Bayesian Analysis of Simple Random Densities

A tractable nonparametric prior over densities is introduced which is closed under sampling and exhibits proper posterior asymptotics.Comment: 19 pages; 6 figure

Predictive analysis of microarray data

Microarray gene expression data are analyzed by means of a Bayesian nonparametric model, with emphasis on prediction of future observables, yielding a method for selection of differentially expressed genes and a classifier

Confidence Statements for Ordering Quantiles

This work proposes Quor, a simple yet effective nonparametric method to compare independent samples with respect to corresponding quantiles of their populations. The method is solely based on the order statistics of the samples, and independence is its only requirement. All computations are performed using exact distributions with no need for any asymptotic considerations, and yet can be run using a fast quadratic-time dynamic programming idea. Computational performance is essential in high-dimensional domains, such as gene expression data. We describe the approach and discuss on the most important assumptions, building a parallel with assumptions and properties of widely used techniques for the same problem. Experiments using real data from biomedical studies are performed to empirically compare Quor and other methods in a classification task over a selection of high-dimensional data sets

The Likelihood Ratio Test and Full Bayesian Significance Test under small sample sizes for contingency tables

Hypothesis testing in contingency tables is usually based on asymptotic results, thereby restricting its proper use to large samples. To study these tests in small samples, we consider the likelihood ratio test and define an accurate index, the P-value, for the celebrated hypotheses of homogeneity, independence, and Hardy-Weinberg equilibrium. The aim is to understand the use of the asymptotic results of the frequentist Likelihood Ratio Test and the Bayesian FBST -- Full Bayesian Significance Test -- under small-sample scenarios. The proposed exact P-value is used as a benchmark to understand the other indices. We perform analysis in different scenarios, considering different sample sizes and different table dimensions. The exact Fisher test for $2 \times 2$ tables that drastically reduces the sample space is also discussed. The main message of this paper is that all indices have very similar behavior, so the tests based on asymptotic results are very good to be used in any circumstance, even with small sample sizes

Ordering Quantiles through Confidence Statements

Ranking variables according to their relevance to predict an outcome is an important task in biomedicine. For instance, such ranking can be used for selecting a smaller number of genes for then applying other sophisticated experiments only on genes identified as important. A nonparametric method called Quor is designed to provide a confidence value for the order of arbitrary quantiles of different populations using independent samples. This confidence may provide insights about possible differences among groups and yields a ranking of importance for the variables. Computations are efficient and use exact distributions with no need for asymptotic considerations. Experiments with simulated data and with multiple real -omics data sets are performed, and they show advantages and disadvantages of the method. Quor has no assumptions but independence of samples, thus it might be a better option when assumptions of other methods cannot be asserted. The software is publicly available on CRAN

BayGO: Bayesian analysis of ontology term enrichment in microarray data

BACKGROUND: The search for enriched (aka over-represented or enhanced) ontology terms in a list of genes obtained from microarray experiments is becoming a standard procedure for a system-level analysis. This procedure tries to summarize the information focussing on classification designs such as Gene Ontology, KEGG pathways, and so on, instead of focussing on individual genes. Although it is well known in statistics that association and significance are distinct concepts, only the former approach has been used to deal with the ontology term enrichment problem. RESULTS: BayGO implements a Bayesian approach to search for enriched terms from microarray data. The R source-code is freely available at in three versions: Linux, which can be easily incorporated into pre-existent pipelines; Windows, to be controlled interactively; and as a web-tool. The software was validated using a bacterial heat shock response dataset, since this stress triggers known system-level responses. CONCLUSION: The Bayesian model accounts for the fact that, eventually, not all the genes from a given category are observable in microarray data due to low intensity signal, quality filters, genes that were not spotted and so on. Moreover, BayGO allows one to measure the statistical association between generic ontology terms and differential expression, instead of working only with the common significance analysis

Ultrasound measures of Nellore cattle supplemented of yeast and probiotic in the north of Mato Grosso.

The search for better results on the performance and carcass traits of cattle under grazing has required efforts in the elaboration of diets that satisfy them both the producer and the consumer; therefore, the supplementation of grazing cattle is one of the main strategies for the intensification of systems. It is important to identify the effects of dietary supplementation on bovine growth through ultrasound imaging, which in addition to being an indication of the carcass composition allows estimation of the thickness of subcutaneous fat, as it helps to protect the carcass cold shortening. The objective of this study was to evaluate bovine carcass alterations, by means of ultrasound images, finished with pasture with additives supplementation. Twenty-eight noncastrated males of the Nellore breed were randomly divided into four supplementation groups (Group 1 = Urea; Group 2 = Urea + Optygen; Group 3 = Group 2 + Yeasts; and Group 4 = Group 3 + Probiotic). The experimental area used was of eight hectares, with Brachiaria brizantha cv. BRS Piatã, subdivided into four pens. The experiment lasted for 98 days, with 14 initial days of adaptation and the remainder subdivided into three sub-periods of 28 days, with the performance of ultrasonic readings at the end of each sub-period. For the measurement of the rib eye area (REA) and the subcutaneous fat thickness of loin (SFTL), images were taken between the 12th and 13th ribs, transversal to Musculus longissimus thoracis. For fat thickness of the rump (P8), the images were taken at the junction between M. gluteos medium and M biceps femoris, with the use of vegetable oil as an acoustic coupling. Data were analyzed using the Statistical Analyzes System software in a completely randomized design. The animal of Group 3 showed high (P 0.05) was observed among treatments, with general means of 5.53 mm in the end period. It can be concluded that the use of yeasts as an additive in the supplementation of cattle to pasture presented beneficial effects on carcass composition