Lectures related to Variance-stabilizing transformation

Estimating R: Moments of a Distribution

Explains the importance of moments in measuring distribution properties, such as expectation and variance.

Sampling a Probability Distribution

Explores sampling a probability distribution and structure functions in statistical analysis.

Stochastic Processes: Symmetric Random Walk

Covers the properties of the symmetric random walk in stochastic processes.

Estimating Deviations

Covers Markov's and Chebyshev's Inequalities for random variables and probability distributions.

Conditional Expectation and Variance

Explores conditional expectation and variance, showing how variables influence each other's probability distribution.

Generalized Linear Models

Introduces Generalized Linear Models, showcasing examples with different distributions and real-world data.

Max Entropy and Monte Carlo

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

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.

Poisson Process: Properties

Covers the properties of Poisson processes, including arrival times and stochastic models for communications.

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.

Probability Distributions: Basics and Properties

Covers the basics of probability distributions, including mean, variance, and properties of random variables.

Bias, Variance, Consistency, EMV

Covers bias, variance, mean squared error, consistency, and maximum likelihood estimation in the Poisson model.

Common Distributions: Moments and MGFs

Covers common distributions, moment generating functions, and covariance matrices in statistics for data science.

Probability Distributions: Moments and Quantiles

Explains moments, expectation, variance, and quantiles in probability distributions with examples like Poisson and exponential distributions.

Applications of Quantum Science: Densities and Statistics

Covers the applications of densities and statistics in quantum science, focusing on binomial and Poisson distributions.

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Generalised Linear Models: Regression with Exponential Family Responses

Covers regression with exponential family responses using Generalised Linear Models.