Statistical Theory: Fundamentals

This lecture introduces the fundamental concepts of statistical theory, focusing on the job of probabilists and statisticians, the three main questions of statistics (estimation, comparison, prediction), and the connection between probability and statistics. It covers topics such as algebra of events, probability measures, conditional probability, random variables, distribution functions, and sampling distributions. The lecture also discusses parametric models, identifiability, and parametric inference for regular models, emphasizing the importance of understanding parameters of probability models.