Traditional phylogenetic inference assumes that the history of a set of taxa can be explained by a tree. This assumption is often violated as some biological entities can exchange genetic material giving rise to non-treelike events often called reticulations. Failure to consider these events might result in incorrectly inferred phylogenies, and further consequences, for example stagnant and less targeted drug development. Phylogenetic networks provide a flexible tool which allow us to model the evolutionary history of a set of organisms in the presence of reticulation events. In recent years, a number of methods addressing phylogenetic network reconstruction and evaluation have been introduced. One of suchmethods has been proposed byMoret et al. (2004). They defined a phylogenetic network as a directed acyclic graph obtained by positing a set of edges between pairs of the branches of an underlying tree to model reticulation events. Recently, two works by Jin et al. (2006), and Snir and Tuller (2009), respectively, using this definition of phylogenetic network, have appeared. Both works demonstrate the potential of using maximum likelihood estimation for phylogenetic network reconstruction. We propose a Bayesian approach to the estimation of phylogenetic network parameters. We allow for different phylogenies to be inferred at different parts of our DNA alignment in the presence of reticulation events, at the species level, by using the idea that a phylogenetic network can be naturally decomposed into trees. A Markov chainMonte Carlo algorithmis provided for posterior computation of the phylogenetic network parameters. Also a more general algorithm is proposed which allows the data to dictate how many phylogenies are required to explain the data. This can be achieved by using stochastic search variable selection. Both algorithms are tested on simulated data and also demonstrated on the ribosomal protein gene rps11 data from five flowering plants. The proposed approach can be applied to a wide variety of problems which aim at exploring the possibility of reticulation events in the history of a set of taxa.

Submitted by EDISON AMERICO HUARSAYA TITO (edison.tito@gmail.com) on 2016-06-23T14:02:55Z No. of bitstreams: 1 EdisonMscFGV(20160619).pdf: 2366030 bytes, checksum: 231be2cde1e7f8e01331fddff3f227a1 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2016-06-23T14:36:07Z (GMT) No. of bitstreams: 1 EdisonMscFGV(20160619).pdf: 2366030 bytes, checksum: 231be2cde1e7f8e01331fddff3f227a1 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2016-06-24T12:51:11Z (GMT) No. of bitstreams: 1 EdisonMscFGV(20160619).pdf: 2366030 bytes, checksum: 231be2cde1e7f8e01331fddff3f227a1 (MD5) / Made available in DSpace on 2016-06-29T12:06:48Z (GMT). No. of bitstreams: 1 EdisonMscFGV(20160619).pdf: 2366030 bytes, checksum: 231be2cde1e7f8e01331fddff3f227a1 (MD5) Previous issue date: 2016-06-03 / This work has the objective to address the problem of asset allocation (portfolio analysis) under a Bayesian perspective. For this it was necessary to review all the theoretical analysis of the classical mean-variance model and following identify their deficiencies that compromise its effectiveness in real cases. Interestingly, its biggest deficiency this not related to the model itself, but by its input data in particular the expected return calculated on historical data. To overcome this deficiency the Bayesian approach (Black-Litterman model) treat the expected return as a random variable and after that builds a priori distribution (based on the CAPM model) and a likelihood distribution (based on market investor’s views) to finally apply Bayes theorem resulting in the posterior distribution. The expected value of the return of this posteriori distribution is to replace the estimated expected return calculated on historical data. The results showed that the Bayesian model presents conservative and intuitive results in relation to the classical model of mean-variance. / Este trabalho tem com objetivo abordar o problema de alocação de ativos (análise de portfólio) sob uma ótica Bayesiana. Para isto foi necessário revisar toda a análise teórica do modelo clássico de média-variância e na sequencia identificar suas deficiências que comprometem sua eficácia em casos reais. Curiosamente, sua maior deficiência não esta relacionado com o próprio modelo e sim pelos seus dados de entrada em especial ao retorno esperado calculado com dados históricos. Para superar esta deficiência a abordagem Bayesiana (modelo de Black-Litterman) trata o retorno esperado como uma variável aleatória e na sequência constrói uma distribuição a priori (baseado no modelo de CAPM) e uma distribuição de verossimilhança (baseado na visão de mercado sob a ótica do investidor) para finalmente aplicar o teorema de Bayes tendo como resultado a distribuição a posteriori. O novo valor esperado do retorno, que emerge da distribuição a posteriori, é que substituirá a estimativa anterior do retorno esperado calculado com dados históricos. Os resultados obtidos mostraram que o modelo Bayesiano apresenta resultados conservadores e intuitivos em relação ao modelo clássico de média-variância.