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.

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.

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.

Quantifying Statistical Dependence

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

Linear Regression: Theory and Applications

Covers the theory and practical applications of linear regression.

Probability Distributions: Discrete and Continuous

Covers discrete and continuous probability distributions, including joint and conditional probabilities.

Random Variables and Expected Value

Introduces random variables, probability distributions, and expected values through practical examples.

Graphical Models: Joint Probability Distribution

Covers the concept of graphical models and joint probability distributions.

Derivation of EM for the GMM

Covers the derivation of the EM algorithm for the Gaussian Mixture Model.

Maximum Likelihood: Inference and Model Comparison

Explores maximum likelihood inference, model selection, and comparing models using likelihood ratios.

Probability and Statistics

Covers Simpson's paradox, probability distributions, and real-life examples in probability and statistics.

Advanced Probability: Summary

Covers random variables, sample spaces, probability distributions, functions, expected value, variance, and estimations.

Statistical Thermodynamics: Phase Space and Probability Distributions

Covers phase space, ensembles of particles, probability distributions, and probability density functions.

Quantum Mechanics: Principles and Operators

Covers wave functions, electron density, probability distributions, and quantum operators.

Probability Distributions

Covers various probability distributions and their applications in real-world scenarios.

Property Testing: Uniform Distribution

Covers property testing for uniform distributions and the importance of reliable predictions.

Precipitation and Hydrologic Design Log in to Mediaspace to watch this video

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

Expectation Maximization: Learning Parameters Log in to Mediaspace to watch this video

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

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