Regular Exponential Family Models

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Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.

Generalized Linear Models

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

Large Deviations: Theory and Applications

Delves into large deviations in statistical mechanics, exploring Kramer's theorem, Varadhan's lemma, and Laplace's method.

Estimation Methods in Probability and Statistics

Discusses estimation methods in probability and statistics, focusing on maximum likelihood estimation and confidence intervals.

Elementary Distributions Factsheet

Covers elementary distributions like Bernoulli, Binomial, Geometric, Negative Binomial, Poisson, and Multinomial.

Testing: t-tests

Covers t-tests, p-values calculation, and comparison of coefficients.

Sampling Theory: Statistics and Inference

Covers sampling theory, statistics, and inference, focusing on the sampling distribution of statistics.

Special Families of Models

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

Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.