Lectures related to Empirical probability

Probability Theory: Midterm Solutions

Covers the solutions to the midterm exam of a Probability Theory course, including calculations of probabilities and expectations.

Bayesian Inference: Optimal Estimation

Explores optimal Bayesian inference, denoising, scalar estimation, and phase transitions.

The Law of Large Numbers: Proof and Applications

Explores the proof and applications of the law of large numbers, emphasizing convergence of the empirical distribution.

Extreme Region Likelihood Estimation

Covers extreme region likelihood estimation, model complexity, oceanographic data modeling, and threshold likelihood estimation.

Estimating Extreme Quantiles

Covers the estimation of extreme quantiles using empirical quantiles and sample data.

Central Limit Theorem: Illustration and Applications

Explores the Central Limit Theorem and its applications in statistical analysis.

Genetic Inheritance: Phenotype and Probability

Explores genetic inheritance, focusing on phenotype expression and probability calculations in red hair inheritance.

Statistics: Laws of Large Numbers

Explores fundamental theorems in statistics, including laws of large numbers and the central limit theorem.

Large Deviations: Theory and Applications

Delves into large deviations in statistical mechanics, exploring Kramer's theorem, Varadhan's lemma, and Laplace's method.

Data Classification: Gaussian Mixture Models

Explores Gaussian Mixture Models for data classification, focusing on denoising signals and estimating original data using likelihood and posteriori approaches.

Statistical Inference: Exponential Families and Likelihoods

Explores exponential families, likelihood functions, and model regularity in statistical inference.

Generative Models: Logistic Regression & Gaussian Distribution

Explores generative models, logistic regression, and Gaussian distribution for approximating posterior probabilities and optimizing model performance.

Multi-arm bandits: Distribution Estimation

Covers multi-arm bandits and distribution estimation, emphasizing the importance of robust estimators.

Nonparametric Estimation: Empirical Likelihood Approach

Explores nonparametric estimation using the empirical likelihood approach and discusses the computation of probabilities and empirical estimation.

Risk, Variation, and Uncertainty

Explores risk, variation, and uncertainty in disaster risk reduction through probability models and loss functions.

Law of Large Numbers: Probability

Explores the convergence of averages of random variables and empirical frequencies in probability theory.

Generalized Bayes Theorem: Vaccines and Population Probability

Explores the Generalized Bayes Theorem with three vaccines and population probabilities.

Price Returns Analysis

Covers the analysis of heavy-tailed price returns and clustered volatility in financial data.

Logistic Regression: Probability Modeling

Covers logistic regression for binary classification using probability modeling and optimization methods.

Random Variables and Expected Value

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