Research Reports

4/2017 Bayesian General Cholesky Decomposition Based Modeling of Longitudinal Multiple-Group IRT Data with Skewed Latent Distributions and Growth Curves
José Roberto Silva dos Santos , Caio Lucidius Naberezny Azevedo
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3/2017 A General Cholesky Decomposition Based Modeling of Longitudinal IRT Data: Handling Skewed Latent Traits Distributions
José Roberto Silva dos Santos, Caio Lucidius Naberezny Azevedo
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2/2017 A General Cholesky Decomposition Based Modeling of Longitudinal IRT Data.
José Roberto Silva dos Santos, Caio Lucidius Naberezny Azevedo
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1/2017 Counting Numerical Semigroups by Genus and Even Gaps
Matheus Bernardini, Fernando Torres

We present an approach to count numerical semigroups of a given genus by using even gaps. Our method is motivated by the interplay between double covering of curves and γ-hyperelliptic semigroups [15], [12], [28], [18], [17].

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17/2016 On the curve Y^n = X^l (X^m + 1) over finite fields
Saeed Tafazolian, Fernando Torres

Let X be the nonsingular model of a plane curve of type y^n = f (x) over the finite field F of order q^2 , where f(x) is a separable polynomial of degree coprime to n. If the number of F-rational points of X attains the Hasse-Weil bound, then the condition n divides q + 1 is equivalente to the solubility of f(x) in F. In this paper, we investigate this condition for f(x) = x^l (x^m + 1)

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16/2016 On the spectrum for the genera of maximal curves over small fields
Nazar Arakelian, Saeed Tafazolian, Fernando Torres

Motivated by previous computations in Garcia, Stichtenoth and Xing (2000) paper [9], we discuss the spectrum M(q 2 ) for the genera of maximal curves over finite fields of order q 2 with 7 ≤ q ≤ 16. In particular, by using a result in Kudo and Harashita(2016) paper [17], the set M(7 2 ) is completely determined.

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15/2016 Finite mixture modeling of censored data using the multivariate Student-t distribution
Víctor H. Lachos, Edgar J. López Moreno, Kun Chen

Finite mixture models have been widely used for the modelling and analysis of data froma heterogeneous population. Moreover, these kind of data can be subjected to some upper and/or lower detection limits because of the restriction of experimental apparatus. Another complication arises when measures of each population depart significantly from normality, for instance, in the presence of heavy tails or atypical observations. For such data structures, we propose a robust model for censored data based on finite mixtures of multivariate Student-t distributions. This approach allows us to model data with great flexibility, accommodating multimodality, heavy tails and also skewness depending on the structure of the mixture components. We develop an analytically simple yet efficient EM-type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the multivariate truncated Student-t distributions. Further, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real data sets are reported to demonstrate the effectiveness of the proposed methodology. The proposed algorithm and methods are implemented in the new R package CensMixReg.

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14/2016 Bayesian estimation, residual analysis and prior sensitivity study for zero-one augmented beta regression model with an application to psychometric data
Danilo Covaes Nogarotto, Caio L. N. Azevedo, Jorge Luiz Bazán

The interest on the analysis of the zero-one augmented beta regres sion (ZOABR) model has been increasing over the last years. In this paper we developed an extensive study on parameter recovery, prior sensitivity and the impact of some factors (scenarios of interest) comparing the Bayesian paradigm with the Maximum Likelihood (ML) approach. Jeffreys-rule, independence Jeffreys and improper priors were compared with usual choices. The results indicate, in a general way, that: the Bayesian approach, under the Jeffreys-rule prior, was as accurate as the ML one. In addition, as expected, the larger the sample size and the lower the variability of the data the more accurate are the parameter estimates. Also, we use the predictive distribution of the response to implement some available residual techniques (previously developed under the frequentist approach). To further illustrate the advantages of our approach, we conduct an analysis of a psychometric real data set including Bayesian residual analysis, where is showed that misleading inference can be obtained when the data is transformed. That is, when the observedzeros and ones are transformed to suitable values and the usual beta regression model is considered, instead using the ZOABR model. Finally, future developments are discussed.

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13/2016 Stochastic Neighborhood Structure in Bayesian Spatial Models
Aline Piroutek, R. Assunção, D. Duarte
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12/2016 Probabilistic Context Neighborhood: A New Tree Topology and Hypothese Tests
Aline Piroutek, D. Duarte, R. Assunção, Aluísio Pinheiro

We introduce the Probabilistic Context Neighborhood model for two dimensional lattices as an extension of the Probabilistic Context Tree model in one dimensional space preserving some of its interesting properties. This model has a variable neighborhood structure with a fixed geometry but varying radius. In this way we are able to compute the cardinality of the set of neighborhoods and use the Pseudo-Likelihood Bayesian Criterion to select an appropriate model given the data. We represent the dependence neighborhood structure as a tree making easier to understand the model complexity. We provide an algorithm to estimate the model that explores the sparse tree structure to improve computational efficiency. We also present an extension of the previous model, the Non-Homogeneous Probabilistic Context Neighborhood model, which allows a spatially changing Probabilistic Context Neighborhood as we move on the lattice.

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