Lectures related to Biclustering & latent variables: statistical analysis of network data

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Parameter Estimation

Discusses parameter estimation, including checks, quality, distribution, and statistical properties of estimates.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Random Variables and Expected Value

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

Random Variables: Expected Value

Covers advanced probability concepts, including random variables and expected value calculation.

Confidence Intervals: Student, Asymptotic Wald

Covers confidence intervals for Gaussian means, Student distribution, and Wald confidence intervals for maximum likelihood estimators.

Hoeffding's Inequality: Binomial Distribution

Explores Hoeffding's inequality and the binomial distribution, focusing on error minimization and generalization gaps in predictor selection.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Probability Measures and Random Variables

Covers the Caratheodory extension theorem, uniqueness and existence of probability measures, Bernoulli random variables, and spaces of random variables.

Discrete Random Variables: Functions and Probabilities

Explores discrete random variables, their functions, and probabilities in various scenarios.

Statistical Estimation: Properties and Distributions

Explores statistical parameter estimation, sample accuracy, and Bernoulli variables' properties.

Probability Distributions: Basics and Properties

Covers the basics of probability distributions, including mean, variance, and properties of random variables.

Random Variables: Basics and Examples

Explains random variables, distributions, and Bernoulli trials with coin flip examples.

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Expectation of a Random Variable

Defines the expectation for random variables, emphasizing the importance of absolute values.

Variance and Independent Random Variables

Covers variance, independent random variables, and their properties, including examples and proofs.

Variance: Definition, Examples, and Theorems

Covers the definition of variance, examples, theorems, and applications in probability theory.

Probability and Stochastic Processes: Fundamentals and Applications

Discusses the fundamentals of probability and stochastic processes, focusing on random variables, their properties, and applications in statistical signal processing.