Tail conditional probabilities to predict academic performance

Abstract

In this paper, we estimate tail conditional probabilities by incorporating copula models and adopting a Bayesian estimation process for the copula’s parameter. Based on the records of student’s classifications in (a) Mathematics and (b) Natural Sciences/Physics (of the entrance exam to the University of Campinas, from 2013 to 2015), by means of tail conditional probabilities we predict the performance, of the same students, in Calculus I which is a mandatory subject of the undergraduate course of Statistics, and we compare the conditional probabilities year after year. We see that (a), (b) and Calculus I show maximal trivariate correlations in tail events given by classifications which are jointly high/low in the three subjects. We compare the evolution of the tail conditional probabilities from 2013 to 2015 and, according to our results there has been an improvement (from 2013 to 2015) of at most 12%. This improvement being more incisive in the settings with conditional events given by jointly high classifications in comparison with settings with conditional events given by jointly lower classifications.

Keywords

• Directional dependence
• Conditional probability
• Joe’s copula
• Bayesian estimation