arXiv subjects

Cristian Meza

Publications and source records attributed to Cristian Meza.

9 recordsLinked to original sources

arXiv2026

Stochastic EM Estimation and Inference for Zero-Inflated Beta-Binomial Mixed Models for Longitudinal Count Data

Analyzing overdispersed, zero-inflated, longitudinal count data poses significant modeling and computational challenges, which standard count models (e.g., Poisson or negative binomial mixed effects models) fail to adequately address. We propose a Zero-Inflated Beta-Binomial Mixed Effects Regression (ZIBBMR) model that augments a beta-binomial count model with a zero-inflation component, fixed effects for covariates, and subject-specific random effects, accommodating excessive zeros, overdispersion, and within-subject correlation. Maximum likelihood estimation is performed via a Stochastic Approximation EM (SAEM) algorithm with latent variable augmentation, which circumvents the model's intractable likelihood and enables efficient computation. Simulation studies show that ZIBBMR achieves accuracy comparable to leading mixed-model approaches in the literature and surpasses simpler zero-inflated count formulations, particularly in small-sample scenarios. As a case study, we analyze longitudinal microbiome data, comparing ZIBBMR with an external Zero-Inflated Beta Regression (ZIBR) benchmark; the results indicate that applying both count- and proportion-based models in parallel can enhance inference robustness when both data types are available.

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arXiv2025

A stochastic method to estimate a zero-inflated two-part mixed model for human microbiome data

Human microbiome studies based on genetic sequencing techniques produce compositional longitudinal data of the relative abundances of microbial taxa over time, allowing to understand, through mixed-effects modeling, how microbial communities evolve in response to clinical interventions, environmental changes, or disease progression. In particular, the Zero-Inflated Beta Regression (ZIBR) models jointly and over time the presence and abundance of each microbe taxon, considering the compositional nature of the data, its skewness, and the over-abundance of zeros. However, as for other complex random effects models, maximum likelihood estimation suffers from the intractability of likelihood integrals. Available estimation methods rely on log-likelihood approximation, which is prone to potential limitations such as biased estimates or unstable convergence. In this work we develop an alternative maximum likelihood estimation approach for the ZIBR model, based on the Stochastic Approximation Expectation Maximization (SAEM) algorithm. The proposed methodology allows to model unbalanced data, which is not always possible in existing approaches. We also provide estimations of the standard errors and the log-likelihood of the fitted model. The performance of the algorithm is established through simulation, and its use is demonstrated on two microbiome studies, showing its ability to detect changes in both presence and abundance of bacterial taxa over time and in response to treatment.

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arXiv2025

Conditional GLMMs for reaction times in choice tasks

This study connects two methods for modeling reaction times (RTs) in choice tasks: (1) the first-hitting time of a simple diffusion model with a single barrier, representing the cognitive process leading to a response, and (2) Generalized Linear Mixed Models (GLMMs). We achieve this by analyzing RT distributions conditioned on each response alternative. Because certain diffusion model variants yield Inverse Gaussian (IG) and Gamma distributions for first-hitting times, we can justify using these distributions in RT models. Conversely, employing IG and Gamma distributions within GLMMs allows us to infer the underlying cognitive processes. We demonstrate this concept through simulations and apply it to previously published real-world data. Finally, we discuss the scope and potential extensions of our approach.

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arXiv2019

AutoRegressive Planet Search: Application to the Kepler Mission

The 4-year light curves of 156,717 stars observed with NASA's Kepler mission are analyzed using the AutoRegressive Planet Search (ARPS) methodology described by Caceres et al. (2019). The three stages of processing are: maximum likelihood ARIMA modeling of the light curves to reduce stellar brightness variations; constructing the Transit Comb Filter periodogram to identify transit-like periodic dips in the ARIMA residuals; Random Forest classification trained on Kepler Team confirmed planets using several dozen features from the analysis. Orbital periods between 0.2 and 100 days are examined. The result is a recovery of 76% of confirmed planets, 97% when period and transit depth constraints are added. The classifier is then applied to the full Kepler dataset; 1,004 previously noticed and 97 new stars have light curve criteria consistent with the confirmed planets, after subjective vetting removes clear False Alarms and False Positive cases. The 97 Kepler ARPS Candidate Transits mostly have periods $P<10$ days; many are UltraShort Period hot planets with radii $<1$% of the host star. Extensive tabular and graphical output from the ARPS time series analysis is provided to assist in other research relating to the Kepler sample.

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arXiv2019

AutoRegressive Planet Search: Methodology

The detection of periodic signals from transiting exoplanets is often impeded by extraneous aperiodic photometric variability, either intrinsic to the star or arising from the measurement process. Frequently, these variations are autocorrelated wherein later flux values are correlated with previous ones. In this work, we present the methodology of the Autoregessive Planet Search (ARPS) project which uses Autoregressive Integrated Moving Average (ARIMA) and related statistical models that treat a wide variety of stochastic processes, as well as nonstationarity, to improve detection of new planetary transits. Providing a time series is evenly spaced or can be placed on an evenly spaced grid with missing values, these low-dimensional parametric models can prove very effective. We introduce a planet-search algorithm to detect periodic transits in the residuals after the application of ARIMA models. Our matched-filter algorithm, the Transit Comb Filter (TCF), is closely related to the traditional Box-fitting Least Squares and provides an analogous periodogram. Finally, if a previously identified or simulated sample of planets is available, selected scalar features from different stages of the analysis -- the original light curves, ARIMA fits, TCF periodograms, and folded light curves -- can be collectively used with a multivariate classifier to identify promising candidates while efficiently rejecting false alarms. We use Random Forests for this task, in conjunction with Receiver Operating Characteristic (ROC) curves, to define discovery criteria for new, high fidelity planetary candidates. The ARPS methodology can be applied to both evenly spaced satellite light curves and densely cadenced ground-based photometric surveys.

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arXiv2017

A Bayesian approach for the segmentation of series corrupted by a functional part

We propose a Bayesian approach to detect multiple change-points in a piecewise-constant signal corrupted by a functional part corresponding to environmental or experimental disturbances. The piecewise constant part (also called segmentation part) is expressed as the product of a lower triangular matrix by a sparse vector. The functional part is a linear combination of functions from a large dictionary. A Stochastic Search Variable Selection approach is used to obtain sparse estimations of the segmentation parameters (the change-points and the means over the segments) and of the functional part. The performance of our proposed method is assessed using simulation experiments. Applications to two real datasets from geodesy and economy fields are also presented.

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arXiv2014

Bayesian Regression Analysis of Data with Random Effects Covariates from Nonlinear Longitudinal Measurements

Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to asses association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. The most common joint model in this framework is based on a linear mixed model for the longitudinal data. However, for complex datasets the linearity assumption may be too restrictive. Some works have considered generalizing this setting with the use of a nonlinear mixed-effects model for the longitudinal trajectories but the proposed estimation procedures based on likelihood approximations have been shown De la Cruz et al. (2011) to exhibit some computational efficiency problems. In this article we propose an MCMC-based estimation procedure in the joint model with a nonlinear mixed-effects model for the longitudinal data and a generalized linear model for the primary response. Moreover, we consider that the errors in the longitudinal model may be correlated. We apply our method to the analysis of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. We also conduct a simulation study to asses the importance of modelling correlated errors and quantify the consequences of model misspecification.

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arXiv2014

Segmentation of multiple series using a Lasso strategy

We propose a new semi-parametric approach to the joint segmentation of multiple series corrupted by a functional part. This problem appears in particular in geodesy where GPS permanent station coordinate series are affected by undocumented artificial abrupt changes and additionally show prominent periodic variations. Detecting and estimating them are crucial, since those series are used to determine averaged reference coordinates in geosciences and to infer small tectonic motions induced by climate change. We propose an iterative procedure based on Dynamic Programming for the segmentation part and Lasso estimators for the functional part. Our Lasso procedure, based on the dictionary approach, allows us to both estimate smooth functions and functions with local irregularity, which permits more flexibility than previous proposed methods. This yields to a better estimation of the bias part and improvements in the segmentation. The performance of our method is assessed using simulated and real data. In particular, we apply our method to data from four GPS stations in Yarragadee, Australia. Our estimation procedure results to be a reliable tool to assess series in terms of change detection and periodic variations estimation giving an interpretable estimation of the functional part of the model in terms of known functions.

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arXiv2012

Lasso-type estimators for Semiparametric Nonlinear Mixed-Effects Models Estimation

Parametric nonlinear mixed effects models (NLMEs) are now widely used in biometrical studies, especially in pharmacokinetics research and HIV dynamics models, due to, among other aspects, the computational advances achieved during the last years. However, this kind of models may not be flexible enough for complex longitudinal data analysis. Semiparametric NLMEs (SNMMs) have been proposed by Ke and Wang (2001). These models are a good compromise and retain nice features of both parametric and nonparametric models resulting in more flexible models than standard parametric NLMEs. However, SNMMs are complex models for which estimation still remains a challenge. The estimation procedure proposed by Ke and Wang (2001) is based on a combination of log-likelihood approximation methods for parametric estimation and smoothing splines techniques for nonparametric estimation. In this work, we propose new estimation strategies in SNMMs. On the one hand, we use the Stochastic Approximation version of EM algorithm (Delyon et al., 1999) to obtain exact ML and REML estimates of the fixed effects and variance components. On the other hand, we propose a LASSO-type method to estimate the unknown nonlinear function. We derive oracle inequalities for this nonparametric estimator. We combine the two approaches in a general estimation procedure that we illustrate with simulated and real data.

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