Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

Stein's method has emerged as a critical framework in the study of distributional approximations, providing quantitative bounds between probability distributions through the formulation and solution ...

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical ...

We start by embedding probability theory into a general theory of measure and integration. This will allow us to derive theorems that may not have been included in the Analysis III course but that are ...