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Alejandro Hernandez Wences
Alejandro Hernandez Wences
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mathematician
mathematician
Researcher at IIMAS - UNAM
My Career Drivers and Interests are:
Curiosity
Purpose and Meaning
Analytical Problem Solving
Multidisciplinarity
Programming and Data Analysis
Research interests
Research interests
Population genetics
Population genetics
The study of stochastic processes inspired by biology, such as branching and coalescing processes, serves two purposes:
Supporting biological research with formal analytical and statistical tools.
Advancing the theory of self-similar measure-valued stochastic processes.
manifold learning and applications to machine learning
manifold learning and applications to machine learning
The application of Fermat's principle of light within a probability framework helps infer shapes and structures from data, which supports the development of novel machine learning algorithms and their application to real world problems.
non parametric bayesian statistics
non parametric bayesian statistics
Building new probability measure–valued stochastic processes leads to:
Novel time-dynamic models in non-parametric Bayesian statistics.
New tools for analyzing Bayesian models, using random time changes and duality relations between stochastic processes.
A brief overview of my career
A brief overview of my career
I have always been fascinated by both the theoretical and applied aspects of the Probability and Statistics fields. I began my career in Computational Biology, where I developed a software package (in C++, Python, and R) for analyzing extensive datasets of DNA sequences with the goal of building up entire genomic sequences from a vast array of small pieces. In this period, I developed skills in collecting and analyzing large datasets, in the development of software packages, in working with parallel computing, and in testing and comparing scientific methods and results.
Subsequently, during my MSc and PhD studies in Mathematics (UNAM), I delved deeply into the theoretical aspects of Stochastic Processes, Probability, and Statistics. I gained extensive experience in mathematical modeling and its applications, particularly in the field of Mathematical Population Genetics. During this stage, I gained experience in collaborative work, in exploring and learning entirely new fields (and in incorporating them into my prior knowledge), in analytical problem-solving, and in presenting complex ideas in a simple way. I also had the opportunity to teach undergraduate courses where I gained experience in managing a small team of educators and in formulating, organizing, and teaching new courses.
In parallel to my PhD studies, I did freelance voluntary work at an NGO (Partners in Health Mexico), where I developed an R-Shiny application with the aim of collecting medical data offline in uncommunicated rural areas, and of computing relevant statistical indicators and presenting them to decision-makers. I also developed a second R-Shiny application with the aim of informing diagnostic and treatment options for a particular disease using Bayesian decision analysis.
During my postdoctoral experience (at CIMI-Toulouse, and briefly at Bielefeld University), I continued research in mathematical population genetics while also developing mathematical tools for Machine Learning, with a focus on clustering algorithms. This work involves inferring general metric spaces from distance matrices by applying Fermat's principle of light within a probabilistic framework
Currently, as a researcher at IIMAS - UNAM, I continue my research in statistics and probability theory, developing new models in, and establishing new connections between, Bayesian statistics, population genetics, and unsupervised machine learning.
CONTACT
CONTACT
ahwences@sigma.iimas.unam.mx
https://www.researchgate.net/profile/Alejandro-Hernandez-Wences-2
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