Lectures in course EE-209: Elements of statistics for data science

Covers randomized clinical trials, confounding variables, ethical challenges, and Simpson's paradox in data analysis.

Covariances and Random Variable Sums: Insights and Applications

Covers advancements in sensory feedback restoration through peripheral nerve stimulation and the integration of cognitive complexity in prosthetic technology.

Simpson's Paradox: Understanding and Randomized Trials

Explores Simpson's Paradox with a real-world example and emphasizes the significance of randomized trials.

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.

Gaussian Conditional Model and Properties

Explores the Gaussian conditional model for linear regression and the properties of Gaussian data, illustrated with the example of kidney stone treatment comparison.

Linear Regression: General Form

Covers the design matrix, response vector, and linear vs affine regression.

Vectors of Random Variables: Empirical Distributions

Discusses vectors of random variables and empirical distributions, including their properties and significance in statistics.

Linear Regression: Simple

Introduces simple linear regression, properties of residuals, variance decomposition, and the coefficient of determination in the context of Okun's law.

Bayesian Inference: Precision in Gaussian Model

Explores Bayesian inference for precision in the Gaussian model with known mean, using a Gamma prior and discussing subjective vs objective priors.

Statistics for Data Science: Introduction to Statistical Methods

Covers the fundamental concepts of statistics and their application in data science.

Dirichlet-Multinomial Model

Discusses the Dirichlet distribution, Bayesian inference, posterior mean and variance, conjugate priors, and predictive distribution in the Dirichlet-Multinomial model.

Statistical Hypothesis Testing: Concepts and Applications

Provides an overview of statistical hypothesis testing, including its purpose, formulation, and significance in data analysis.

Bayesian Inference: Gaussian Prior for Mean

Discusses Bayesian inference for the mean of a Gaussian distribution with known variance, covering posterior mean, variance, and MAP estimator.

Hypothesis Testing: Q-Q Plots and Non-Parametric Tests

Covers hypothesis testing, Q-Q plots, and non-parametric tests in statistics.

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Bayesian Inference: Beta-Bernoulli Model

Explores the Beta distribution, Bayesian inference, and posterior calculation in the Beta-Bernoulli model.

Bayesian Statistics: Hypothesis Testing and Estimation

Covers hypothesis testing, p-values, significance levels, and Bayesian estimation.

Confidence Interval for Bernoulli Model Score

Explains how to calculate the confidence interval for the score parameter in the Bernoulli model.

Confidence Intervals: Margins, Coverage, Pivots

Explains margins of error, coverage, and pivots in constructing confidence intervals for scalar parameters.

Hypothesis Testing: Neyman-Pearson Framework

Covers hypothesis testing, types of errors, Neyman-Pearson framework, and one-sided Gaussian tests.