scholarly journals Hierarchical correction of p-values via an ultrametric tree running Ornstein-Uhlenbeck process

2021 ◽  
Author(s):  
Antoine Bichat ◽  
Christophe Ambroise ◽  
Mahendra Mariadassou
Keyword(s):  
Multiple Testing ◽  
R Package ◽  
Statistical Testing ◽  
Uhlenbeck Process ◽  
Explanatory Variables ◽  
New Associations ◽  
Penalized Estimation ◽  
Ultrametric Tree ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

AbstractStatistical testing is classically used as an exploratory tool to search for association between a phenotype and many possible explanatory variables. This approach often leads to multiple testing under dependence. We assume a hierarchical structure between tests via an Ornstein-Uhlenbeck process on a tree. The process correlation structure is used for smoothing the p-values. We design a penalized estimation of the mean of the Ornstein-Uhlenbeck process for p-value computation. The performances of the algorithm are assessed via simulations. Its ability to discover new associations is demonstrated on a metagenomic dataset. The corresponding R package is available from https://github.com/abichat/zazou.

Some mean first-passage time approximations for the Ornstein-Uhlenbeck process

1975 ◽  
Vol 12 (3) ◽  
pp. 600-604 ◽  
Author(s):  
Marlin U. Thomas
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Accurate Method ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Numerical Comparisons ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

This paper describes an accurate method of approximating the mean of the first-passage time distribution for an Ornstein-Uhlenbeck process with a single absorbing barrier. The accuracy of the approximation is demonstrated through some numerical comparisons.

A generalized stochastic competitive system with Ornstein–Uhlenbeck process

2020 ◽  
pp. 2150001
Author(s):  
Baodan Tian ◽  
Liu Yang ◽  
Xingzhi Chen ◽  
Yong Zhang
Keyword(s):  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Competitive System ◽  
Uhlenbeck Process ◽  
Stochastic Perturbations ◽  
Stochastic Permanence ◽  
Persistence In The Mean ◽  
Ornstein Uhlenbeck Process ◽  
Global Positive Solution ◽  
The Mean

A generalized competitive system with stochastic perturbations is proposed in this paper, in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process. By theories of stochastic differential equations, such as comparison theorem, Itô’s integration formula, Chebyshev’s inequality, martingale’s properties, etc., the existence and the uniqueness of global positive solution of the system are obtained. Then sufficient conditions for the extinction of the species almost surely, persistence in the mean and the stochastic permanence for the system are derived, respectively. Finally, by a series of numerical examples, the feasibility and correctness of the theoretical analysis results are verified intuitively. Moreover, the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.

Some mean first-passage time approximations for the Ornstein-Uhlenbeck process

1975 ◽  
Vol 12 (03) ◽  
pp. 600-604 ◽  
Author(s):  
Marlin U. Thomas
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Accurate Method ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Numerical Comparisons ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

This paper describes an accurate method of approximating the mean of the first-passage time distribution for an Ornstein-Uhlenbeck process with a single absorbing barrier. The accuracy of the approximation is demonstrated through some numerical comparisons.

Electronic dynamics in chains with Ornstein–Uhlenbeck correlated disorder

2020 ◽  
Vol 31 (12) ◽  
pp. 2050176
Author(s):  
J. L. S. Soares ◽  
R. D. dos Santos ◽  
F. J. S. Sousa ◽  
M. O. Sales ◽  
F. A. B. F. Moura
Keyword(s):  
Differential Equation ◽  
Evolution Operator ◽  
Mean Square Displacement ◽  
Time Dependent ◽  
Mean Square ◽  
Strong Correlations ◽  
Uhlenbeck Process ◽  
Electronic Dynamics ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

In this paper, we present a detailed study of the electronic dynamics in systems with correlated disorder generated from the Ornstein–Uhlenbeck process (OU). In short, we used numeric methods for solving the time-dependent Schrödinger equation. We apply a Taylor’s expansion of the evolution operator in order to solve the differential equation. We calculate some typical tools, such as the participation function [Formula: see text], the mean square displacement [Formula: see text] and the probability of return [Formula: see text]. In our analysis, we show that for low correlations the system behaves as in the standard Anderson model (i.e. all eigenstates are localized). For strong correlations, our results suggest the existence of a quasi-ballistic dynamics.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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