Exchangeability is a fundamental concept in probability theory which has profound theoretical implications, but it is seldom satisfied in a dependence modelling setting. I wrote a report studying some extensions of exchangeability—some of which even have de Finetti-like representation theorems—that can be used in settings with covariates. I then studied how these translate in a particular dependence setting: that of Gaussian Process regression. This report was written as a final project for STAT 547C: Topics in Probability at UBC.
For my undergraduate thesis I studied experimental design from a Bayesian perspective, focusing on Overstall and Woods' (2017) ACE algorithm to find optimal designs. The algorithm employs Monte Carlo approximations to estimate the expected loss as a function of a single coordinate of the design. It then smooths these values via a Gaussian process emulator, obtaining a surrogate expected loss function that is then minimized. I analyzed the impact that different loss functions and prior distributions have on optimal Bayesian designs for some generalized linear model examples in the literature. My conclusion was that the former led to similar posterior distributions for the parameters, while the latter produced completely different optimal designs.
My thesis won an honorary mention in the yearly prize to the best undergraduate theses at ITAM. I am still interested in doing further research on this topic, specifically related to the optimization of the expected loss function via GPs and the design of the underlying computer experiment.
I developed a dashboard to help explain the concept of statistical power and its relationship with sample size. The purpose is to develop a visual understanding of the balance between power, specificity, sample size, and effect size. By playing with these factors in a toy example (one-sided test with Normal distributions and known variance), the user can get a feeling of the impact that each one has on the rest. The dashboard also includes a sample size calculator: given a significance level, effect size, and desired power, what is the smallest sample size that guarantees the desired power? Finally, I also created a set of slides to complement the dashboard. This project was developed for STAT 550: Techniques of Statistical Consulting at UBC, and has since been published in StatSpace along with an ad-hoc activity sheet.
I wrote an article exploring the sentiments behind the lyrics of Grammy award winners. Using text mining and sentiment analysis, I tried to understand how albums' average sentiment relates to them winning (or not) a Grammy Award. An edited and slightly modified version of this article was published in Significance in 2019.
Anáhuac is one of Mexico’s most renowned higher learning institutions, and its curriculum is focused on so-called positive action leadership. But what exactly does it mean to be a leader? I devised a leadership-themed online survey and asked undergraduate students at Anáhuac University to answer it. I then analyzed the results to understand what traits Anáhuac students consider paramount for good leadership.