Steve Brunton Courses

Parameter Estimation and Fitting Distributions

Explore parameter estimation in statistics through radioactive decay examples, covering classic and modern ML approaches with hands-on coding demonstrations.

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

Could Tobacco be Good for You? Two Sided Rejection Regions in Hypothesis Testing

Explore one-sided vs two-sided rejection regions in hypothesis testing through a tobacco health study example, covering test design, statistics, and rejection criteria.

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

Method of Moments to Fit Distributions from Data

Master the method of moments technique for fitting probability distribution parameters using sample data, with practical examples including Poisson and normal distributions.

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

Hypothesis Testing Example - Salk Vaccine Trial

Explore hypothesis testing through the historic Salk Vaccine trial, learning to design hypotheses, build test statistics, and interpret results in this practical statistics example.

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

Introduction to Statistics and Data Analysis

Discover the fundamentals of statistics and data analysis, covering survey sampling, hypothesis testing, distribution fitting, and Bayesian methods as foundations for machine learning.

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

Population Statistics and Random Sampling

Discover how to estimate population statistics through random sampling, including mean and variance calculations, uncertainty quantification, and practical coding demonstrations.

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

Random Sampling in Statistics - Expected Value and Variance of the Sample Mean

Discover how sample means provide unbiased population estimates and learn to calculate their expected values and variance for applications in polling, drug trials, and A/B testing.

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

The Moment Generating Function

Discover how moment generating functions connect probability densities to Taylor series expansions, with examples using Poisson, normal, and exponential distributions.

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

Maximum Likelihood Estimation Example - Fitting a Normal Distribution with Data

Master maximum likelihood estimation by fitting normal distributions to data through joint PDFs, log-likelihood calculations, and parameter optimization for mu and sigma.

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

The Standard Unit Normal and Probability Computations

Master probability calculations using the standard unit normal distribution, including mean-centering, scaling, and computing percentiles through real-world examples and practical applications.

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

The Geometric Distribution: The First Success of a Bernoulli Distribution

Explore the geometric distribution, derived from Bernoulli processes, to understand the probability of first success occurring on the n-th trial, with practical examples using die rolls.

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

TOTEM - Tokenized Time Series Embeddings for General Time Series Analysis

Discover how TOTEM revolutionizes time series analysis through tokenized embeddings, enabling unified modeling across multiple domains and tasks with minimal tuning requirements.

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

The Exponential Distribution: Time Between Poisson Events

Explore the exponential distribution for time between Poisson events, including memoryless properties and applications in lightbulb lifetimes and radioactive decay.

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

The Expected Value - Mean of a Probability Distribution

Explore the expected value of probability distributions, from basic definitions to statistical estimation, moments, and comparisons between mode, mean, and median.

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

Joint Probability Distributions

Explore joint probability distributions, understanding how they quantify dependence between random variables and the concept of independence where P(X=x,Y=y) = P(X=x)P(Y=y).

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