Regular Exponential Family Models

This lecture covers the concept of regular exponential family models, where various distributions like Poisson, binomial, and normal are unified under a common framework. The theory defines a d-dimensional statistic s as minimal sufficient for the parameter 0, with a canonical parameter y and mean parameter n. The cumulant-generating function and its properties are discussed, emphasizing the importance of the canonical statistic S. The lecture explores the log moment-generating function and its relation to the cumulant-generating function, providing insights into the statistical inference of exponential family models.