Probability Distributions: Understanding Parameters and Transformations

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Explains the E-step and M-step calculations in the Gaussian Mixture Model, including the pseudocode of the EM algorithm.

Precipitation and Hydrologic Design

Covers methods to define the design storm, empirical distribution of rainfall maxima, Gumbel distribution, and intensity-duration-frequency relationships.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Probability Distributions: Moments and Transformations

Covers moments computation and probability distribution transformations.

Expectation Maximization: Learning Parameters

Covers the Expectation Maximization algorithm for learning parameters and dealing with unknown variables.

Probabilistic Linear Regression

Explores probabilistic linear regression, covering joint and conditional probability, ridge regression, and overfitting mitigation.

Maximum Likelihood Inference

Explores maximum likelihood inference, comparing models based on likelihood ratios and demonstrating with a coin example.

Introduction to Inference

Covers the basics of probability theory, random variables, joint probability, and inference.

Quantifying Statistical Dependence

Delves into quantifying statistical dependence through covariance, correlation, and mutual information.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.