Applied Statistics
The theoretical aspects of Statistics, based on Probability Theory and other areas of Mathematics, serve as the basis for statistical methods and techniques. Since the beginning of the last century, and especially since its second half, the impressive development of Statistics has generated problems of increasing complexity, which have raised the elaboration of analysis and modeling methodologies that require very diverse mathematical tools for their foundation and for the understanding of their virtues and possible limitations in the application to concrete problems.
The Area of Concentration in Statistical Theory seeks to promote research in theoretical problems of Statistics that are novel and relevant for the development of the discipline and to face the new challenges posed to it by science and technology. To this end, it fosters multidisciplinary and interdisciplinary research relationships between Statistics and other disciplines of mathematics, especially Probability Theory.
Historically, Statistics has always been nourished by problems posed by other branches of knowledge and currently this interaction poses novel challenges. The concentration areas of Stochastic Modeling and Inference in Science, Industry and Technology, Probability and Statistical Inference in Data Science, and Finance and Risk are vigorous examples of contexts that generate basic research problems in statistical theory with diverse thematic origins. Among the emerging challenges of multidisciplinary interactions, it is worth mentioning the development of statistics for new sample spaces associated with complex data such as functional spaces, varieties and topological spaces; statistics for parameters of non-finite dimension; and statistics of massive and high-dimensional data.
Within the area of Probability and Statistics at CIMAT, lines of theoretical statistical research stand out in the following topics:
Senior Researchers
Associate Researchers
Researchers for Mexico
Post-Doctorates
Statistical Inference
Senior Researchers
Associate Researchers
Researchers for Mexico
Post-Doctorates
Stochastic Modeling
Mathematical modeling has been clearly present in science since its origins. Since the observation of nature inevitably involves random aspects, the incorporation of non-deterministic models in research in Physics, Biology, Chemistry, Engineering, etc. is becoming more and more relevant. By non-deterministic or stochastic models we mean mathematical descriptions of random components in diverse phenomena. Typically, these descriptions are based on probability theory, whose parameters regulate the models describing the random nature of such phenomena. These stochastic models have also shown great importance in technological development in industry and decision making in government and private companies. When there is a record of physical observations of a random phenomenon, one is faced with a problem of statistical inference. This consists of knowing about the unknown parameters and making scientifically supported qualitative and quantitative assertions about the situation under study. This leads to the important task of quantifying the uncertainty associated with such assertions. This area of concentration comprehensively covers the modeling and inference described above, taking into account theoretical aspects, implementation issues, scientific computation and inference in real problems of scientific linkage as well as with the government, services and industry sectors. Nowadays, data of very diverse nature and in large quantities are generated, and problems with high degrees of complexity arise. This generates a great dynamism between research areas in probability and statistics and applications. It is more common for statistical modeling to take into account specialized knowledge in other subjects, thus giving rise to various multidisciplinary interactions. The area of probability and statistics at CIMAT has a long-standing tradition of collaborations with various public institutions, research institutes, national and foreign universities, and private companies to address research problems motivated by questions originating in a wide range of knowledge areas. The accumulated historical experience lies in ecology, medicine, physics, biogeography, epidemiology, public health, government, social sciences, industrial production, molecular biology, neurosciences and genetics, among others. The area cultivates research topics in probability and statistics that are motivated by specific problems arising from interdisciplinary interactions. This process requires the development of problem-specific stochastic models that incorporate general knowledge from the other research areas involved, to then evaluate the qualities of the statistical inference obtained. Some of these concrete problems originated in this way naturally nourish the areas of concentration of Probability Theory in the modeling phase, and of Statistical Theory in the inference phase insofar as the derived approaches are eminently abstract. Some of the recent topics that have given rise to theoretical research in statistics include:
Senior Researchers
Associate Researchers
Researchers for Mexico
Post-Doctorates
Probability Theory
Juan Carlos Pardo Millán, PhD
Coordinator of the Probability and Statistics
E-mail:
jcpardo@cimat.mx
Joly Emilien Antoine Marie, PhD
Graduate Coordinator of Probability and Statistics
E-mail:
