Lectures related to Beta distribution

Bayesian Inference: Beta-Bernoulli Model

Explores the Beta distribution, Bayesian inference, and posterior calculation in the Beta-Bernoulli model.

Threshold Exceedances: Generalized Pareto Distribution

Explores threshold exceedances and the Generalized Pareto Distribution for modeling extreme data points above a specified level.

Common Distributions: Moment Generating Functions

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

Bayesian Inference: Gaussian Prior for Mean

Discusses Bayesian inference for the mean of a Gaussian distribution with known variance, covering posterior mean, variance, and MAP estimator.

Bayesian Estimation: Overview and Examples

Introduces Bayesian estimation, covering classical versus Bayesian inference, conjugate priors, MCMC methods, and practical examples like temperature estimation and choice modeling.

Relevance Vector Machine: Addressing SVM Shortcomings

Introduces the Relevance Vector Machine as a sparse solution to SVM shortcomings.

Exploration vs. Exploitation: Softmax Policy Quiz

Presents a quiz on the exploration vs. exploitation dilemma using the softmax policy.

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.

Sexing Guppy Fish: Bayesian Inference and Decision Rules

Covers the sexing of guppy fish using Bayesian inference and decision rules.

Probability and Statistics: Fundamental Theorems

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

Capital Asset Pricing Model: Theory and Applications

Explores the Capital Asset Pricing Model, covering risk-return trade-off, SML, betas estimation, and applications in finance.

Bayes Estimator: Definition and Application

Introduces the Bayes estimator, explaining its definition, application in quadratic cost scenarios, and importance in probabilistic reasoning.

Markov Chain Monte Carlo

Covers the Markov Chain Monte Carlo method and the Metropolis-Hastings algorithm for generating samples from a target probability distribution.

Maximum Likelihood: Estimation and Inference

Introduces maximum likelihood estimation, discussing its properties and applications in statistical analysis.

Random Walk: Hitting Probabilities

Explores random walks, hitting probabilities, recursive structures, and Gaussian processes.

Quantum Random Number Generation

Explores quantum random number generation, discussing the challenges and implementations of generating good randomness using quantum devices.

Bernoulli convolutions: The dimension of Bernoulli convolutions

Explores the dimension of Bernoulli convolutions, discussing fair tosses and polynomial roots.

Bayesian Statistics: Hypothesis Testing and Estimation

Covers hypothesis testing, p-values, significance levels, and Bayesian estimation.

Fading Channels: Model & Performance

Covers fading channels in wireless communication, discussing models, performance, diversity, and attenuation effects.

Advanced Probability: Examples

Covers the Geometric Distribution, biased coins, expected number of flips, and generating random numbers.