Classical Statistical Inference—Hypothesis Testing and Parameter Estimation

Fecha: Viernes 21 de Abril de 2023.
Hora: 12:00h.
Lugar: Laboratorio de Física Computacional. Edificio de Física. Facultad de Ciencias. 

Ponente: Michalis Skotiniotis. 

Organiza: Grupo de Termodinámica y Computación Cuántica.

Animamos especialmente a estudiantes a asistir.

Statistical inference is an important branch of decision theory and deals with taking optimal decisions in the face of uncertainty. For instance, the decision of whether a new drug combats a given disease or not is taken based on samples taken from medical trials and forms the primary example of classical hypothesis testing. On the other hand, determining the precision in the estimation of a certain physical constant—such as the value of the gravitational constant g—is an example of parameter estimation. In this talk we will go through both these tasks from the point of view of statistical decision theory. In the case of hypothesis testing we will derive the optimal decision rule for minimizing the probability of erroneously identifying the likely hypothesis, as well as several variants of symmetric and asymmetric hypothesis testing (the famous Neyman-Pearson theorem). For parameter estimation we will derive the celebrated Cramér-Rao theorem which sets a lower bound on the precision of any unbiased estimator, and we will connect this to the traditional error propagation formula we all know and love (or hate as the case may be).