Lectures related to Exponential Family: Distributions and Regularity

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Distributions & Interpolation Spaces

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Compression: Prediction

Covers the concepts of compression and prediction using prefix-free codes and distributions.

Fundamental Solutions of Laplace Equation

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.

Compression

Covers the concept of compression and constructing prefix-free codes based on given information.

Distribution & Interpolation Spaces

Covers the concept of distributions with compact support and their interpolation spaces.

Basics of Risk Analysis and Management

Introduces the basics of risk analysis and management in civil engineering, covering distributions, statistical reminders, and mathematical interpretation techniques.

Introduction to Distributions

Covers Green's representation formula, fundamental solutions, and distribution properties.

Elements of Statistics: Probability and Random Variables

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

Signals & Systems I: Distributions and Linear Systems

Explores distributions, linear systems, impulse response, convolution operators, and causal systems in signals and systems.

Elements of Statistics: Probability, Distributions, and Estimation

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

Probability Theory: Random Variables and Distributions

Introduces probability theory, random variables, and distributions, with a focus on their applications in atomic diffusion.

Cut-off Phenomenon: Proof Ideas

Explores proof ideas related to the cut-off phenomenon and its implications in random walks on hypercubes.

Signals & Systems I: Fourier Transformation and Distributions

Explores the Fourier transformation, Parseval relation, weak convergence, and generalized transformations in signals and systems.

Fundamental Solutions of Laplace Equation

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Special Families of Models

Explores completeness, minimal sufficiency, and special statistical models, focusing on exponential and transformation families.

Elements of Statistics: Estimation & Distributions

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

Common Distributions: Moment Generating Functions

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

Generalization Error

Discusses mutual information, data processing inequality, and properties related to leakage in discrete systems.