Lectures related to Poisson Process: Properties

Simulation & Optimization: Poisson Process & Random Numbers

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

Estimating R: Moments of a Distribution

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

Stochastic Processes: Symmetric Random Walk

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

Poisson Process: Probability Law

Covers the Poisson process, a stochastic model for communications, focusing on the probability law.

Stochastic Models for Communications

Covers stochastic models for communications, focusing on random variables, Markov chains, Poisson processes, and probability calculations.

Generalized Linear Models

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

Probability Distributions: Basics and Properties

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

Estimating R: Marking and Convergence

Covers the estimation of R in Poisson processes, focusing on marking points and convergence.

Common Distributions: Moments and MGFs

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

Multivariate Extremes: Applications and Dependence

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

Point Processes: Extremal Limit Theorems

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

Variance and Covariance: Properties and Examples

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

Poisson Process: Density Theory and Applications

Explores Poisson processes, joint density, independence of events, and likelihood estimation.

Mapping and Colouring: Poisson Processes

Covers the theorems of superposition and colouring for Poisson processes.

Rainfall Models: Deterministic vs Stochastic

Covers deterministic and stochastic rainfall models in water resources engineering, including generation, calibration, and spatially explicit models.

Poisson Process: Properties

Covers the properties of Poisson processes, including arrival rate and inter-arrival time.

Statistics of Multivariate Extremes: Inference and Models

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

Poisson Process: Properties

Covers the properties of Poisson processes and their applications in communication stochastic models.

Estimating Deviations

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

Poisson processes

Covers the properties and construction of Poisson processes from i.i.d. Exp(X) random variables, emphasizing the importance of the process rate and jump time distributions.