相关论文: Non-Gaussian Distributions in Extended Dynamical S…

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

Modeling and predicting extreme movements in GDP is notoriously difficult and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large…

Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in…

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

We study the late time dynamics of a single active Brownian particle in two dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that at late times $t\gg D_R^{-1}$, while the position probability distribution…

For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of…

We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace…

A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the…

The observable outputs of many complex dynamical systems consist in time series exhibiting autocorrelation functions of great diversity of behaviors, including long-range power-law autocorrelation functions, as a signature of interactions…

This work tackles the dynamic structure estimation problems for periodically behaved discrete dynamical system in the Euclidean space. We assume the observations become sequentially available in a form of bandit feedback contaminated by a…

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

Multivariate time series (MTS) data often include a heterogeneous mix of non-Gaussian distributional features (asymmetry, multimodality, heavy tails) and data types (continuous and discrete variables). Traditional MTS methods based on…

We present a new method, based on Gaussian process regression, for reconstructing the continuous $x$-dependence of parton distribution functions (PDFs) from quasi-PDFs computed using lattice QCD. We examine the origin of the unphysical…

The nature of the velocity distribution of a driven granular gas, though well studied, is unknown as to whether it is universal or not, and if universal what it is. We determine the tails of the steady state velocity distribution of a…

We present a systematic treatment of non-Gaussianity in stochastic systems using the Schwinger-Keldysh effective field theory framework, in which the non-Gaussianity is realized as nonlinear terms in the fluctuation field. We establish two…

Long tails in the velocity distribution are observed in plasmas and gravitational systems. Some experiments and observations in far-from-equilibrium conditions show that these tails behave as 1/v^(5/2). We show here that such heavy tails…

An isotropic passive scalar field $T$ advected by a rapidly-varying velocity field is studied. The tail of the probability distribution $P(\theta,r)$ for the difference $\theta$ in $T$ across an inertial-range distance $r$ is found to be…

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…