2018-03-29 - H. Dennis Tolley - What's the Likelihood?

The likelihood function plays a major role in both frequentist and Bayesian methods of data analysis. Non-parametric Bayesian models also rely heavily on the form of the likelihood. Despite its heuristic foundation, the likelihood has several desirable large sample statistical properties that prompt its use among frequentists. Additionally, there are other important facets of the likelihood that warrant its formulation in many circumstances. As fundamental as the likelihood is, however, beginning students are only given a cursory introduction into how to formulate the likelihood. This seminar illustrates the formulation of the likelihood for a family of statistical problems common in the physical sciences. By examining the basic scientific principles associated with an experimental set-up, we show the step by step construction of the likelihood, starting with the discrete random walk model as a paradigm. The resulting likelihood is the solution to a stochastic differential equation. Elementary applications of the likelihood are illustrated.
Mar 29, 2018