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Carlos A. de B. Pereira

Publications and source records attributed to Carlos A. de B. Pereira.

7 recordsLinked to original sources
arXiv2020

Assessing Dynamic Effects on a Bayesian Matrix-Variate Dynamic Linear Model: an Application to fMRI Data Analysis

In this work, we propose a modeling procedure for fMRI data analysis using a Bayesian Matrix-Variate Dynamic Linear Model (MVDLM). With this type of model, less complex than the more traditional temporal-spatial models, we are able to take into account the temporal and -- at least locally -- the spatial structures that are usually present in this type of data. Despite employing a voxel-wise approach, every voxel in the brain is jointly modeled with its nearest neighbors, which are defined through a euclidian metric. MVDLM's have been widely used in applications where the interest lies in to perform predictions and/or analysis of covariance structures among time series. In this context, our interest is rather to assess the dynamic effects which are related to voxel activation. In order to do so, we develop three algorithms to simulate online-trajectories related to the state parameter and with those curves or simulated trajectories we compute a Monte Carlo evidence for voxel activation. Through two practical examples and two different types of assessments, we show that our method can be viewed for the practitioners as a reliable tool for fMRI data analysis. Despite all the examples and analysis are illustrated just for a single subject analysis, we also describe how more general group analysis can be implemented.

stat.AP↗
arXiv2017

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.

stat.ME↗
arXiv2014

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.

stat.ME↗
arXiv2014

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.

stat.ME↗
arXiv2013

Reliability estimators for the components of series and parallel systems: The Weibull model

This paper presents a hierarchical Bayesian approach to the estimation of components' reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component's reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.

stat.ME↗
arXiv2008

Significance tests for comparing digital gene expression profiles

Most of the statistical tests currently used to detect differentially expressed genes are based on asymptotic results, and perform poorly for low expression tags. Another problem is the common use of a single canonical cutoff for the significance level (p-value) of all the tags, without taking into consideration the type II error and the highly variable character of the sample size of the tags. This work reports the development of two significance tests for the comparison of digital expression profiles, based on frequentist and Bayesian points of view, respectively. Both tests are exact, and do not use any asymptotic considerations, thus producing more correct results for low frequency tags than the chi-square test. The frequentist test uses a tag-customized critical level which minimizes a linear combination of type I and type II errors. A comparison of the Bayesian and the frequentist tests revealed that they are linked by a Beta distribution function. These tests can be used alone or in conjunction, and represent an improvement over the currently available methods for comparing digital profiles.

q-bio.GN↗