Lectures related to Quantitative Risk Management: Copulas and Generative Adversarial Networks

Elements of Statistics: Estimation & Distributions

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

Copulas and Tail Dependence

Explores copulas, rank correlations, and tail dependence measures in risk management.

Precipitation and Hydrologic Design

Covers methods to define the design storm, empirical distribution of rainfall maxima, Gumbel distribution, and intensity-duration-frequency relationships.

Probability Distributions in Environmental Studies

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

Extreme Value Theory: GEV and GPD

Covers Extreme Value Theory, focusing on GEV and GPD distributions and the POT Model for threshold exceedances.

Extreme Value Theory: Limiting Distributions and Applications

Covers Extreme Value Theory, GEV distributions, GPD, and threshold exceedances.

Dependence Concepts and Copulas

Explores dependence concepts, copulas, correlation fallacies, and rank correlations in statistics.

Elements of Statistics: Probability, Distributions, and Estimation

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

L-Moment Estimation: Probability-Weighted Moments

Covers L-moment estimation, probability-weighted moments, and maximum likelihood inference basics.

Estimation and Confidence Intervals

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

Common Distributions: Moment Generating Functions

Explores common probability distributions, special distributions, and entropy concepts.

Describing Data: Statistics and Hypothesis Testing

Covers descriptive statistics, hypothesis testing, and correlation analysis with various probability distributions and robust statistics.

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Dependence Measures: Rank Correlations

Covers rank correlations, tail dependence, and copula fitting methods.

Principal Component Analysis: Introduction

Introduces Principal Component Analysis, focusing on maximizing variance in linear combinations to summarize data effectively.

Maximum Likelihood Estimation

Covers Maximum Likelihood Estimation, focusing on ML Estimation-Distribution, Shrinkage Estimation, and Loss functions.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

Probability Models: Fundamentals

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

Max Entropy and Monte Carlo

Explores max entropy, Shannon's entropy, Lagrange multipliers, and Monte Carlo sampling techniques.