Spatio-temporal GAMLSS modeling of the incidence of schistosomiasis in the central region of the State of Minas Gerais, Brazil. / Modelagem GAMLSS espaçotemporal da incidência de esquistossomose na região central do Estado de Minas Gerais, Brasil.

In Brazil, millions of people live in areas with risk of schistosomiasis, a neglected chronic disease with high morbidity. The Schistosoma mansoni helminth is present in all macroregions of Brazil, including the State of Minas Gerais, one of the most endemic states. For this reason, the identification of potential foci is essential to support educational and prophylactic public policies to control this disease. This study aims to model schistosomiasis data based on spatial and temporal aspects and assess the importance of some exogenous socioeconomic variables and the presence of the main Biomphalaria species. Considering that, when working with incident cases, a discrete count variable requires an appropriate modeling, the GAMLSS modeling was chosen since it jointly considers a more appropriate distribution for the response variable due to zero inflation and spatial heteroscedasticity. Several municipalities presented high incidence values from 2010 to 2012, and a downward trend was observed until 2020. We also noticed that the distribution of incidence behaves differently in space and time. Municipalities with dams presented risk 2.25 times higher than municipalities without dams. The presence of B. glabrata was associated with the risk of schistosomiasis. On the other hand, the presence of B. straminea represented a lower risk of the disease. Thus, the control and monitoring of B. glabrata snails is essential to control and eliminate schistosomiasis; and the GAMLSS model was effective in the treatment and modeling of spatio-temporal data.

No Brasil, milhões de pessoas vivem em áreas de risco para a esquistossomose, uma doença negligenciada, de caráter crônico e com elevada morbidade. O helminto Schistosoma mansoni está presente em todas as macrorregiões, incluindo o Estado de Minas Gerais, um dos mais endêmicos. Por essa razão, a identificação de potenciais focos é fundamental para subsidiar políticas públicas de cunho educativo e profilático no controle desse desfecho. Nesse contexto, o objetivo do trabalho consiste em modelar dados de esquistossomose em relação aos aspectos espaciais e temporais, além de avaliar a importância de algumas variáveis exógenas socioeconômicas e a presença das principais espécies de Biomphalaria. Como trabalhar com casos incidentes, uma variável discreta de contagem, exige uma modelagem apropriada, foi escolhida a modelagem GAMLSS por considerar conjuntamente uma distribuição mais adequada à variável resposta devido à inflação de zeros e à heterocedasticidade espacial. Verificaram-se valores elevados de incidência em diversos municípios de 2010 a 2012 e uma tendência de queda até 2020. Também foi identificado que a distribuição da incidência se comporta de maneira diferente no espaço e no tempo. Municípios com barragem apresentaram risco 2,25 vezes maior do que os que não a continham. A presença de B. glabrata foi relacionada ao risco de ocorrência da doença. Por outro lado, a presença de B. straminea refletiu em menor risco de ocorrência da esquistossomose. Conclui-se que o controle e o acompanhamento dos caramujos da B. glabrata podem ser fundamentais para a contenção e a eliminação da esquistossomose e o modelo GAMLSS foi eficaz para tratamento e modelagem de dados espaçotemporais.

En Brasil, millones de personas viven en áreas de riesgo de esquistosomiasis, una enfermedad crónica desatendida y con alta morbilidad. El helminto Schistosoma mansoni está presente en todas las macrorregiones, incluido el Estado de Minas Gerais, uno de los más endémicos del país. Por ello, la identificación de potenciales brotes es fundamental para promover políticas públicas de carácter educativo y profiláctico en el control de este desenlace. En este contexto, el objetivo de este trabajo es modelar datos sobre esquistosomiasis con respecto a aspectos espaciotemporales, además de evaluar la importancia de algunas variables socioeconómicas exógenas y la presencia de las principales especies de Biomphalaria. Dado que en el trabajo con casos incidentes una variable de conteo discreta requiere un adecuado modelado, se eligió el modelo GAMLSS, ya que en conjunto considera una distribución más adecuada para la variable de respuesta debido a la inflación de ceros y la heterocedasticidad espacial. Se encontraron valores de alta incidencia en varios municipios en el periodo evaluado de 2010 a 2012 y una tendencia a descenso hasta 2020. También se verificó que existe una distribución de incidencia de manera diferente en el espacio y el tiempo. Los municipios con represas presentaban 2,25 veces más riesgo que los que no las tenían. La presencia de B. glabrata estuvo relacionada con el riesgo de la enfermedad. Por otro lado, la presencia de B. straminea ocasionaba un menor riesgo de padecer la enfermedad. Se concluye que el control y seguimiento de caracoles B. glabrata puede ser fundamental para el control y eliminación de la esquistosomiasis y que el modelo GAMLSS resultó ser efectivo para el tratamiento y modelado de datos espaciotemporales.

Temporal relationship between human and canine visceral leishmaniasis in an urban area in southeastern Brazil: An application of the ARIMAX model.

Visceral leishmaniasis (VL) is a neglected disease of public and animal health importance. With the urbanization of the disease, there is evidence of a temporal correlation between the occurrence of human (HVL) and canine (CVL) visceral leishmaniasis, usually with cases in dogs preceding those in humans. In this context, the objective of this study was to develop a time series model suitable for canine-human transmission of Leishmania infantum. Monthly cases of HVL and CVL from 2006 to 2018 in Belo Horizonte, Minas Gerais, Brazil, were evaluated, and monthly health indicators were calculated for HVL and CVL, i.e., incidence coefficient (HVL_IC) and proportion of seropositive dogs (PSD), respectively. The temporal relationship was evaluated using an autoregressive integrated moving average with exogenous variable (ARIMAX) model for two different periods (January 2006-August 2013 and September 2013-December 2018). During the 13 years studied, 1115 new cases of HVL and 103,358 dogs seropositive for CVL were recorded. HVL_IC and PSD exhibited decreasing trends throughout the first study period (January 2006-August 2013). According to the ARIMAX model adjusted for this period, there was a temporal relationship between HVL_IC and PSD, with HVL_IC being influenced by HVL_IC for the last two and five months and by PSD for the third previous month. For the second study period (September 2013-December 2018), it was not possible to fit an ARIMAX model. This study highlights the improvements made by VL surveillance since 2006 in Belo Horizonte and contributes to a better understanding of the epidemiology of the disease by public health policy-makers, doctors and veterinarians involved in the prevention and control of zoonoses.

Modelagem GAMLSS espaçotemporal da incidência de esquistossomose na região central do Estado de Minas Gerais, Brasil / Modelado espaciotemporal GAMLSS para la incidencia de esquistosomiasis en la región central del estado de Minas Gerais, Brasil / Spatio-temporal GAMLSS modeling of the incidence of schistosomiasis in the central region of the State of Minas Gerais, Brazil

Resumo: No Brasil, milhões de pessoas vivem em áreas de risco para a esquistossomose, uma doença negligenciada, de caráter crônico e com elevada morbidade. O helminto Schistosoma mansoni está presente em todas as macrorregiões, incluindo o Estado de Minas Gerais, um dos mais endêmicos. Por essa razão, a identificação de potenciais focos é fundamental para subsidiar políticas públicas de cunho educativo e profilático no controle desse desfecho. Nesse contexto, o objetivo do trabalho consiste em modelar dados de esquistossomose em relação aos aspectos espaciais e temporais, além de avaliar a importância de algumas variáveis exógenas socioeconômicas e a presença das principais espécies de Biomphalaria. Como trabalhar com casos incidentes, uma variável discreta de contagem, exige uma modelagem apropriada, foi escolhida a modelagem GAMLSS por considerar conjuntamente uma distribuição mais adequada à variável resposta devido à inflação de zeros e à heterocedasticidade espacial. Verificaram-se valores elevados de incidência em diversos municípios de 2010 a 2012 e uma tendência de queda até 2020. Também foi identificado que a distribuição da incidência se comporta de maneira diferente no espaço e no tempo. Municípios com barragem apresentaram risco 2,25 vezes maior do que os que não a continham. A presença de B. glabrata foi relacionada ao risco de ocorrência da doença. Por outro lado, a presença de B. straminea refletiu em menor risco de ocorrência da esquistossomose. Conclui-se que o controle e o acompanhamento dos caramujos da B. glabrata podem ser fundamentais para a contenção e a eliminação da esquistossomose e o modelo GAMLSS foi eficaz para tratamento e modelagem de dados espaçotemporais.

Resumen: En Brasil, millones de personas viven en áreas de riesgo de esquistosomiasis, una enfermedad crónica desatendida y con alta morbilidad. El helminto Schistosoma mansoni está presente en todas las macrorregiones, incluido el Estado de Minas Gerais, uno de los más endémicos del país. Por ello, la identificación de potenciales brotes es fundamental para promover políticas públicas de carácter educativo y profiláctico en el control de este desenlace. En este contexto, el objetivo de este trabajo es modelar datos sobre esquistosomiasis con respecto a aspectos espaciotemporales, además de evaluar la importancia de algunas variables socioeconómicas exógenas y la presencia de las principales especies de Biomphalaria. Dado que en el trabajo con casos incidentes una variable de conteo discreta requiere un adecuado modelado, se eligió el modelo GAMLSS, ya que en conjunto considera una distribución más adecuada para la variable de respuesta debido a la inflación de ceros y la heterocedasticidad espacial. Se encontraron valores de alta incidencia en varios municipios en el periodo evaluado de 2010 a 2012 y una tendencia a descenso hasta 2020. También se verificó que existe una distribución de incidencia de manera diferente en el espacio y el tiempo. Los municipios con represas presentaban 2,25 veces más riesgo que los que no las tenían. La presencia de B. glabrata estuvo relacionada con el riesgo de la enfermedad. Por otro lado, la presencia de B. straminea ocasionaba un menor riesgo de padecer la enfermedad. Se concluye que el control y seguimiento de caracoles B. glabrata puede ser fundamental para el control y eliminación de la esquistosomiasis y que el modelo GAMLSS resultó ser efectivo para el tratamiento y modelado de datos espaciotemporales.

Abstract: In Brazil, millions of people live in areas with risk of schistosomiasis, a neglected chronic disease with high morbidity. The Schistosoma mansoni helminth is present in all macroregions of Brazil, including the State of Minas Gerais, one of the most endemic states. For this reason, the identification of potential foci is essential to support educational and prophylactic public policies to control this disease. This study aims to model schistosomiasis data based on spatial and temporal aspects and assess the importance of some exogenous socioeconomic variables and the presence of the main Biomphalaria species. Considering that, when working with incident cases, a discrete count variable requires an appropriate modeling, the GAMLSS modeling was chosen since it jointly considers a more appropriate distribution for the response variable due to zero inflation and spatial heteroscedasticity. Several municipalities presented high incidence values from 2010 to 2012, and a downward trend was observed until 2020. We also noticed that the distribution of incidence behaves differently in space and time. Municipalities with dams presented risk 2.25 times higher than municipalities without dams. The presence of B. glabrata was associated with the risk of schistosomiasis. On the other hand, the presence of B. straminea represented a lower risk of the disease. Thus, the control and monitoring of B. glabrata snails is essential to control and eliminate schistosomiasis; and the GAMLSS model was effective in the treatment and modeling of spatio-temporal data.

K-mer applied in Mycobacterium tuberculosis genome cluster analysis.

According to studies carried out, approximately 10 million people developed tuberculosis in 2018. Of this total, 1.5 million people died from the disease. To study the behavior of the genome sequences of Mycobacterium tuberculosis (MTB), the bacterium responsible for the development of tuberculosis (TB), an analysis was performed using k-mers (DNA word frequency). The k values ranged from 1 to 10, because the analysis was performed on the full length of the sequences, where each sequence is composed of approximately 4 million base pairs, k values above 10, the analysis is interrupted, as consequence of the program's capacity. The aim of this work was to verify the formation of the phylogenetic tree in each k-mer analyzed. The results showed the formation of distinct groups in some k-mers analyzed, taking into account the threshold line. However, in all groups, the multidrug-resistant (MDR) and extensively drug-resistant (XDR) strains remained together and separated from the other strains.

Risk analysis in the brazilian stock market: copula-APARCH modeling for value-at-risk.

Risk management of stock portfolios is a fundamental problem for the financial analysis since it indicates the potential losses of an investment at any given time. The objective of this study is to use bivariate static conditional copulas to quantify the dependence structure and to estimate the risk measure Value-at-Risk (VaR). There were selected stocks that have been performing outstandingly on the Brazilian Stock Exchange to compose pairs trading portfolios (B3, Gerdau, Magazine Luiza, and Petrobras). Due to the flexibility that this methodology offers in the construction of multivariate distributions and risk aggregation in finance, we used the copula-APARCH approach with the Normal, T-student, and Joe-Clayton copula functions. In most scenarios, the results showed a pattern of dependence at the extremes. Moreover, the copula form seems not to be relevant for VaR estimation, since in most portfolios the appropriate copulas lead to significant VaR estimates. It has found that the best models fitted provided conservative risk measures, estimates at 5% and 1%, in a scenario more aggressive.

Climate influence the human leptospirosis cases in Brazil, 2007-2019: a time series analysis.

BACKGROUND: Human leptospirosis is responsible for great losses and deaths, especially in developing countries, which can be mitigated by knowing the correct health indicators and climate influence on the disease. METHODS: Leptospirosis cases and deaths, population and precipitation were recovered from different databases (2007-2019). Annual incidence, mortality and case fatality rates (CFRs) of human leptospirosis and average precipitation were calculated for Brazil and its regions. Time series analysis using an moving average with external variable (ARMAX) model was used to analyse the monthly contribution and precipitation influence over leptospirosis cases for each Brazilian region and for the whole country. A forecast model to predict cases for 2020 was created for Brazil. RESULTS: Human leptospirosis exhibited heterogeneous distribution among Brazilian regions, with most cases occurring during the rainy season and precipitation influenced the disease occurrence in all regions but the South. The forecast model predicted 3276.99 cases for 2020 (mean absolute percentage error 14.680 and root mean square error 53.013). Considering the annual average for the period, the leptospirosis incidence was 1913 cases per 100 000 inhabitants, mortality was 0.168 deaths per 100 000 inhabitants and the CFR was 8.83%. CONCLUSIONS: The models built can be useful for planning leptospirosis surveillance and control actions for the whole country and its regions and, together with the health indicators, revealed no uniform epidemiological situation of leptospirosis in Brazil.

Asymmetric dependence of intraday frequency components in the Brazilian stock market.

The multivariate dependence plays an important role in financial instrument management. Due to the inherent characteristics in the financial market, such as heavy tails in the returns unconditional distribution and asymmetry between gain and loss, we obtained the asymmetric dependence structure in different short-term variation scales based on the wavelet technique MODWT. The study sought to capture the relations between financial returns represented by its frequency components. Intraday returns series was used in the 15-min sampling interval from stocks and applied the D-Vine pair-copula to decompose in trade frequencies of 15 min, 1 h, 1 day, and 1 week with margin adjustments of ARIMA-APARCH class and BB7 copula function, responsible for measuring the dependence on tails. The results indicated the prevalence of a high dependence during market upturns, rising over the analyzed frequencies. Being an important tool in financial management and allowing short-term strategies of diversification.

Suicide cases in developed and emerging countries: an analysis using wavelets / Casos de suicídio em países desenvolvidos e emergentes: uma análise usando ondaletas

OBJECTIVE: The aim of this study was to use a wavelet technique to determine whether the number of suicides is similar between developed and emerging countries. METHODS: Annual data were obtained from World Health Organization (WHO) reports from 1986 to 2015. Discrete nondecimated wavelet transform was used for the analysis, and the Daubechies wavelet function was applied with five-level decomposition. Regarding clustering, energy (variance) was used to analyze the clusters and visualize the clustering process. We constructed a dendrogram using the Mahalanobis distance. The number of groups was set using a specific function in the R program. RESULTS: The cluster analysis verified the formation of four groups as follows: Japan, the United States and Brazil were distinct and isolated groups, and other countries (Austria, Belgium, Chile, Israel, Mexico, Italy and the Netherlands) constituted a single group. CONCLUSION: The methods utilized in this paper enabled a detailed verification of countries with similar behaviors despite very distinct socioeconomic, geographic and climate characteristics.

OBJETIVO: Verificar se existe relação de similaridade entre o número de suicídio em países desenvolvidos e emergentes usando a técnica de ondaletas. MÉTODOS: Os dados anuais foram obtidos a partir do relatório da Organização Mundial da Saúde (OMS), no período de 1986 a 2015. Para análise, foi empregada a transformada discreta não decimada de ondaleta (NDWT), a função ondaleta aplicada foi a Daubechies com cinco níveis de decomposição. Com relação ao agrupamento, utilizou-se a energia (variância) para analisar os clusters e, para a visualização do processo de clusterização, trabalhamos com o dendograma, no qual se empregou a distância de Mahalanobis. A quantidade de grupos foi definida por meio da função NbCluster. RESULTADOS: A partir da análise de cluster, verificou-se a formação de quatros grupos. No qual, Japão e Estados Unidos e Brasil localizam-se em grupos distintos e isolados. E os demais países (Áustria, Bélgica, Chile, Israel, México, Itália e Holanda) em um único grupo. CONCLUSÃO: Utilizando esse método, foi possível verificar com mais detalhes quais países apresentaram comportamentos semelhantes, mesmo apresentando características bem distintas entre si, tanto socioeconômica, geográfica e climática.

Evaluation of genome similarities using a wavelet-domain approach.

INTRODUCTION: Tuberculosis is listed among the top 10 causes of deaths worldwide. The resistant strains causing this disease have been considered to be responsible for public health emergencies and health security threats. As stated by the World Health Organization (WHO), around 558,000 different cases coupled with resistance to rifampicin (the most operative first-line drug) have been estimated to date. Therefore, in order to detect the resistant strains using the genomes of Mycobacterium tuberculosis (MTB), we propose a new methodology for the analysis of genomic similarities that associate the different levels of decomposition of the genome (discrete non-decimated wavelet transform) and the Hurst exponent. METHODS: The signals corresponding to the ten analyzed sequences were obtained by assessing GC content, and then these signals were decomposed using the discrete non-decimated wavelet transform along with the Daubechies wavelet with four null moments at five levels of decomposition. The Hurst exponent was calculated at each decomposition level using five different methods. The cluster analysis was performed using the results obtained for the Hurst exponent. RESULTS: The aggregated variance, differenced aggregated variance, and aggregated absolute value methods presented the formation of three groups, whereas the Peng and R/S methods presented the formation of two groups. The aggregated variance method exhibited the best results with respect to the group formation between similar strains. CONCLUSION: The evaluation of Hurst exponent associated with discrete non-decimated wavelet transform can be used as a measure of similarity between genome sequences, thus leading to a refinement in the analysis.

Evaluation of genome similarities using a wavelet-domain approach

Abstract INTRODUCTION: Tuberculosis is listed among the top 10 causes of deaths worldwide. The resistant strains causing this disease have been considered to be responsible for public health emergencies and health security threats. As stated by the World Health Organization (WHO), around 558,000 different cases coupled with resistance to rifampicin (the most operative first-line drug) have been estimated to date. Therefore, in order to detect the resistant strains using the genomes of Mycobacterium tuberculosis (MTB), we propose a new methodology for the analysis of genomic similarities that associate the different levels of decomposition of the genome (discrete non-decimated wavelet transform) and the Hurst exponent. METHODS: The signals corresponding to the ten analyzed sequences were obtained by assessing GC content, and then these signals were decomposed using the discrete non-decimated wavelet transform along with the Daubechies wavelet with four null moments at five levels of decomposition. The Hurst exponent was calculated at each decomposition level using five different methods. The cluster analysis was performed using the results obtained for the Hurst exponent. RESULTS: The aggregated variance, differenced aggregated variance, and aggregated absolute value methods presented the formation of three groups, whereas the Peng and R/S methods presented the formation of two groups. The aggregated variance method exhibited the best results with respect to the group formation between similar strains. CONCLUSION: The evaluation of Hurst exponent associated with discrete non-decimated wavelet transform can be used as a measure of similarity between genome sequences, thus leading to a refinement in the analysis.

Wavelet-domain elastic net for clustering on genomes strains.

We propose to evaluate genome similarity by combining discrete non-decimated wavelet transform (NDWT) and elastic net. The wavelets represent a signal with levels of detail, that is, hidden components are detected by means of the decomposition of this signal, where each level provides a different characteristic. The main feature of the elastic net is the grouping of correlated variables where the number of predictors is greater than the number of observations. The combination of these two methodologies applied in the clustering analysis of the Mycobacterium tuberculosis genome strains proved very effective, being able to identify clusters at each level of decomposition.

Independent Component Analysis (ICA) based-clustering of temporal RNA-seq data.

Gene expression time series (GETS) analysis aims to characterize sets of genes according to their longitudinal patterns of expression. Due to the large number of genes evaluated in GETS analysis, an useful strategy to summarize biological functional processes and regulatory mechanisms is through clustering of genes that present similar expression pattern over time. Traditional cluster methods usually ignore the challenges in GETS, such as the lack of data normality and small number of temporal observations. Independent Component Analysis (ICA) is a statistical procedure that uses a transformation to convert raw time series data into sets of values of independent variables, which can be used for cluster analysis to identify sets of genes with similar temporal expression patterns. ICA allows clustering small series of distribution-free data while accounting for the dependence between subsequent time-points. Using temporal simulated and real (four libraries of two pig breeds at 21, 40, 70 and 90 days of gestation) RNA-seq data set we present a methodology (ICAclust) that jointly considers independent components analysis (ICA) and a hierarchical method for clustering GETS. We compare ICAclust results with those obtained for K-means clustering. ICAclust presented, on average, an absolute gain of 5.15% over the best K-means scenario. Considering the worst scenario for K-means, the gain was of 84.85%, when compared with the best ICAclust result. For the real data set, genes were grouped into six distinct clusters with 89, 51, 153, 67, 40, and 58 genes each, respectively. In general, it can be observed that the 6 clusters presented very distinct expression patterns. Overall, the proposed two-step clustering method (ICAclust) performed well compared to K-means, a traditional method used for cluster analysis of temporal gene expression data. In ICAclust, genes with similar expression pattern over time were clustered together.

Analysis of time series of cattle rabies cases in Minas Gerais, Brazil, 2006-2013.

Vampire bats are potential transmitters of rabies in rural areas. Cattle rabies is relevant in the state of Minas Gerais due to the increasing cattle herds and geographical features of the area, which are favorable to bat populations. This study evaluated the occurrence of rabies in state cattle by analyzing the time series of monthly values, 2006-2012, describing some aspects of the areas and species affected. The study also pointed out the disease prediction for January-December 2013. We used monthly data of cases reported to the Continental Epidemiological Surveillance System (SIVCONT) of the Ministry of Agriculture, Livestock, and Supply (MAPA), January 2006-March 2013. We also collected data on municipalities and other animal species affected by rabies for a descriptive analysis of the disease. The results indicate that cattle rabies is endemic in the State, with different intensities in different regions. The variables frequency of notifications and bat shelters had a positive and regular correlation (P = 0.035; r = 0.567) between them. With respect to data series, there was a fluctuation of the number of cases (5 to 29 cases per month) over 2006 and 2013, without trend or seasonality, although there would visually appear to be a downward trend. The results also suggest that the forecasting method is suitable for predicting future cases. Bovine species had the highest number of reporting, with 1007 cases (88.88 %), followed by equine species with 112 (9.89 %). The information provided by this study may help understand disease occurrence and find the most effective measures for rabies control in endemic areas.

Bayesian model-based clustering of temporal gene expression using autoregressive panel data approach.

MOTIVATION: In a microarray time series analysis, due to the large number of genes evaluated, the first step toward understanding the complex time network is the clustering of genes that share similar expression patterns over time. Up until now, the proposed methods do not point simultaneously to the temporal autocorrelation of the gene expression and the model-based clustering. We present a Bayesian method that considers jointly the fit of autoregressive panel data models and hierarchical gene clustering. RESULTS: The proposed methodology was able to cluster genes that share similar expression over time, which was determined jointly by the estimates of autoregression parameters, by the average level of expression) and by the quality of the fitted model. AVAILABILITY AND IMPLEMENTATION: The R codes for implementation of the proposed clustering method and for simulation study, as well as the real and simulated datasets, are freely accessible on the Web http://www.det.ufv.br/~moyses/links.php. CONTACT: moysesnascim@ufv.br.

Comparação bayesiana de modelos com uma aplicação para o equilíbrio de Hardy-Weinberg usando o coeficiente de desequilíbrio / Bayesian comparison of models with an application to the Hardy-Weinberg equilibrium using the disequilibrium coefficient

O equilíbrio de Hardy-Weinberg é um dos principais assuntos estudados pela Genética de populações. Neste contexto, o presente trabalho aborda a análise e a comparação bayesiana de modelos utilizando o coeficiente de desequilíbrio (D A). Para isso, realizou-se um estudo de simulação no qual as seguintes distribuições a priori foram consideradas: Dirichlet (modelo 1); beta - função degrau uniforme (modelo 2); uniforme - função degrau uniforme (modelo 3); e as prioris independentes uniformes (modelo 4). Exemplos de aplicação a dados reais de grupos raciais também são apresentados e discutidos. As amostras das distribuições marginais a posteriori para os parâmetros de interesse foram obtidas mediante o algoritmo Metropolis-Hastings, o qual foi implementado no software livre R. A convergência das cadeias geradas por este algoritmo foi monitorada pelos critérios de Geweke e Gelman & Rubin, os quais estão implementados no pacote BOA do R. Quanto às comparações entre os modelos, efetuadas por meio do fator de Bayes, observa-se que, para os dados simulados, o modelo 4 é o mais indicado para os casos de D A=0,146, D A=0,02 e D A=-0,02 com n=200; o modelo 2 é o mais indicado para D A=-0,02 e n=50 e o modelo 3 é o mais indicado para D A=-0,02 e n=1000. Para os dados reais, em cada caso analisado, nota-se uma grande diferenciação na escolha de modelos, em que apenas o modelo 1 não é recomendado.

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 real data for racial groups are presented and discussed. Samples from the marginal posterior distributions for parameters of interest were obtained by Metropolis-Hastings algorithm, which was implemented in the software R. The convergence of the chains generated by this algorithm was monitored by criteria of Geweke and Gelman & Rubin, which are implemented in the BOA package R. Regarding comparisons between models, performed using the Bayes factor, it was observed that model 4 is the most suitable for the cases of D A=0.146, D A=0.02 and D A=-0.02 with n=200, the model 2 is the most suitable for D A=-0.02 with n=50 and the model 3 is the most suitable for D A=-0.02 and n=1000. For real data, in each case examined, there is a large difference in choice of models, where model 1 is the only one not recommended.

Análise bayesiana para modelos de degradabilidade ruminal / Bayesian analisys for ruminal degradability models

Neste estudo, utilizou-se a metodologia bayesiana para ajustar os modelos de ORSKOV & MCDONALD (1979) e MCDONALD (1981) a conjuntos de dados simulados e a um conjunto de dados de porcentagem de degradação da fibra em detergente neutro da gramínea coastcross (Cynodon dactylon x Cynodon nlemfuensis), ao longo do tempo. As amostras das distribuições marginais a posteriori dos parâmetros foram obtidas por meio dos métodos de Monte Carlo com cadeias de Markov (MCMC), especificamente, os algoritmos Amostrador de Gibbs e Metropolis-Hastings. A metodologia bayesiana mostrou-se eficiente, sendo avaliada e comprovada pelo estudo de simulação, que apresentou estimativas bem próximas ao valor paramétrico. As estimativas obtidas para os parâmetros dos modelos por meio da abordagem bayesiana mostraram-se bastante coerentes com os valores relatados na literatura. O modelo de Orskov e McDonald foi mais plausível que o modelo de McDonald na descrição dos dados de degradação.

The bayesian methodology was used to estimate the parameters of ORSKOV & MCDONALD (1979) and MCDONALD (1981) models. A study was conducted by using both simulated and real data percentage of coastcross grass (Cynodon dactylon x Cynodon nlemfuensis) fiber degradation with neutral detergent fiber degradation over the time. The posterior marginal samples distributions for the parameters were obtained by Gibbs Sampler and Metropolis-Hastings algorithms. The bayesian approach, evaluated and verified by the simulation studied, has proved to be efficient and the parameter estimated were quite close to the parametric values. The parameters estimated for both models using bayesian approach from real data were fairly consistent with the values reported in the literature. The Orskov and McDonald model was more plausible than the description degradation data made by the McDonald model.

Abordagem bayesiana da sensitividade de modelos para o coeficiente de endogamia / Bayesian approach to sensitivity of models for inbreeding coefficient

Este trabalho tem como objetivo realizar uma análise bayesiana de modelos, por meio do fator de Bayes, para o desequilíbrio de Hardy-Weinberg. Pretende-se também testar a metodologia por meio da simulação de dados e aplicá-la a um conjunto de dados reais. Na definição dos modelos, utilizaram-se as prioris Dirichlet (modelo 1), Beta - função degrau Uniforme (modelo 2), Uniforme - função degrau Uniforme (modelo 3) e as prioris independentes Uniformes (modelo 4) relacionadas aos parâmetros coeficiente de endogamia e proporção alélica. Foi implementado um algoritmo no software livre R para realizar a amostragem pelo Metropolis-Hastings das distribuições condicionais a posteriori dos parâmetros dos modelos. A convergência das cadeias foram monitoradas por meio de procedimentos implementados no pacote BOA do software livre R. As comparações entre os modelos indicaram que o mais adequado, ou seja, o que melhor descreve o fenômeno em estudo, é o modelo 1, em comparação aos demais, tanto para os dados simulados, quanto para os dados reais. Em virtude dos resultados apresentados, pode-se atestar que a abordagem Bayesiana apresentou bons resultados, ou seja, por meio das distribuições a posteriori condicionais completas, foram verificadas a confiabilidade e a precisão da metodologia na comparação dos modelos.

The aim of this research is to perform a Bayesian characterization of the Hardy-Weinberg disequilibrium through the Bayes factor. The methodology is tested by using both simulation study and actual data. It was used the following priors for the Bayesian models: Dirichlet (model 1), beta - step uniform function (model 2), uniform - step uniform function (model 3) and independent uniforms for the inbreeding coefficients and allele frequencies (model 4). Metropolis-Hasting algorithms were implemented using the software R to simulate multiple draws from the posterior distribution. Convergence of the Metropolis-Hasting algorithms was assessed by many methods available at R package BOA. Results showed that the model 1 presents the best performance for both simulation study and actual data. The results also showed that the Bayesian approach provides models that are useful for the analysis of the Hardy-Weinberg disequilibrium and inbreeding coefficient.

Comparação de matrizes de covariâncias de populações normais dependentes: um estudo de caso / Comparing the covariance matrices of dependent normal populations: a case study

Inferências sobre comparações de matrizes de covariâncias em populações normais dependentes são usualmente obtidas considerando testes assintóticos baseados na maximização de funções de verossimilhanças. Entretanto, se o número de populações e/ou de variáveis consideradas é excessivo pode-se ter problemas na convergência dos métodos numéricos utilizados para obtenção dos estimadores de máxima verossimilhança. Face a esse problema, objetivou-se, neste trabalho, ilustrar por meio de um conjunto de dados reais, a aplicação de um teste para comparar matrizes de covariâncias de populações correlacionadas, usando uma estatística baseada na razão de variâncias generalizadas, cuja distribuição empírica foi obtida por meio da técnica bootstrap.

Inferences about dependent normal populations are usually obtained considering asymptotic tests based on the maximization likelihood functions. However, if the number of populations and/or variables considered are too high one way have convergence problems with the numerical methods used to obtain the maximum likelihood estimators. This work aimed to illustrate, using a real data set, the application of a test to compare covariance matrices of correlated populations using a statistic based on generalized variances ratio, whose empirical distribution was obtained via bootstrap methods.

Comparação entre modelos para predição do nitrogênio mineralizado: uma abordagem bayesiana / Comparison of the models for prediction of the mineralized nitrogen: a bayesian approach

Neste trabalho, desenvolveu-se uma abordagem bayesiana para predizer as quantidades de nitrogênio mineralizados por intermédio de modelos não lineares. Os modelos não lineares considerados para avaliar a dinâmica da mineralização do nitrogênio e para ilustrar o procedimento bayesiano foram: modelo de Cabrera, Marion, Stanford e Smith. A comparação dos modelos foi feita por meio do Fator de Bayes (FB) e do Critério de Informação Bayesiano (BIC). A inferência sobre os parâmetros realizou-se por intermédio do Amostrador de Gibbs e do Metropolis Hastings. O modelo de Cabrera (1993) foi o que proporcionou melhor qualidade de ajuste ao conjunto de dados de mineralização de nitrogênio, sendo seguido pelo modelo de Stanford & Smith (1972) e, por último, o de Marion et al. (1981).

In this work one developed a Bayesian approach to predict the amount of mineralized nitrogen through nonlinear models. The nonlinear models considered to evaluate the mineralization of organic nitrogen and to illustrate the Bayesian procedure were: models of Cabrera, Marion, Stanford and Smith. The comparison of the models was promoted through the Bayes Factor (FB) and Bayes Information Criterion (BIC). Inference on the parameters was carried out through the Gibbs Sampling and Metropolis Hastings. The model that provided better adjustment quality to the group of data was Cabrera's model (1993), followed by the model of Stanford & Smith (1972) and the last one by Marion et al. (1981).

Avaliação de métodos de estimação intervalar para funções lineares binomiais via bootstrap infinito / Evaluation of intervalar estimation methods for binomial linear functions through infinity bootstrap

Objetivou-se, neste trabalho, avaliar intervalos de confiança de diferentes funções lineares compostas por proporções binomiais construídas com base no método de Wald e Wald ajustado utilizando a técnica de bootstrap infinito. Considerados diversos tamanhos amostrais (n is), parâmetros (p) e número de coeficientes das funções lineares. Concluiu-se, por meio das probabilidades de cobertura dos intervalos de confiança das populações binomiais, cujas proporções foram baixas (p=0,2) e considerando diferentes tamanhos de amostras, que a generalização bootstrap do método de Wald ajustado foi eficiente para funções lineares cujos coeficientes indicaram a comparação de uma proporção versus as demais.

This work aimed to evaluate confidence intervals of different linear functions of binomial proportions base on Wald and Wald's adjusted method using the infinity bootstrap technique. Several sample sizes (n i), binomial parameters (p) and number of coefficients of the linear functions were considered. One concluded through the probabilities of binomial population confidence covered intervals that the bootstrap generalization of adjusted Wald's method was efficient for linear functions whose coefficients indicated a comparison of versus the others proportion (p=0.2) considering different sample sizes.