A Bayesian Approach for Decision Making on the Identification of Genes with Different Expression Levels: An Application to Escherichia coli Bacterium Data

A common interest in gene expression data analysis is to identify from a large pool of candidate genes the genes that present significant changes in expression levels between a treatment and a control biological condition. Usually, it is done using a statistic value and a cutoff value that are used to separate the genes differentially and nondifferentially expressed. In this paper, we propose a Bayesian approach to identify genes differentially expressed calculating sequentially credibility intervals from predictive densities which are constructed using the sampled mean treatment effect from all genes in study excluding the treatment effect of genes previously identified with statistical evidence for difference. We compare our Bayesian approach with the standard ones based on the use of the t-test and modified t-tests via a simulation study, using small sample sizes which are common in gene expression data analysis. Results obtained report evidence that the proposed approach performs better than standard ones, especially for cases with mean differences and increases in treatment variance in relation to control variance. We also apply the methodologies to a well-known publicly available data set on Escherichia coli bacterium

A Bayesian Approach for Decision Making on the Identification of Genes with Different Expression Levels: An Application to Escherichia coli Bacterium Data

A common interest in gene expression data analysis is to identify from a large pool of candidate genes the genes that present significant changes in expression levels between a treatment and a control biological condition. Usually, it is done using a statistic value and a cutoff value that are used to separate the genes differentially and nondifferentially expressed. In this paper, we propose a Bayesian approach to identify genes differentially expressed calculating sequentially credibility intervals from predictive densities which are constructed using the sampled mean treatment effect from all genes in study excluding the treatment effect of genes previously identified with statistical evidence for difference. We compare our Bayesian approach with the standard ones based on the use of the t-test and modified t-tests via a simulation study, using small sample sizes which are common in gene expression data analysis. Results obtained report evidence that the proposed approach performs better than standard ones, especially for cases with mean differences and increases in treatment variance in relation to control variance. We also apply the methodologies to a well-known publicly available data set on Escherichia coli bacterium

Continuous and discrete stochastic models applied to finance

Os modelos do volatilidade estocástica (MVE) são bastante utilizados pela sua semelhança com os modelos habitualmente usados na Teoria Financeira. Nos MVE a volatilidade independe dos retornos passados e é modelada como uma variável latente não observada, através de uma componente preditível e outra aleatória. A função de verossimilhança desses modelos é difícil de ser obtida e maximizada. Neste trabalho descrevemos as suposições em que os modelos do difusão para séries de retornos se baseiam, assim como as suposições tomadas pela modelagem discreta. Apresentamos os MVE e alguns de seus métodos de estimação. Tratamos de dois modelos contínuos, do algumas do suas propriedades e também do dois MVE discretos que convergem para tais contínuos. Trabalhamos com uma aproximação linear de um deles, apresentando o filtro de Kalman, e sua verossimilhança obtida depois da filtragem. O algoritmo de Metropolis-Hastings foi empregado na abordagem da verossimilhança, assim como na bayesiana do caso linear. Utilizamos o filtro estendido do Kalman combinado com a aproximação do Laplace na construção da função do verossimilhança dos dois MVE abordados neste trabalho.The stochastic volatility models (SVM) are quite habitually used by their simiilaritv with the models used in the Financial Theory. In them the volatility is described through their last values and it does not depend on the last returns. The likelihood function of SV is difficult of being obtained and maximizecl. In this paper, we have described the hypothesis in which the diffusion models for series of returns are based, as well as the suppositions taken by the discrete modelling. We presented SVM and some of their estimate methods. We treated of two continuous models, of some of their properties and also of two discrete SVM that converge for the continuous ones. We worked with a linear approach of one of them, presenting the Kalinan filter, and it.s likelihood obtained alter the filtration. The Metropolis-Hastings algorithm was used in the approach of the likelihood, as well as in the Bayesian of the linear case. We used t.he extended Kahnan filter combined wit.h the Laplace approxiniation in the construction of the likelihood function of the two SVM approached in this work

Continuous and discrete stochastic models applied to finance

Os modelos do volatilidade estocástica (MVE) são bastante utilizados pela sua semelhança com os modelos habitualmente usados na Teoria Financeira. Nos MVE a volatilidade independe dos retornos passados e é modelada como uma variável latente não observada, através de uma componente preditível e outra aleatória. A função de verossimilhança desses modelos é difícil de ser obtida e maximizada. Neste trabalho descrevemos as suposições em que os modelos do difusão para séries de retornos se baseiam, assim como as suposições tomadas pela modelagem discreta. Apresentamos os MVE e alguns de seus métodos de estimação. Tratamos de dois modelos contínuos, do algumas do suas propriedades e também do dois MVE discretos que convergem para tais contínuos. Trabalhamos com uma aproximação linear de um deles, apresentando o filtro de Kalman, e sua verossimilhança obtida depois da filtragem. O algoritmo de Metropolis-Hastings foi empregado na abordagem da verossimilhança, assim como na bayesiana do caso linear. Utilizamos o filtro estendido do Kalman combinado com a aproximação do Laplace na construção da função do verossimilhança dos dois MVE abordados neste trabalho.The stochastic volatility models (SVM) are quite habitually used by their simiilaritv with the models used in the Financial Theory. In them the volatility is described through their last values and it does not depend on the last returns. The likelihood function of SV is difficult of being obtained and maximizecl. In this paper, we have described the hypothesis in which the diffusion models for series of returns are based, as well as the suppositions taken by the discrete modelling. We presented SVM and some of their estimate methods. We treated of two continuous models, of some of their properties and also of two discrete SVM that converge for the continuous ones. We worked with a linear approach of one of them, presenting the Kalinan filter, and it.s likelihood obtained alter the filtration. The Metropolis-Hastings algorithm was used in the approach of the likelihood, as well as in the Bayesian of the linear case. We used t.he extended Kahnan filter combined wit.h the Laplace approxiniation in the construction of the likelihood function of the two SVM approached in this work

A multiple time scale survival model with a cure fraction

Many recent survival studies propose modeling data with a cure fraction, i.e., data in which part of the population is not susceptible to the event of interest. This event may occur more than once for the same individual (recurrent event). We then have a scenario of recurrent event data in the presence of a cure fraction, which may appear in various areas such as oncology, finance, industries, among others. This paper proposes a multiple time scale survival model to analyze recurrent events using a cure fraction. The objective is analyzing the efficiency of certain interventions so that the studied event will not happen again in terms of covariates and censoring. All estimates were obtained using a sampling-based approach, which allows information to be input beforehand with lower computational effort. Simulations were done based on a clinical scenario in order to observe some frequentist properties of the estimation procedure in the presence of small and moderate sample sizes. An application of a well-known set of real mammary tumor data is provided.CNPQCNPqCAPESCAPE

A Bayesian Approach for Decision Making on the Identification of Genes with Different Expression Levels: An Application to Escherichia coli Bacterium Data

A common interest in gene expression data analysis is to identify from a large pool of candidate genes the genes that present significant changes in expression levels between a treatment and a control biological condition. Usually, it is done using a statistic value and a cutoff value that are used to separate the genes differentially and nondifferentially expressed. In this paper, we propose a Bayesian approach to identify genes differentially expressed calculating sequentially credibility intervals from predictive densities which are constructed using the sampled mean treatment effect from all genes in study excluding the treatment effect of genes previously identified with statistical evidence for difference. We compare our Bayesian approach with the standard ones based on the use of the t-test and modified t-tests via a simulation study, using small sample sizes which are common in gene expression data analysis. Results obtained report evidence that the proposed approach performs better than standard ones, especially for cases with mean differences and increases in treatment variance in relation to control variance. We also apply the methodologies to a well-known publicly available data set on Escherichia coli bacterium

A Bayesian Approach for Decision Making on the Identification of Genes with Different Expression Levels: An Application to Escherichia coli Bacterium Data

A common interest in gene expression data analysis is to identify from a large pool of candidate genes the genes that present significant changes in expression levels between a treatment and a control biological condition. Usually, it is done using a statistic value and a cutoff value that are used to separate the genes differentially and nondifferentially expressed. In this paper, we propose a Bayesian approach to identify genes differentially expressed calculating sequentially credibility intervals from predictive densities which are constructed using the sampled mean treatment effect from all genes in study excluding the treatment effect of genes previously identified with statistical evidence for difference. We compare our Bayesian approach with the standard ones based on the use of the t-test and modified t-tests via a simulation study, using small sample sizes which are common in gene expression data analysis. Results obtained report evidence that the proposed approach performs better than standard ones, especially for cases with mean differences and increases in treatment variance in relation to control variance. We also apply the methodologies to a well-known publicly available data set on Escherichia coli bacterium

Factors that May Lead on the Non-renewal of Certified Organic Product According to Organic Producers in Brazil

The regulatory process of the organic sector in Brazil began in 1999 and has gone through several changes, culminating in the Decree-Law of December 2007, which established rules for the production and trading of organic products in Brazil. In such Decree, the certification has become a compulsory requirement for production and trading of such products, whose rules governing their obtaining follow rigorous controls standards. As the certification process of organic products is recent and there is a lack of studies carried on this subject, this study will contribute to fill the existing gap in the international literature, mainly national about this topic, once that aimed to identify factors that influence the possibility of non-renewal of organic production certificate, according to the perception of certified producers in Brazil. Through this effort, this research should contribute to wider adherence and maintenance of the producer in the certified system or, at least, proposals for further works. A total of 200 producers from several Brazilian states participated in this study, and data analysis was performed using descriptive statistics and, later, exploratory factor analysis. The results achieved holds that the determining factors to the non-renewal of the certificate involve variables related to transactions among operators, organization of the supply chain and to the regulations. Furthermore, to overcome the challenges imposed to rural producers, one of the proposals is for greater effective actions from representative industry entities of the sector in aspects that are related to the certification process