[12/01/2024] Σεμινάριο Μεταπτυχιακών Φοιτητών του Τμήματος Μαθηματικών Α.Π.Θ.

Τίτλος: Decoding COVID-19: Insights from Frequentist/Bayesian Generalized Linear Models

Περίληψη:Linear models are a powerful tool in analyzing and predicting the behavior of complex systems and are heavily used in financial and biological data. They describe a continuous response as a function of one or more predictor variables. However, what happens when the response is not continuous, e.g. binary, count etc.? How do we generalize the idea of regression to deal with the relationship between categorical/count responses and the set of regression variables? In this presentation, we will introduce the concept of Generalized Linear Models (GLMs), specifically focusing on the cases of Logistic and Poisson Regression to handle binary and count data, respectively. Furthermore, we will not restrict ourselves to the well-known frequentist case of GLMs but will also expand on the Bayesian framework of GLMs. In Bayesian GLMs we approach the GLMs within the context of Bayesian inference. Instead of treating the regression coefficients as unknown fixed constants, we treat them as random variables assuming a prior distribution and make inference based on their posterior distribution using Bayes’ Theorem, rather than receiving single values. We will provide a detailed analysis of real COVID data to provide insight on the relationship between cases of death/hospitalization and the age covariate. Our focus will be the analysis of the data from both Frequentist and Bayesian perspectives using the R programming software and the probabilistic language Stan within R.