Lectures related to Linear Algebra in Data Science

Covers statistical estimation methods, including maximum likelihood and Bayesian estimation.

Optimality in Decision Theory: Unbiased Estimation

Explores optimality in decision theory and unbiased estimation, emphasizing sufficiency, completeness, and lower bounds for risk.

Statistical Models and Parameter Estimation

Explores statistical models, parameter estimation, and sampling distributions in probability and statistics.

Elements of Statistics: Probability, Distributions, and Estimation

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

Linear Regression: Ozone Data Analysis

Explores linear regression analysis of ozone data using statistical models.

Linear Regression: Estimation and Testing

Explores linear regression estimation, hypothesis testing, and practical applications in statistics.

Maximum Likelihood Estimation: Theory and Examples

Covers maximum likelihood estimation, including the Rao-Blackwell Theorem proof and practical examples of deriving estimators.

Theoretical Properties of Linear Regression Estimator

Covers the theoretical properties of the linear regression estimator, including the hat matrix and the Gauss-Markov theorem.

Linear Regression Basics

Covers the basics of linear regression, including OLS, heteroskedasticity, autocorrelation, instrumental variables, Maximum Likelihood Estimation, time series analysis, and practical advice.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Linear Regression: Regularization

Covers linear regression, regularization, and probabilistic models in generating labels.

Probability Models: Fundamentals

Introduces the basics of probability models, covering random variables, distributions, and statistical estimation.

Maximum Likelihood Theory & Applications

Covers maximum likelihood theory, applications, and hypothesis testing principles in econometrics.

Weighted Least Squares Estimation: IRLS Algorithm

Explores the IRLS algorithm for weighted least squares estimation in GLM.

Probabilistic Linear Regression

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

Regression: Simple and Multiple Linear

Covers simple and multiple linear regression, including least squares estimation and model diagnostics.

Linear Regression Basics

Covers the basics of linear regression, instrumental variables, heteroskedasticity, autocorrelation, and Maximum Likelihood Estimation.

Nonparametric Statistics: Bayesian Approach

Explores non-parametric statistics, Bayesian methods, and linear regression with a focus on kernel density estimation and posterior distribution.