Related papers: Covariance Models for Multivariate Random Fields r…

Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$, a common…

Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…

A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…

Cross-validation (CV) is a common method to tune machine learning methods and can be used for model selection in regression as well. Because of the structured nature of small, traditional experimental designs, the literature has warned…

We consider the use of deep learning for covariance estimation. We propose to globally learn a neural network that will then be applied locally at inference time. Leveraging recent advancements in self-supervised foundational models, we…

We reconsider cosmological perturbation theory for multi-component scalars, enforcing covariance in field-space, and ensuring that phyical observations are independent of field re-definitions. We use the formalism to clarify some issues in…

We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…

We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations…

We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…

In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…

Varying coefficient models are useful in applications where the effect of the covariate might depend on some other covariate such as time or location. Various applications of these models often give rise to case-specific prior distributions…

Multivariate associated kernel estimators, which depend on both target point and bandwidth matrix, are appropriate for partially or totally bounded distributions and generalize the classical ones as Gaussian. Previous studies on…

In modern engineering, computer simulations are a popular tool to analyse, design, and optimize systems. Furthermore, concepts of uncertainty and the related reliability analysis and robust design are of increasing importance. Hence, an…

In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…

We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance…

No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…

Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…

As a continuation of [GasparPopa] this paper treats the stationary and stationarily cross-correlated multivariate stochastic mappings. Moreover for the case of multivariate random distribution fields, a particular form for the operator…

Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…

Structural equation models (SEMs) are commonly used to study the structural relationship between observed variables and latent constructs. Recently, Bayesian fitting procedures for SEMs have received more attention thanks to their potential…