Lectures related to Exchangeability and Network Statistics

Probability Distributions in Environmental Studies

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

Likelihood Ratio Tests: Optimality and Extensions

Covers Likelihood Ratio Tests, their optimality, and extensions in hypothesis testing, including Wilks' Theorem and the relationship with Confidence Intervals.

Statistical analysis of network data

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Statistical Analysis of Network Data: Structures and Models

Explores statistical analysis of network data, covering graph structures, models, statistics, and sampling methods.

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

Statistics: Hypothesis Testing & Confidence Intervals

Covers hypothesis testing, confidence intervals, data distributions, and statistical significance in data analysis.

Likelihood Ratio Tests: Optimality and Applications

Explores the theory and applications of likelihood ratio tests in statistical hypothesis testing.

Graph Statistics: Random Graphs, Graph Homomorphisms, and Network Analysis

Explores graph statistics, random graph generation, network analysis, centrality measures, and clustering coefficients.

Extreme Value Analysis: Applications and Consequences

Explores extremal limit theorems and statistical analysis for analyzing extreme events like Venezuela rainfall and Venice data.

Distances and Motif Counts

Explores distances on graphs, cut norms, spanning trees, blockmodels, metrics, norms, and ERGMs in network data analysis.

Stochastic Blockmodel Estimation

Explores Stochastic Blockmodel estimation, spectral clustering, network modularity, Laplacian matrix, and k-means clustering.

Review Session: Module 1

Introduces inferential statistics, covering sampling, central tendency, dispersion, histograms, z-scores, and the normal distribution.

Vectors of Random Variables: Empirical Distributions

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

Sampling Theory: Statistics for Mathematicians

Covers the theory of sampling, focusing on statistics for mathematicians.

Descriptive Statistics: Hypothesis Testing

Introduces descriptive statistics, hypothesis testing, p-values, and confidence intervals, emphasizing their importance in data analysis.

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

Statistical Analysis of Networks: Link Prediction and Biclustering

Explores link prediction, logistic regression, causal inference, and biclustering in statistical network analysis.

Statistical Inference: Approximate Critical Values and Confidence Intervals

Covers the construction of confidence intervals and approximate critical values in statistical inference.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Optimality in Decision Theory: Unbiased Estimation

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