Alexandre G. Patriota

A non-parametric method to estimate the number of clusters

An important and yet unsolved problem in unsupervised data clustering is how to determine the number of clusters. The proposed slope statistic is a non-parametric and data driven approach for estimating the number of clusters in a dataset. This technique uses the output of any clustering algorithm and identifies the maximum number of groups that breaks down the structure of the dataset. Intensive Monte Carlo simulation studies show that the slope statistic outperforms (for the considered examples) some popular methods that have been proposed in the literature. Applications in graph clustering, in iris and breast cancer datasets are shown.

Influence diagnostics in Birnbaum--Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum–Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum–Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.

A classical measure of evidence for general null hypotheses

Abstract In science, the most widespread statistical quantities are perhaps p-values. A typical advice is to reject the null hypothesis H 0 if the corresponding p-value is sufficiently small (usually smaller than 0.05). Many criticisms regarding p-values have arisen in the scientific literature. The main issue is that in general optimal p-values (based on likelihood ratio statistics) are not measures of evidence over the parameter space Θ . Here, we propose an objective measure of evidence for very general null hypotheses that satisfies logical requirements (i.e., operations on the subsets of Θ ) that are not met by p-values (e.g., it is a possibility measure). We study the proposed measure in the light of the abstract belief calculus formalism and we conclude that it can be used to establish objective states of belief on the subsets of Θ . Based on its properties, we strongly recommend this measure as an additional summary of significance tests. At the end of the paper we give a short listing of possible open problems.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators.

Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simulations to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.

The impact of measurement errors in the identification of regulatory networks

BackgroundThere are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise.ResultsThis article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data.ConclusionsMeasurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.

A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets

UNLABELLED We propose a likelihood ratio test (LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrap-based approach. LRT is shown to be significantly faster and statistically powerful even within non-Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided. AVAILABILITY http://dnagarden.ims.u-tokyo.ac.jp/afujita/en/doku.php?id=ggranger.

Functional clustering of time series gene expression data by Granger causality

BackgroundA common approach for time series gene expression data analysis includes the clustering of genes with similar expression patterns throughout time. Clustered gene expression profiles point to the joint contribution of groups of genes to a particular cellular process. However, since genes belong to intricate networks, other features, besides comparable expression patterns, should provide additional information for the identification of functionally similar genes.ResultsIn this study we perform gene clustering through the identification of Granger causality between and within sets of time series gene expression data. Granger causality is based on the idea that the cause of an event cannot come after its consequence.ConclusionsThis kind of analysis can be used as a complementary approach for functional clustering, wherein genes would be clustered not solely based on their expression similarity but on their topological proximity built according to the intensity of Granger causality among them.

Short communication: A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the @D matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms.

Vector autoregressive models with measurement errors for testing Granger causality

Abstract This paper develops a method for estimating the parameters of a vector autoregression (VAR) observed in white noise. The estimation method assumes that the noise variance matrix is known and does not require any iterative process. This study provides consistent estimators and the asymptotic distribution of the parameters required for conducting tests of Granger causality. Methods in the existing statistical literature cannot be used for testing Granger causality, since under the null hypothesis the model becomes unidentifiable. Measurement error effects on parameter estimates were evaluated by using computational simulations. The results suggest that the proposed approach produces empirical false positive rates close to the adopted nominal level (even for small samples) and has a satisfactory performance around the null hypothesis. The applicability and usefulness of the proposed approach are illustrated using a functional magnetic resonance imaging dataset.