Applied Statistics
Senior Researchers
Associate Researchers
Researchers for Mexico
Development and Implementation of New Statistical and Stochastic Techniques in Complex Models Duration: 3 years – 02/01/2024 to 11/30/2026. Responsible: Graciela María González Farías Organization: CIMAT Campus Monterrey. Grantor: National Council of Humanities, Science and Technology: CBF2023-2024-3976, Scientific Research Projects, Amount: 1,499,116.
Statistical Inference
Statistical theory provides the foundation for learning from data, enabling the estimation of parameters, the quantification of uncertainty, and the evaluation of hypotheses in the presence of randomness. Modern challenges in science, technology, and industry require inference procedures that remain valid under complex data-generating mechanisms, such as dependence, high dimensionality, heterogeneous structures, and nonstandard sampling designs. Advancing these theoretical foundations is essential for the development of reliable, interpretable, and efficient statistical methodologies.
Research in statistical inference within the Probability and Statistics group at CIMAT focuses on rigorous methodological development supported by probability theory, asymptotic analysis, stochastic processes, functional analysis, and optimization. The group works on establishing fundamental properties of estimators, understanding the limits of inference, and designing procedures that are robust, efficient, and applicable to modern data structures. This work is carried out in collaboration with national and international research groups and is closely aligned with active areas of contemporary statistical science.
The research covers both classical and modern paradigms of inference, including frequentist, Bayesian, and likelihood-based approaches. Current methodological questions stem from challenges in data science, machine learning, stochastic modeling, and emerging scientific applications, motivating the development of new theoretical frameworks for uncertainty quantification, optimal estimation, and hypothesis testing.
Active research lines in statistical inference within the Area include:
Asymptotic theory, consistency, and efficiency of estimators
Inference under dependence, including time series, stochastic processes, and spatial models
Nonparametric and semiparametric inference, with applications to complex data
Bayesian inference and approximation methods such as variational techniques and sequential Monte Carlo
High-dimensional inference, including shrinkage methods, penalized likelihood, and sparse modeling
Empirical process theory and concentration inequalities
Robust inference and methods stable under model misspecification
Inference for stochastic models, including branching processes, Markov processes, and diffusions
Uncertainty quantification for models in science and engineering
This line of research aims to advance the mathematical foundations of statistical learning and contribute to the development of inference tools capable of addressing contemporary scientific challenges. By combining rigorous theory with methodological innovation, the group strengthens CIMAT’s role as a national and international reference in the statistical sciences.
Senior Researchers
Associate Researchers
Researchers for Mexico
Investigadora Emérita del SNII, México.
Development and Implementation of New Statistical and Stochastic Techniques in Complex Models Duration: 3 years – 02/01/2024 to 11/30/2026. Responsible: Graciela María González Farías Organization: CIMAT Campus Monterrey. Grantor: National Council of Humanities, Science and Technology: CBF2023-2024-3976, Scientific Research Projects, Amount: 1,499,116.
Stochastic Modeling
Stochastic modeling focuses on the mathematical representation of phenomena that involve uncertainty, variability, or random noise. In many biological, physical, social, industrial, and technological systems, randomness plays a fundamental role that cannot be captured by deterministic models. Rigorous study of stochastic models makes it possible to describe complex dynamics, understand emergent behaviors, and develop reliable predictions in contexts where uncertainty is intrinsic.
Within the Probability and Statistics group at CIMAT, the Stochastic Modeling line encompasses the formulation, analysis, and application of models based on stochastic processes, stochastic differential equations, particle systems, random structures, and spatio-temporal models. The work integrates probability theory, functional analysis, Markov process theory, and advanced computational methods, and it is strengthened by extensive national and international collaborations with researchers and institutions across scientific, technological, and industrial domains.
Research in this line covers both the theoretical development of stochastic models and their application to real-world problems. This includes the study of fundamental properties such as stability, asymptotic behavior, existence and uniqueness, absorption times, explosion, tail behavior, and phenomena such as coming down from infinity. Applications often generate new mathematical questions that drive advances in branching processes, dispersal models, population dynamics, epidemiology, transport phenomena, communication systems, stochastic finance, and other fields.
Current research topics in stochastic modeling within the area include:
Markov processes in continuous and discrete time, and their structural properties
Branching processes, discrete or in continuous spaces or in random environments (J.A. Lopez Mimbela)
Spatio-temporal models and interacting particle systems
Stochastic differential equations, with additive or multiplicative noise (E. Todorova Kolkovska; J.A. López Mimbela)
Stochastic population models, epidemiological dynamics, and ecological processes
Models for environmental and climate-related phenomena, including extremes and space–time dependence
Applications in social sciences, industry, and technology
Numerical methods and stochastic simulation, including Monte Carlo techniques and process approximations
Asymptotic properties, hydrodynamic limits, and scaling behaviors (J.A. Lopez Mimbela)
This research line combines advanced mathematical tools with substantive applications, contributing to a deeper understanding of random systems and the development of models that support a wide range of scientific and applied fields. Through this work, CIMAT strengthens its national and international leadership in stochastic processes and probabilistic modeling.
Senior Researchers
Associate Researchers
Post-Doctorates
Proyecto de Ciencia de Frontera “Soluciones Positivas de Ecuaciones Estocásticas de Reacción-Difusión” 202.1-2023
Procesos Gaussianos Fraccionarios (2024), Proyecto de Ciencia de Frontera.
Genealogies of random individuals in stochastic populations, Marsden Fund, Nueva Zelanda
Genealogías aleatorias: estructura probabilística y aplicaciones , Ciencia de Frontera 2023.
Probability Theory
Probability Theory provides the mathematical foundation for modeling random phenomena, analyzing stochastic processes, and understanding the behavior of complex systems subject to uncertainty. Within the Probability and Statistics Area at CIMAT, the research line in Probability Theory develops both classical and cutting-edge aspects of the discipline, establishing rigorous frameworks that support stochastic process theory, statistical inference, mathematical analysis, and a wide range of scientific applications.
The group encompasses a broad spectrum of topics, including limit theorems, stochastic dynamics, free probability, convex analysis applied to random structures, and information-theoretic methods. This diversity reflects the central role of probability as a unifying discipline connecting pure mathematics, stochastic modeling, and contemporary applications.
Main Research Areas
Markov processes and stochastic dynamics
Study of continuous- and discrete-time Markov processes, ergodic properties, mixing rates, coupling techniques, and stability of stochastic systems.
Limit theorems and asymptotic probability
Central limit theorems, concentration inequalities, asymptotic behavior, and probabilistic limits in both classical and high-dimensional settings.
Information-theoretic methods in probability
Entropy, divergences, Fisher information, information inequalities, and information geometry, with applications to probabilistic limits, convergence rates, and optimal bounds.
Free probability
Free independence, free convolutions, spectral properties of random matrices, and operator-based noncommutative techniques for studying large random systems.
Convex and geometric aspects of probability
Log-concave measures, transport inequalities, geometric functional analysis, and convexity-based tools for the study of probabilistic structures.
Stochastic processes and random structures
Lévy processes, branching processes, interacting particle systems, random networks, and stochastic models with jumps, dependence, or non-Markovian behavior.
Research in Probability Theory at CIMAT is characterized by:
A rigorous mathematical approach grounded in analysis, geometry, and functional methods.
Continuous interaction with central themes in data science, statistical physics, learning theory, stochastic modeling, and high-dimensional phenomena.
National and international collaborations with leading groups in probability and related fields.
Contributions that advance both the fundamental development of the discipline and applied methodologies in statistics, optimization, machine learning, and complex systems.
This research line positions CIMAT as a leading center in the advancement of modern probability theory, fostering theoretical development and its interplay with scientific and technological applications.
Senior Researchers
Associate Researchers
Juan Carlos Pardo Millán, PhD
Coordinator of the Probability and Statistics
E-mail:
jcpardo@cimat.mx
