Abstract: Astract- This paper presents a new energy-based continuous time series probability model that has stochastic process in its latent dynamics. Because the model assuming its output is used for ...

A courseware module that covers the fundamental concepts in probability theory and their implications in data science. Topics include probability, random variables, and Bayes' Theorem.

simulate a simple game where 30 players roll a die 300 times and keep track of their rolls. The game ends when all players have the same number.

An illustration of a magnifying glass. An illustration of a magnifying glass.

John von Neumann's spectral theorem for self-adjoint operators is a cornerstone of quantum mechanics. Among other things, it also provides a connection between expectation values of self-adjoint ...

Abstract: Mathematical methods for describing univariate and bivariate non-Gaussian random variables and processes in their modeling are considered. A decomposition of probability density functions ...

ABSTRACT: The original Bell inequality was obtained in a statistical derivation assuming three mutually cross-correlated random variables (four in the later version). Given that observations destroy ...

We will discuss stochastic processes, Le Jan-Sznitman cascades, that can be associated with certain nonlinear PDE and how explosion of these cascades can be exploited to prove non-uniques for the ...