Steve Brunton Courses

Gentle Introduction to Probability: Counting Coin Flips and Dice

Explore fundamental probability concepts through coin flips and dice rolls, uncovering the nature of randomness and its practical applications in everyday scenarios.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Bayes' Theorem for Drug Testing and Screening Analysis

Explore Bayes' theorem through practical drug testing scenarios, learning how to calculate conditional probabilities and understand sensitivity versus specificity in medical screening.

• YouTube
• 13 minutes
• Self-Paced
• Free Video

The Law of Total Probability - Understanding Conditional Probability Fundamentals

Master the Law of Total Probability through clear explanations and practical examples, understanding its fundamental role in probability theory and statistical analysis.

• YouTube
• 10 minutes
• Self-Paced
• Free Video

The Normal Distribution - From Binomial Distribution to Gaussian Limits

Explore the relationship between Normal and Binomial distributions, focusing on large-n scenarios, the Central Limit Theorem, and practical applications in statistical analysis through visual demonstrations and code examples.

• YouTube
• 17 minutes
• Self-Paced
• Free Video

Two Examples of Expected Values and Functions - Temperature in C vs F and the Kinetic Theory of Gases

Explore temperature conversions and kinetic theory through expected values, covering linear transformations and Maxwell's distribution in gas dynamics applications.

• YouTube
• 15 minutes
• Self-Paced
• Free Video

The Law of Large Numbers

Discover how sample means converge to true means through the law of large numbers, a fundamental probability concept that underpins statistical analysis and leads to the central limit theorem.

• YouTube
• 13 minutes
• Self-Paced
• Free Video

The Central Limit Theorem

Discover how the sum of independent random variables converges to a normal distribution and its applications in statistics and survey sampling.

• YouTube
• 11 minutes
• Self-Paced
• Free Video

Variance and Standard Deviation

Master variance and standard deviation concepts to measure probability distribution spread with practical examples and mathematical derivations.

• YouTube
• 13 minutes
• Self-Paced
• Free Video

Computing the Expectation and Variance of an Exponential Distribution

Master expectation and variance calculations for exponential distributions through step-by-step mathematical examples and median computation techniques.

• YouTube
• 12 minutes
• Self-Paced
• Free Video

Properties of the Expected Value

Explore key properties of expected values including sums, independent products, and functions of random variables with mathematical derivations and examples.

• YouTube
• 10 minutes
• Self-Paced
• Free Video

Covariance and Correlation in Probability

Explore covariance and correlation between random variables, essential concepts for probability, statistics, data science, and machine learning in higher-dimensional systems.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Density Estimation with Gaussian Mixture Models and Empirical Priors

Discover advanced density estimation techniques using Gaussian Mixture Models and empirical priors for complex data distributions in this machine learning foundation.

• YouTube
• 18 minutes
• Self-Paced
• Free Video

Monte Carlo Sampling and Bootstrapping in Bayesian Inference

Explore Monte Carlo sampling techniques and bootstrapping methods for Bayesian inference through practical algorithms and coin flip demonstrations.

• YouTube
• 18 minutes
• Self-Paced
• Free Video

Bayesian Inference - Overview

Discover how Bayesian inference balances data with prior beliefs to learn probability distributions, including practical hypothesis testing and key limitations.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Bayesian Updates and Conjugate Priors

Discover how to update Bayesian models with new data using conjugate priors, ensuring posterior distributions remain in the same family as priors for efficient computation.

• YouTube
• 18 minutes
• Self-Paced
• Free Video