Natural exponential family

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Related lectures (31)

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Generalised Linear Models: Regression with Exponential Family Responses

Covers regression with exponential family responses using Generalised Linear Models.

Special Families of Models

Explores completeness, minimal sufficiency, and special statistical models, focusing on exponential and transformation families.

Generalized Linear Models

Covers probability, random variables, expectation, GLMs, hypothesis testing, and Bayesian statistics with practical examples.

Exponential Family: Definition and Properties

Covers the Exponential Family, including its definition, sufficient statistics, and distribution properties.

Exponential Family Models: Statistical Inference

Covers exponential family models and their statistical properties, including canonical statistics and cumulant-generating functions.

Regular Exponential Family Models

Explores regular exponential family models, unifying distributions like Poisson, binomial, and normal under a common framework.

Maximum Likelihood Estimation: Properties and Applications

Covers Maximum Likelihood Estimation properties, applications, and assumptions, providing a comprehensive understanding of MLE concepts and their practical implications.

Statistical Justification of Least Squares

Explores the statistical justification of Least Squares and Generalized Linear Models.

Exponential Family: Maximum Entropy Distribution

Covers exponential families, maximum entropy, and Moxwell-Boltzmann distribution properties.

Statistical Tests for Exponential Families

Covers the optimal statistical tests for exponential families and the use of approximations in hypothesis testing.