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 ...

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 ...

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

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 ...

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 ...