Description

The presentation “Measuring Statistical Risk – Expectation-Maximization Algorithm” first motivates the use of the EM algorithm in modern quantitative work where important parts of the data-generating process are hidden or incomplete, highlighting applications in areas such as genetics, signal processing, medical imaging, psychometrics, portfolio risk management, and speech recognition. It then explains EM in accessible terms as an iterative procedure that alternates between computing expected “complete data” quantities given the observed data and current parameter guesses, and updating the parameters to improve the fit, noting its local rather than global convergence and sensitivity to starting values. Building on this, the talk introduces mixture copula models as a flexible way to describe complex dependence by combining several copula components with different weights and treating the component labels as latent, and shows how EM can be used to estimate both the mixing weights and the dependence parameters. The presentation culminates in an applied example using daily standardized BMW and Siemens stock log-returns, where the margins are modeled with Student-t distributions and two mixture copulas (Gumbel–Clayton and Frank–Clayton) are fitted, providing a concrete illustration of EM-based mixture copula estimation for measuring statistical risk.