influência do GEP. As herdabilidades estimadas para GIM, ET e GP foram de 0,37, 0,24 e 0,37 respectivamente. A metodologia Bayesiana foi implementada satisfatoriamente usando o pacote computacional FlexQTLTM. Estudos futuros baseados neste experimento que usem marcadores moleculares para mapear os genes de efeito principal que afetem, principalmente GIM e ET, poderão lograr êxito. / Abstract: A Bayesian marker-free segregation analysis was applied to search for evidence of segregation genes affecting two carcass traits: Intramuscular Fat in % (IMF) and Backfat Thickness in mm (BF), and one growth trait: Liveweight Gain from approximately 25 to 90 kg liveweight, in g/day (LG). For this study 1257 animals from an experimental cross between pigs Meishan (male) and Dutch Large White and Landrace lines (female) were used. In animal breeding, Finite Polygenic Models (FPM) may be an alternative to the Infinitesimal Polygenic Model (IPM) for genetic evaluation of pedigree multiple-generations populations for multiple quantitative traits. FPM, IPM and FPM combined with IPM were empirically tested for estimation of variance components and number of genes in the FPM. Estimation of marginal posteriori means of variance components and parameters was performed by use Markov Chain Monte Carlo techniques by use of the Gibbs sampler and the reversible Jump sampler (Metropolis-Hastings). The results showed evidence for four Major Genes (MG), i.e., two for IMF and two BF. For BF, the MG explained almost all of the genetic variance while for IMF, the MG reduced the polygenic variance significantly. For LG was not found to be likely influenced by MG. The polygenic heritability estimates for IMF, BF and LG were 0.37, 0.24 and 0.37 respectively. The Bayesian methodology was satisfactorily implemented in the software package FlexQTLTM. Further molecular genetic research, based on the same experimental data, effort to map single genes affecting, mainly IMF and BF, has a high probability of success. / Doutor

Multivariate ordinal response data, such as severity of pain, degree of disability, and satisfaction with a healthcare provider, are prevalent in many areas of research including public health, biomedical, and social science research. Ignoring the multivariate features of the response variables, that is, by not taking the correlation between the errors across models into account, may lead to substantially biased estimates and inference. In addition, such multivariate ordinal outcomes frequently exhibit a high percentage of zeros (zero inflation) at the lower end of the ordinal scales, as compared to what is expected under a multivariate ordinal distribution. Thus, zero inflation coupled with the multivariate structure make it difficult to analyze such data and properly interpret the results. Methods that have been developed to address the zero-inflated data are limited to univariate-logit or univariate-probit model, and extension to bivariate (or multivariate) probit models has been very limited to date. In this research, a latent variable approach was used to develop a Mixture Bivariate Zero-Inflated Ordered Probit (MBZIOP) model. A Bayesian MCMC technique was used for parameter estimation. A simulation study was then conducted to compare the performances of the estimators of the proposed model with two existing models. The simulation study suggested that for data with at least a moderate proportion of zeros in bivariate responses, the proposed model performed better than the comparison models both in terms of lower bias and greater accuracy (RMSE). Finally, the proposed method was illustrated with a publicly-available drug-abuse dataset to identify highly probable predictors of: (i) being a user/nonuser of marijuana, cocaine, or both; and (ii), conditional on user status, the level of consumption of these drugs. The results from the analysis suggested that older individuals, smokers, and people with a prior criminal background have a higher risk of being a marijuana only user, or being the user of both drugs. However, cocaine only users were predicted on the basis of being younger and having been engaged in the criminal-justice system. Given that an individual is a user of marijuana only, or user of both drugs, age appears to have an inverse effect on the latent level of consumption of marijuana as well as cocaine. Similarly, given that a respondent is a user of cocaine only, all covariates--age, involvement in criminal activities, and being of black race--are strong predictors of the level of cocaine consumption. The finding of older age being associated with higher drug consumption may represent a survival bias whereby previous younger users with high consumption may have been at elevated risk of premature mortality. Finally, the analysis indicated that blacks are likely to use less marijuana, but have a higher latent level of cocaine given that they are user of both drugs.

Dissertação(mestrado) - Universidade Federal do Rio Grande, Programa de Pós–Graduação em Oceanografia Biológica, Instituto de Oceanografia, 2013. / Submitted by Cristiane Gomides (cristiane_gomides@hotmail.com) on 2013-11-19T12:52:38Z No. of bitstreams: 1 florencia.pdf: 2100442 bytes, checksum: 41f46ff0b9c28e5fa20e9fad129e691f (MD5) / Approved for entry into archive by Angelica Miranda (angelicacdm@gmail.com) on 2013-11-20T21:43:14Z (GMT) No. of bitstreams: 1 florencia.pdf: 2100442 bytes, checksum: 41f46ff0b9c28e5fa20e9fad129e691f (MD5) / Made available in DSpace on 2013-11-20T21:43:14Z (GMT). No. of bitstreams: 1 florencia.pdf: 2100442 bytes, checksum: 41f46ff0b9c28e5fa20e9fad129e691f (MD5) Previous issue date: 2013 / O tubarão anequim Isurus oxyrinchus é uma espécie frequente na captura incidental da pesca oceânica de espinhel no Atlântico Sul. Apesar disso, estudos de idade e crescimento não têm sido realizados para a espécie na região. O presente estudo forneceu as primeiras estimativas de idade e crescimento do tubarão anequim no Atlântico Sudoeste através da análise de secções vertebrais de 245 exemplares (126 fêmeas, 116 machos e 3 com sexo indeterminado), com uma amplitude de tamanhos de 78 a 330 cm de comprimento furcal (CF). A relação entre o raio da vértebra e o CF foi linear. As análises do incremento marginal não foram conclusivas em relação à periodicidade de formação das bandas de crescimento na área do estudo. Assumindo uma periodicidade anual (uma banda de crescimento por ano), a amplitude de idades estimada foi de 0 a 28 anos. O modelo de crescimento de Schnute, escolhido por sua flexibilidade e ajustado sob uma abordagem bayesiana, forneceu uma boa descrição do crescimento individual para ambos os sexos até os 15 anos de idade. O crescimento no primeiro ano de vida foi 33.9 cm (ICr95% = 19.9 – 40.8) para as fêmeas e 30.5 cm (ICr95% = 25.6 - 35.4) para os machos. Até aproximadamente 15 anos de idade, fêmeas e machos apresentaram crescimento semelhante, atingindo ~217 cm CF. A forma sigmoide que apresentaram as curvas de crescimento de ambos os sexos indicou que existe uma mudança no padrão de crescimento em torno dos 7 anos de idade. Os resultados inconclusivos sobre a periodicidade na deposição das bandas de crescimento na área de estudo fazem com que seja necessária a aplicação de técnicas mais robustas de validação no futuro. Enquanto isso, uma abordagem preventiva que assuma um padrão de deposição anual no Atlântico Sudoeste pode ser utilizada para a avaliação e manejo dos estoques dessa espécie, caracterizada por uma baixa fertilidade e uma maturidade tardia. / The shortfin mako shark Isurus oxyrinchus is a frequent by-catch species in oceanic longline fisheries in the South Atlantic. Despite this, no age and growth studies have been conducted for the species in the region. This study provided the first age and growth estimates of female and male shortfin mako sharks from the western South Atlantic through the analysis of vertebral sections of 245 specimens (126 females, 116 males and 3 with undetermined sex), ranging in size from 78 to 330 cm fork length (FL). A significant linear relationship was found between FL and vertebral radius for sexes combined. Marginal increment analyses were inconclusive about periodicity of growth band deposition and an annual periodicity (one growth band per year) was assumed to make age estimations. Specimens were estimated to be between 0 and 28 years of age. The Schnute growth model (SGM), chosen for its flexibility and fitted with a Bayesian approach, provided a good description of the individual growth for both sexes up to 15 years of age. Shortfin mako growth during the first year of life was 33.9 cm (ICr95% = 19.9 – 40.8) for females and 30.5 cm (ICr95% = 25.6 - 35.4) for males. Until approximately 15 years of age, both sexes showed similar growth and reached ~217 cm FL. Sigmoid shaped growth curves obtained for both sexes indicated a change in the growth pattern close to 7 years of age. Inconclusive results about periodicity of growth band deposition in the study area make necessary the application of more robust validation techniques in the future. Meanwhile, a precautionary approach that assumes an annual deposition pattern in the western South Atlantic can be used for the assessment and management of stocks of this species, characterized by low fecundity and late maturity.

En Europe, la France est située entre des zones à haut et bas risque de Sclérose en Plaques (SEP).Nous avons estimé la prévalence de la SEP en France au 31 octobre 2004 et l’incidence entre 2000 et 2007 à partir des données de la Caisse Nationale d’Assurance Maladie des Travailleurs Salariés (CNAMTS) qui assure 87 % de la population. La SEP, comme d’autres maladies chroniques, fait partie des affections de longue durée (ALD). Les variations géographiques de la prévalence et de l’incidence ont été analysées par un modèle Bayesien.La prévalence standardisée sur l’âge était de 94,7 pour 100 000 ; 130,5 pour les femmes ; 54,8 pour les hommes. Le taux de notification de SEP (2000-2007) standardisé sur la population Européenne était de 6,8 pour 100 000 ; 9,8 parmi les femmes et 3,7 parmi les hommes. Avec le modèle Bayesien, la prévalence était plus forte au nord-est et plus faible dans la région parisienne et sur la Côte d’Azur. L’incidence était également plus forte au nord-est mais plus faible sur la côte atlantique et de part et d’autre du Rhône.A partir des autres ALD, les comorbidités survenant avant l’ALD SEP ont été étudiées. Elles étaient rares et essentiellement représentées par les troubles psychiatriques (40,2%) et le diabète (20,3%). Cette étude a été réalisée parmi une population représentative avec une seule et même méthodologie. Le modèle Bayesien prenant en compte l’hétérogénéité et l’auto-corrélation spatiales ne confirme pas l’existence d’un gradient net mais des zones à sur ou sous risque. La meilleure connaissance de l’épidémiologie de la SEP permettra d’avancer sur ses facteurs étiologiques. / In Europe, France is located between high and low risk areas of Multiple Sclerosis (MS). We estimated the national prevalence of MS in France on 31st October 2004 and the incidence between 2000 and 2007 based on data from the ‘Caisse Nationale d’Assurance Maladie des Travailleurs Salariés’ which insures 87% of the population. MS like other chronic diseases is one of the 30 long-term illnesses (Affections de Longue Durée, ALD). We analysed geographic variations in the prevalence and incidence of MS in France using the Bayesian approach.Total MS prevalence in France standardised for age was 94.7 per 100,000; 130.5 in women; 54.8 in men. The notification rate for MS (2000-2007) after age-standardisation according to the European population was 6.8 per 100,000; 9.8 in women and 3.7 in men. With a Bayesian approach, the prevalence of MS was higher in northeast and lower in the Paris area and on the Mediterranean coast. The notification rate was higher in northeast and lower on the Atlantic coast and in the Alps as well as on both sides of the Rhône River.The study of other chronic diseases for which ALD status was registered before MS revealed that comorbidities were rare, essentially represented by psychiatric diseases (40.2%) and diabetes (20.3%).This study is performed among a representative population using the same method throughout. The Bayesian approach which takes into account spatial heterogeneity and spatial autocorrelation did not confirm the existence of a clear gradient but only higher or lower areas of MS. The better knowledge of MS epidemiology will allow to venture hypothesis its etiological factors.

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 concept of portfolio optimization has been widely studied in the academy and implemented in the financial markets since its introduction by Markowitz 70 years ago. The problem of the mean-variance optimization framework caused by input uncertainty has been one of the foci in the previous research. In this study, several models (linear shrinkage and Black-Litterman) based on Bayesian approaches are studied to improve the estimation of inputs. Moreover, a new framework based on robust optimization is presented to mitigate the input uncertainty further.  An out-of-sample test is specially designed, and the results show that Bayesian models in this study can improve the optimization results in terms of higher Sharpe ratios (the quotient between portfolio returns and their risks). Both covariance matrix estimators based on the linear shrinkage method contain less error and provide better optimization results, i.e. higher Sharpe ratios. The Black-Litterman model with a proper choice of inputs can significantly improve the portfolio return. The new framework based on the combination of shrinkage estimators, Black-Litterman, and robust optimization presents a better way for portfolio optimization than the classical framework of mean-variance optimization.

京都大学 / 新制・課程博士 / 博士(医学) / 甲第24201号 / 医博第4895号 / 新制||医||1061(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 西浦 博, 教授 森田 智視, 教授 松村 由美 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

Background and Objectives: I investigated the use of sensitivity analyses in assessing statistical results or analytical approaches in three different statistical issues: (1) accounting for within-subject correlations in analyzing discrete choice data, (2) handling both-armed zero-event studies in meta-analyses for rare event outcomes, and (3) incorporating external information using Bayesian approach to estimate rare-event rates. Methods: Project 1: I empirically compared ten statistical models in analyzing correlated data from a discrete choice survey to elicit patient preference for colorectal cancer screening. Logistic and probit models with random-effects, generalized estimating equations or robust standard errors were applied to binary, multinomial or bivariate outcomes. Project 2: I investigated the impacts of including or excluding both-armed zero-event studies on pooled odds ratios for classical meta-analyses using simulated data. Five commonly used pooling methods: Peto, Mantel-Haenszel fixed/random effects and inverse variance fixed/random effects, were compared in terms of bias and precision. Project 3: I explored the use of Bayesian approach to incorporate external information through priors to verify, enhance or modify the study evidence. Three study scenarios were derived from previous studies to estimate inhibitor rates for hemophilia A patients treated with rAHF-PFM: 1) a single cohort of previously treated patients, 2) individual patient data meta-analysis, and 3) an previously unexplored patient population with limited data. Results and Conclusion: Project 1: When within-subject correlations were substantial, the results from different statistical models were inconsistent. Project 2: Including both-armed zero-event studies in meta-analyses increased biases for pooled odd ratios when true treatment effects existed. Project 3: Through priors, Bayesian approaches effectively incorporated different types of information to strengthen or broaden research evidence. Through this thesis I demonstrated that when analyzing complicated health research data, it was important to use sensitivity analyses to assess the robustness of analysis results or proper choice of statistical models. / Dissertation / Doctor of Philosophy (PhD)

Classifying individuals into binary disease categories can be challenging due to complex relationships across different exposures of interest. In this thesis, we investigate three different approaches for disease classification using multiple biomarkers. First, we consider combining information from literature reviews and INTERHEART data set to identify the threshold of ApoB, ApoA1 and the ratio of these two biomarkers to classify individuals at risk of developing myocardial infarction. We develop a Bayesian estimation procedure for this purpose that utilizes the conditional probability distribution of these biomarkers. This method is flexible compared to standard logistic regression approach and allows us to identify a precise threshold of these biomarkers. Second, we consider the problem of disease classification using two dependent biomarkers. An independently identified threshold for this purpose usually leads to a conflicting classification for some individuals. We develop and describe a method of determining the joint threshold of two dependent biomarkers for a disease classification, based on the joint probability distribution function constructed through copulas. This method will allow researchers uniquely classify individuals at risk of developing the disease. Third, we consider the problem of classifying an outcome using a gene and miRNA expression data sets. Linear principal component analysis (PCA) is a widely used approach to reduce the dimension of such data sets and subsequently use it for classification, but many authors suggest using kernel PCA for this purpose. Using real and simulated data sets, we compare these two approaches and assess the performance of components towards genetic data integration for an outcome classification. We conclude that reducing dimensions using linear PCA followed by a logistic regression model for classification seems to be acceptable for this purpose. We also observe that integrating information from multiple data sets using either of these approaches leads to a better performance of an outcome classification. / Thesis / Doctor of Philosophy (PhD)