This set of notes will cover basic concepts in multivariate probability models, i.e., probability models involving multiple random variables. We will begin by discussing the important concepts of independence and conditional independence and then look at the general framework of graphical models. We will then look at specific examples of models: for joint distributions we will look at the naive...

Abstract. Let (X, Y ) be a bivariate elliptical random vector with associated random radius in the Gumbel maxdomain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P{X > x, Y > y} for x, y large. Further, based on the asymptotic bounds we discuss some aspects of the statistical modelling of joint survival probabilities and the surviva...

Any decomposition of the total trajectory entropy production for markovian systems have a joint probability distribution satisfying a generalized detailed fluctuation theorem, without relying in dual probability distributions, when all the contributing terms are odd with respect to time reversal. We show that several fluctuation theorems for perturbed non-equilibrium steady states are unified a...

This paper proposes an algorithm for combinatorial optimizations that uses reinforcement learning and estimation of joint probability distribution of promising solutions to generate a new population of solutions. We call it Reinforcement Learning Estimation of Distribution Algorithm (RELEDA). For the estimation of the joint probability distribution we consider each variable as univariate. Then ...

We analyze copulas with a non-trivial singular component by using their Markov kernel representation. In particular, we provide existence results for copulas with a prescribed singular component. The constructions do not only help to deal with problems related to multivariate stochastic systems of lifetimes when joint defaults can occur with a non-zero probability, but even provide a copula max...

We develop a theoretical methodology for estimating joint probability density functions from marginals by, transforming the set of random variables into another set of independent random variables is necessary. To test this theory in practice, we developed a software application which implemented a reduced form of this methodology, and worked well with several datasets. Finally, we discuss how ...

Functional MRI (fMRI) time-series studies are plagued by varying degrees of subject head motion. Faithful head motion correction is essential to accurately detect brain activation using statistical analyses of these time-series. Mutual information (MI) based slice-to-volume (SV) registration is used for motion estimation when the rate of change of head position is large. SV registration account...

We introduce Multi-Conditional Learning, a framework for optimizing graphical models based not on joint likelihood, or on conditional likelihood, but based on a product of several marginal conditional likelihoods each relying on common sets of parameters from an underlying joint model and predicting different subsets of variables conditioned on other subsets. When applied to undirected models w...

Our topic traces back to DEMING AND STEPHAN [1] who sought to reconcile an empirical joint distribution of two random variables with a priori known marginals for each and proposed an iterative scheme for determining a solution. Thus, in the case of finite probability spaces, the problem data consist of two probability vectors p0 and p1 together with the empirical joint probability matrix P = [p...

Any decomposition of the total trajectory entropy production for Markovian systems has a joint probability distribution satisfying a generalized detailed fluctuation theorem, when all the contributing terms are odd with respect to time reversal. The expression of the result does not bring into play dual probability distributions, hence easing potential applications. We show that several fluctua...