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The CompModels package for R provides a suite of computer model test functions that can be used for computer model prediction/emulation, uncertainty quantification, and calibration, but in particular, the sequential optimization of computer…
Precisely estimating out-of-sample upper quantiles is very important in risk assessment and in engineering practice for structural design to prevent a greater disaster. For this purpose, the generalized extreme value (GEV) distribution has…
Multi-output Gaussian process (MOGP) regression allows modelling dependencies among multiple correlated response variables. Similarly to standard Gaussian processes, MOGPs are sensitive to model misspecification and outliers, which can…
Mixture-of-experts (MoE) models are a powerful paradigm for modeling of data arising from complex data generating processes (DGPs). In this article, we demonstrate how different MoE models can be constructed to approximate the underlying…
Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it…
Data in many applications follows systems of Ordinary Differential Equations (ODEs). This paper presents a novel algorithmic and symbolic construction for covariance functions of Gaussian Processes (GPs) with realizations strictly following…
Large language models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing tasks. Exploiting the heterogeneous capabilities of edge LLMs is crucial for diverse emerging applications, as it…
Let $f(y|\theta), \; \theta \in \Omega$ be a parametric family, $\eta(\theta)$ a given function, and $G$ an unknown mixing distribution. It is desired to estimate $E_G (\eta(\theta))\equiv \eta_G$ based on independent observations…
In the present paper, the author discusses the Generalized Odd Median Base Unit Rayleigh (GOMBUR) in relation to the Median Based Unit Rayleigh (MBUR) to evaluate the additive value of the new shape parameter on the estimation process as…
I describe an empirical-yet-rigorous, algorithm, based on Riordan's rook polynomials and the so-called C-finite ansatz, fully implemented in the accompanying Maple package (http://www.math.rutgers.edu/~zeilberg/tokhniot/MENAGES ), MENAGES,…
Linear mixed models are able to handle an extraordinary range of complications in regression-type analyses. Their most common use is to account for within-subject correlation in longitudinal data analysis. They are also the standard vehicle…
This article describes the R package moodlequizR, which allows the user to easily create fully randomized quizzes and exams for Moodle, or indeed any online assessment platform that uses XML files for importing questions. In such a quiz the…
We present a suite of packages in R, Python, Julia, and C++ that efficiently solve the Sorted L-One Penalized Estimation (SLOPE) problem. The packages feature a highly efficient hybrid coordinate descent algorithm that fits generalized…
Estimation of heterogeneous treatment effects (HTE) is of prime importance in many disciplines, ranging from personalized medicine to economics among many others. Random forests have been shown to be a flexible and powerful approach to HTE…
We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…
The convex envelopes of the direct discrete measures, for the sparsity of vectors or for the low-rankness of matrices, have been utilized extensively as practical penalties in order to compute a globally optimal solution of the…
This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as…
Current decision support systems address domains that are heterogeneous in nature and becoming progressively larger. Such systems often require the input of expert judgement about a variety of different fields and an intensive computational…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…