Probability Theory and Applications
Explore advanced probability concepts, stochastic processes, and queueing models. Gain insights into Markov chains, Poisson processes, and reliability theory for practical applications.
Statistics for Data Science
Comprehensive statistics tutorial covering key concepts, distributions, hypothesis testing, and advanced topics for data science applications.
Some Tales of Universality from the World of Probability by Riddhipratim Basu
Explore universality in probability theory, from the central limit theorem to contemporary research, examining how complex systems share large-scale features despite microscopic differences.
Convolutions and Adding Random Variables, Visually Explained
Visual explanation of convolutions and adding random variables, exploring discrete and continuous cases, with connections to the central limit theorem and practical examples.
From Newton to Boltzmann - Fluctuations and Large Deviations in Hard Sphere Gas Dynamics
Explore macroscopic fluctuations in hard sphere gases, including deviations from the Boltzmann equation, central limit theorem, and large deviation bounds in the Boltzmann-Grad limit.
A Generalized Central Limit Conjecture for Convex Bodies
Explore a generalized central limit theorem for convex bodies, its connection to the KLS conjecture, and implications for asymptotic convex geometry in this advanced mathematics lecture.
Central Limit Theorems for Poisson Functionals - The Malliavin-Stein Approach
Explore central limit theorems in stochastic geometry using the Malliavin-Stein method, with applications to random point collections and the Online Nearest Neighbour Graph.
Fluctuations of Linear Eigenvalue Statistics in Sample Covariance Matrices - Tensor Product Data
Explore fluctuations in linear eigenvalue statistics of sample covariance matrices with tensor product data, comparing normal and uniform distributions on unit sphere.
A Survey of Central Limit Theorems in Number Theory
Explore key central limit theorems in number theory, examining their applications and implications for understanding mathematical distributions and patterns.
Counting Limit Theorems for Representations of Gromov-Hyperbolic Groups
Explore limit theorems for Gromov-hyperbolic group representations, examining statistical results analogous to random matrix products theory for spherical averages in the S-metric.
Fractional Response and Parameter Almost Sure Invariance Principle for the Quadratic Family
Explore statistical properties of quadratic family dynamics, including almost sure invariance principle and its implications for ergodic averages and fractional response.
Probability and Statistics: An Introductory Overview
Explore probability and statistics fundamentals, from basic concepts to advanced topics, covering applications, history, and key principles in data science and machine learning.
The Central Limit Theorem and its Applications - Part 1
Explore the Central Limit Theorem, its applications, and the concept of standard error of the mean in statistical analysis.
The Central Limit Theorem and its Applications - Part 2
Explore the Central Limit Theorem's applications, focusing on measured values and standard error of the mean in this concise statistical analysis lecture.
Highlights from the History of Probability
Explore key milestones in probability theory, from Hilbert's problems to martingales, with insights on Brownian motion, Central Limit Theorem, and stochastic processes.
Inducing Schemes and Their Role in Thermodynamics - ICTP 2021
Explore inducing schemes in thermodynamics, focusing on Young diffeomorphisms, symbolic representations, and equilibrium measures. Gain insights into pressure analyticity and phase transitions.
Neural Networks as Interacting Particle Systems
Explore neural networks as interacting particle systems, examining their mathematical foundations and applications in complex systems modeling across various scientific disciplines.
Bandits - Kevin Jamieson - University of Washington
Explore bandit algorithms and their applications in machine learning, from drug development to content recommendation, with a focus on regret minimization and stochastic models.
Data Mining: Choosing k for MinHashing - Spring 2023
Delve into advanced min hashing concepts, exploring PAC learning, Central Limit Theorem, and Chernoff-Hoeffding Inequality to optimize k-value selection for accurate Jaccard similarity estimates.
A Connection between Probability, Physics and Neural Networks
Explore the intersection of probability, physics, and neural networks, focusing on constructing physics-consistent models using Gaussian processes and the central limit theorem.
Introduction to Statistics: Independent and Identically Distributed Random Variables - Lecture 12
Explore fundamental statistical concepts including iid random variables, sample realizations, and the Central Limit Theorem while practicing implementations in R programming.