相关论文: A copula-based method to build diffusion models wi…

This paper examines the impact of discrete marginal distributions on copula-based Markov chains. We present results on mixing and parameter estimation for a copula-based Markov chain model with Bernoulli($p$) marginal distribution and…

The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on…

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this…

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter…

In this manuscript, we consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an…

For a bivariate probability distribution, local dependence around a single point on the support is often formulated as the second derivative of the logarithm of the probability density function. However, this definition lacks the invariance…

In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and…

Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature…

We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…

Cylindrical data frequently arise across various scientific disciplines, including meteorology (e.g., wind direction and speed), oceanography (e.g., marine current direction and speed or wave heights), ecology (e.g., telemetry), and…

Diffusion models have been widely used in time series and spatio-temporal data, enhancing generative, inferential, and downstream capabilities. These models are applied across diverse fields such as healthcare, recommendation, climate,…

In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute…

Parametric copula families have been known to flexibly capture various dependence patterns, e.g., either positive or negative dependence in either the lower or upper tails of bivariate distributions. In this paper, our objective is to…

Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…

We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…

Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…

In this paper, we derive copula-based and empirical dependency models (DMs) for simulating non-independent variables, and then propose a new way for determining the distribution of the model outputs conditional on every subset of inputs.…

We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual…

We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…

The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions…