Abstract:One of the main subjects studied by population genetics is the Hardy-Weinberg equilibrium. In this context, this paper addresses the analysis and comparison of bayesian models used in its evaluation by the coefficient of disequilibrium. For this, it was carried out a simulation study in which the following prior distributions were considered: Dirichlet (model 1), beta -uniform step function (model 2), uniform -uniform step function (model 3) and independent uniform priors (model 4). Examples of application to … Show more
“…According to Reis (2011), it is assumed that the best Bayesian model to study Hardy-Weinberg equilibrium through the inbreeding coefficient is that which uses Dirichlet a priori distributions.…”
In population genetics, it is very common to use statistical analysis to test the Hardy-Weinberg genetic equilibrium in a given population. The classical method of approaching this problem is done through the chi-square test that often leads to the verification of the equilibrium hypothesis. In the present work, a Bayesian analysis was developed involving hypothesis testing, estimation and credibility intervals to test this balance. Data on M, MN and N blood groups from the MNS system were used on samples from two populations, one from Brazilians and one from North Americans, obtained by Beiguelman (1977). The HardyWeinberg equilibrium adhesion chi-square test was performed, where the acceptance of the Hardy-Weinberg equilibrium hypothesis was confirmed. By Bayesian analysis, the rejection of the Hardy-Weinberg equilibrium hypothesis was confirmed, mainly by the Bayes factor. Our primary concern was to develop a Bayesian technique as an alternative to testing HardyWeinberg equilibrium using the MNSs blood sample data. The result obtained may encourage researchers mainly in the field of biological sciences to practice Bayesian Methodology, as an alternative in statistical tests.
“…According to Reis (2011), it is assumed that the best Bayesian model to study Hardy-Weinberg equilibrium through the inbreeding coefficient is that which uses Dirichlet a priori distributions.…”
In population genetics, it is very common to use statistical analysis to test the Hardy-Weinberg genetic equilibrium in a given population. The classical method of approaching this problem is done through the chi-square test that often leads to the verification of the equilibrium hypothesis. In the present work, a Bayesian analysis was developed involving hypothesis testing, estimation and credibility intervals to test this balance. Data on M, MN and N blood groups from the MNS system were used on samples from two populations, one from Brazilians and one from North Americans, obtained by Beiguelman (1977). The HardyWeinberg equilibrium adhesion chi-square test was performed, where the acceptance of the Hardy-Weinberg equilibrium hypothesis was confirmed. By Bayesian analysis, the rejection of the Hardy-Weinberg equilibrium hypothesis was confirmed, mainly by the Bayes factor. Our primary concern was to develop a Bayesian technique as an alternative to testing HardyWeinberg equilibrium using the MNSs blood sample data. The result obtained may encourage researchers mainly in the field of biological sciences to practice Bayesian Methodology, as an alternative in statistical tests.
Conhecer o crescimento do tomateiro e de seus frutos, medido através do acúmulo de biomassa ao longo do tempo, são fundamentais para o manejo adequado e a detecção de problemas no desenvolvimento das culturas. Este crescimento pode ser estudado por meio de vários modelos de regressão não linear que podem ser usados para facilitar a interpretação dos processos envolvidos no sistema de produção vegetal. Entre os modelos empíricos usados frequentemente para estimar o crescimento de plantas, e seus componentes, encontra-se a função logística. Um dos métodos utilizados para estimar os parâmetros das curvas de crescimento é o método bayesiano. Este estudo teve como objetivo aplicar a metodologia bayesiana na descrição dos dados – reais e simulados - de crescimento do diâmetro de tomates, utilizando o modelo não linear logístico. Os algoritmos para o amostrador de Gibbs e o Metropolis-Hastings foram implementados utilizando-se a linguagem R. A condição de convergência das cadeias foi verificada por meio do critério de Raftery & Lewis, que está disponível no pacote BOA (“Bayesian Output Analysis”) do software R. A metodologia bayesiana mostrou-se eficiente na estimação dos parâmetros da curva de crescimento, e as estimativas mostraram-se coerentes com os valores relatados na literatura.
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