arXiv subjects

Marcos O. Prates

Publications and source records attributed to Marcos O. Prates.

12 recordsLinked to original sources

arXiv2026

Bridging Theory and Practice in Efficient Gaussian Process-Based Statistical Modeling for Large Datasets

Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating or computing likelihoods with GPs limits their scalability to large datasets. This paper introduces the piecewise continuous Gaussian process (PCGP), a new process that retains the rich probabilistic structure of traditional GPs while offering substantial computational efficiency. As will be shown and discussed, existing scalable approaches that define stochastic processes on continuous domains -- such as the nearest-neighbour GP (NNGP) and the radial-neighbour GP (RNGP) -- rely on conditional independence structures that effectively constrain the measurable space on which the processes are defined, which may induce undesirable probabilistic behaviour and compromise their practical applicability, particularly in complex latent GP models. The PCGP mitigates these limitations and provides a theoretically grounded and computationally efficient alternative, as demonstrated through numerical illustrations.

stat.CO↗

arXiv2024

The Analysis of Criminal Recidivism: A Hierarchical Model-Based Approach for the Analysis of Zero-Inflated, Spatially Correlated recurrent events Data

The life course perspective in criminology has become prominent last years, offering valuable insights into various patterns of criminal offending and pathways. The study of criminal trajectories aims to understand the beginning, persistence and desistence in crime, providing intriguing explanations about these moments in life. Central to this analysis is the identification of patterns in the frequency of criminal victimization and recidivism, along with the factors that contribute to them. Specifically, this work introduces a new class of models that overcome limitations in traditional methods used to analyze criminal recidivism. These models are designed for recurrent events data characterized by excess of zeros and spatial correlation. They extend the Non-Homogeneous Poisson Process, incorporating spatial dependence in the model through random effects, enabling the analysis of associations among individuals within the same spatial stratum. To deal with the excess of zeros in the data, a zero-inflated Poisson mixed model was incorporated. In addition to parametric models following the Power Law process for baseline intensity functions, we propose flexible semi-parametric versions approximating the intensity function using Bernstein Polynomials. The Bayesian approach offers advantages such as incorporating external evidence and modeling specific correlations between random effects and observed data. The performance of these models was evaluated in a simulation study with various scenarios, and we applied them to analyze criminal recidivism data in the Metropolitan Region of Belo Horizonte, Brazil. The results provide a detailed analysis of high-risk areas for recurrent crimes and the behavior of recidivism rates over time. This research significantly enhances our understanding of criminal trajectories, paving the way for more effective strategies in combating criminal recidivism.

stat.ME↗

arXiv2023

Is augmentation effective to improve prediction in imbalanced text datasets?

Imbalanced datasets present a significant challenge for machine learning models, often leading to biased predictions. To address this issue, data augmentation techniques are widely used in natural language processing (NLP) to generate new samples for the minority class. However, in this paper, we challenge the common assumption that data augmentation is always necessary to improve predictions on imbalanced datasets. Instead, we argue that adjusting the classifier cutoffs without data augmentation can produce similar results to oversampling techniques. Our study provides theoretical and empirical evidence to support this claim. Our findings contribute to a better understanding of the strengths and limitations of different approaches to dealing with imbalanced data, and help researchers and practitioners make informed decisions about which methods to use for a given task.

cs.CL↗

arXiv2021

Fast Bayesian inference of Block Nearest Neighbor Gaussian process for large data

This paper presents the development of a spatial block-Nearest Neighbor Gaussian process (block-NNGP) for location-referenced large spatial data. The key idea behind this approach is to divide the spatial domain into several blocks which are dependent under some constraints. The cross-blocks capture the large-scale spatial dependence, while each block captures the small-scale spatial dependence. The resulting block-NNGP enjoys Markov properties reflected on its sparse precision matrix. It is embedded as a prior within the class of latent Gaussian models, thus Bayesian inference is obtained using the integrated nested Laplace approximation (INLA). The performance of the block-NNGP is illustrated on simulated examples and massive real data for locations in the order of $10^4$.

stat.ME↗

arXiv2020

A robust nonlinear mixed-effects model for COVID-19 deaths data

The analysis of complex longitudinal data such as COVID-19 deaths is challenging due to several inherent features: (i) Similarly-shaped profiles with different decay patterns; (ii) Unexplained variation among repeated measurements within each country, these repeated measurements may be viewed as clustered data since they are taken on the same country at roughly the same time; (iii) Skewness, outliers or skew-heavy-tailed noises are possibly embodied within response variables. This article formulates a robust nonlinear mixed-effects model based in the class of scale mixtures of skew-normal distributions for modeling COVID-19 deaths, which allows the analysts to model such data in the presence of the above described features simultaneously. An efficient EM-type algorithm is proposed to carry out maximum likelihood estimation of model parameters. The bootstrap method is used to determine inherent characteristics of the nonlinear individual profiles such as confidence interval of the predicted deaths and fitted curves. The target is to model COVID-19 deaths curves from some Latin American countries since this region is the new epicenter of the disease. Moreover, since a mixed-effect framework borrows information from the population-average effects, in our analysis we include some countries from Europe and North America that are in a more advanced stage of their COVID-19 deaths curve.

stat.AP↗

arXiv2020

Heckman selection-t model: parameter estimation via the EM-algorithm

Heckman selection model is perhaps the most popular econometric model in the analysis of data with sample selection. The analyses of this model are based on the normality assumption for the error terms, however, in some applications, the distribution of the error term departs significantly from normality, for instance, in the presence of heavy tails and/or atypical observation. In this paper, we explore the Heckman selection-t model where the random errors follow a bivariate Student's-t distribution. We develop an analytically tractable and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated Student's-t distributions. Simulations studies show the vulnerability of the Heckman selection-normal model, as well as the robustness aspects of the Heckman selection-t model. Two real examples are analyzed, illustrating the usefulness of the proposed methods. The proposed algorithms and methods are implemented in the new R package HeckmanEM.

stat.ME↗

arXiv2020

Non-Separable Spatio-temporal Models via Transformed Gaussian Markov Random Fields

Models that capture the spatial and temporal dynamics are applicable in many science fields. Non-separable spatio-temporal models were introduced in the literature to capture these features. However, these models are generally complicated in construction and interpretation. We introduce a class of non-separable Transformed Gaussian Markov Random Fields (TGMRF) in which the dependence structure is flexible and facilitates simple interpretations concerning spatial, temporal and spatio-temporal parameters. Moreover, TGMRF models have the advantage of allowing specialists to define any desired marginal distribution in model construction without suffering from spatio-temporal confounding. Consequently, the use of spatio-temporal models under the TGMRF framework leads to a new class of general models, such as spatio-temporal Gamma random fields, that can be directly used to model Poisson intensity for space-time data. The proposed model was applied to identify important environmental characteristics that affect variation in the abundance of Nenia tridens, a dominant species of snail in a well-studied tropical ecosystem, and to characterize its spatial and temporal trends, which are particularly critical during the Anthropocene, an epoch of time characterized by human-induced environmental change associated with climate and land use.

stat.ME↗

arXiv2020

Objective Bayesian analysis for spatial Student-t regression models

The choice of the prior distribution is a key aspect of Bayesian analysis. For the spatial regression setting a subjective prior choice for the parameters may not be trivial, from this perspective, using the objective Bayesian analysis framework a reference is introduced for the spatial Student-t regression model with unknown degrees of freedom. The spatial Student-t regression model poses two main challenges when eliciting priors: one for the spatial dependence parameter and the other one for the degrees of freedom. It is well-known that the propriety of the posterior distribution over objective priors is not always guaranteed, whereas the use of proper prior distributions may dominate and bias the posterior analysis. In this paper, we show the conditions under which our proposed reference prior yield to a proper posterior distribution. Simulation studies are used in order to evaluate the performance of the reference prior to a commonly used vague proper prior.

math.ST↗

arXiv2017

Bayesian linear regression models with flexible error distributions

This work introduces a novel methodology based on finite mixtures of Student-t distributions to model the errors' distribution in linear regression models. The novelty lies on a particular hierarchical structure for the mixture distribution in which the first level models the number of modes, responsible to accommodate multimodality and skewness features, and the second level models tail behavior. Moreover, the latter is specified in a way that no degrees of freedom parameters are estimated and, therefore, the known statistical difficulties when dealing with those parameters is mitigated, and yet model flexibility is not compromised. Inference is performed via Markov chain Monte Carlo and simulation studies are conducted to evaluate the performance of the proposed methodology. The analysis of two real data sets are also presented.

stat.ME↗

arXiv2017

Robust Bayesian model selection for heavy-tailed linear regression using finite mixtures

In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture corresponds to one possible model within the symmetrical class of normal independent distributions. Naturally, the Gaussian model is one of the possibilities. This allows for a simultaneous analysis based on the posterior probability of each model. Inference is performed via Markov chain Monte Carlo - a Gibbs sampler with Metropolis-Hastings steps for a class of parameters. Simulated examples highlight the advantages of this approach compared to a segregated analysis based on arbitrarily chosen model selection criteria. Examples with real data are presented and an extension to censored linear regression is introduced and discussed.

stat.ME↗

arXiv2016

Where geography lives? A projection approach for spatial confounding

Spatial confounding between the spatial random effects and fixed effects covariates has been recently discovered and showed that it may bring misleading interpretation to the model results. Solutions to alleviate this problem are based on decomposing the spatial random effect and fitting a restricted spatial regression. In this paper, we propose a different approach: a transformation of the geographic space to ensure that the unobserved spatial random effect added to the regression is orthogonal to the fixed effects covariates. Our approach, named SPOCK, has the additional benefit of providing a fast and simple computational method to estimate the parameters. Furthermore, it does not constrain the distribution class assumed for the spatial error term. A simulation study and a real data analysis are presented to better understand the advantages of the new method in comparison with the existing ones.

stat.ME↗

arXiv2012

Transformed Gaussian Markov Random Fields and Spatial Modeling

The Gaussian random field (GRF) and the Gaussian Markov random field (GMRF) have been widely used to accommodate spatial dependence under the generalized linear mixed model framework. These models have limitations rooted in the symmetry and thin tail of the Gaussian distribution. We introduce a new class of random fields, termed transformed GRF (TGRF), and a new class of Markov random fields, termed transformed GMRF (TGMRF). They are constructed by transforming the margins of GRFs and GMRFs, respectively, to desired marginal distributions to accommodate asymmetry and heavy tail as needed in practice. The Gaussian copula that characterizes the dependence structure facilitates inferences and applications in modeling spatial dependence. This construction leads to new models such as gamma or beta Markov fields with Gaussian copulas, which can be used to model Poisson intensity or Bernoulli rate in a spatial generalized linear mixed model. The method is naturally implemented in a Bayesian framework. We illustrate the utility of the methodology in an ecological application with spatial count data and spatial presence/absence data of some snail species, where the new models are shown to outperform the traditional spatial models. The validity of Bayesian inferences and model selection are assessed through simulation studies for both spatial Poisson regression and spatial Bernoulli regression.

stat.ME↗