Lectures related to Modeling Extremal Processes

Probabilistic Models for Linear Regression

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

Extreme Statistics: Threshold Models

Covers the theory and applications of extreme statistics, focusing on threshold models for analyzing extremes of time series.

Statistics of Multivariate Extremes: Inference and Models

Explores theory and applications of multivariate extremes, emphasizing fitting marginal and dependence models together for accurate estimation.

Multivariate Extremes: Applications and Dependence

Explores multivariate extremes, including overwhelming sea defenses and heat waves.

Linear Combinations: Moment-Generating Functions

Explores moment-generating functions, linear combinations, and normality of random variables.

Simulation & Optimization: Poisson Process & Random Numbers

Explores simulation pitfalls, random numbers, discrete & continuous distributions, and Monte-Carlo integration.

Extreme Value Analysis: Applications and Consequences

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

Testing: t-tests

Covers t-tests, p-values calculation, and comparison of coefficients.

Extreme Value Theory: Point Processes

Covers the application of extreme value theory to point processes and the estimation of extreme events from equally-spaced time series.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.

Probabilistic Linear Regression

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

Statistical Inference and Machine Learning

Covers statistical inference, machine learning, SVMs for spam classification, email preprocessing, and feature extraction.

Bayesian Estimation: Unsupervised Learning & MCMC

Explores Bayesian estimation for unsupervised learning and MCMC, using a Spin Glass Card game example.

Statistical Inference: Model Selection and Nuisance Parameters

Covers model selection, nuisance parameters, and higher-order inference methods in statistical inference.

Generalized Linear Models: A Brief Review

Provides an overview of Generalized Linear Models, focusing on logistic and Poisson regression models, and their implementation in R.

Interval Estimation

Covers the construction of confidence intervals for a normal distribution with unknown mean and variance.

Exponential Family

Covers the properties of the exponential family and the estimation of parameters.

Statistical Inference: Confidence Intervals

Covers the construction of approximate confidence intervals using the central limit theorem for large sample sizes.

Extreme Value Theory: Statistical Applications

Explores statistical applications of threshold exceedances and GPD modeling in extreme value theory.

Point Processes: Extremal Limit Theorems

Explores the theory of point processes and their applications to extremes, emphasizing the Laplace functional and Kallenberg's theorem.