Related papers: A multivariate piecing-together approach with an a…

In this paper we introduce a new class of multivariate unimodal distributions, motivated by Khintchine's representation. We start by proposing a univariate model, whose support covers all the unimodal distributions on the real line. The…

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…

Machine learning iterative imputation methods have been well accepted by researchers for imputing missing data, but they can be time-consuming when handling large datasets. To overcome this drawback, parallel computing strategies have been…

In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in $\mathbb {R}^d$. We present a…

In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their…

We present a derivation and theoretical investigation of the Adams-Bashforth and Adams-Moulton family of linear multistep methods for solving ordinary differential equations, starting from a Gaussian process (GP) framework. In the limit,…

The privacy loss distribution (PLD) provides a tight characterization of the privacy loss of a mechanism in the context of differential privacy (DP). Recent work has shown that PLD-based accounting allows for tighter $(\varepsilon,…

Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…

This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region.…

The mixed effects model for repeated measures (MMRM) has been widely used for the analysis of longitudinal clinical data collected at a number of fixed time points. We propose a robust extension of the MMRM for skewed and heavy-tailed data…

Copula-based methods provide a flexible approach to build missing data imputation models of multivariate data of mixed types. However, the choice of copula function is an open question. We consider a Bayesian nonparametric approach by using…

We consider the generic problem of performing a global fit to many independent data sets each with a different overall multiplicative normalization uncertainty. We show that the methods in common use to treat multiplicative uncertainties…

Multiple imputation is a highly recommended technique to deal with missing data, but the application to longitudinal datasets can be done in multiple ways. When a new wave of longitudinal data arrives, we can treat the combined data of…

Data privacy has increasingly become a daunting challenge because it limits data availability, which is essential in estimating statistical models such as generalized linear mixed models. Access to personal data often involves considerable…

In this article, we develop a new class of multivariate distributions adapted for count data, called Tree P\'olya Splitting. This class results from the combination of a univariate distribution and singular multivariate distributions along…

When modeling a vector of risk variables, extreme scenarios are often of special interest. The peaks-over-thresholds method hinges on the notion that, asymptotically, the excesses over a vector of high thresholds follow a multivariate…

We propose a dependence-aware predictive modeling framework for multivariate risks stemmed from an insurance contract with bundling features - an important type of policy increasingly offered by major insurance companies. The bundling…

Multivariate partial fractioning is a powerful tool for simplifying rational function coefficients in scattering amplitude computations. Since current research problems lead to large sets of complicated rational functions, performance of…

Probabilistic Regression Trees (PRTrees) generalize traditional decision trees by incorporating probability functions that associate each data point with different regions of the tree, providing smooth decisions and continuous responses.…

The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…