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Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
Background: Clinical prediction models are increasingly used to inform healthcare decisions, but determining the minimum sample size for their development remains a critical and unresolved challenge. Inadequate sample sizes can lead to…
We present a Python module named PyCheb, to solve the ordinary differential equations by using spectral collocation method. PyCheb incorporates discretization using Chebyshev points, barycentric interpolation and iterate methods. With this…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
This paper introduces the R package BayesVarSel which implements objective Bayesian methodology for hypothesis testing and variable selection in linear models. The package computes posterior probabilities of the competing hypotheses/models…
An algorithm is presented that formalizes different steps in a classical Supersymmetric (SUSY) calculation. Based on the algorithm Dill, a symbolic software package, that can perform the calculations, is developed in the Mathematica…
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error due to discretisation in the numerical context. Competing…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
We propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the…
Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving…
The paper deals with solving first-order quasilinear partial differential equations in an online simulation environment, such as Simulink, utilizing the well-known and well-recommended method of characteristics. Compared to the commonly…
This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques. It is…
In an observational study, matching aims to create many small sets of similar treated and control units from initial samples that may differ substantially in order to permit more credible causal inferences. The problem of constructing…
robustloggamma is an R package for robust estimation and inference in the generalized loggamma model. We briefly introduce the model, the estimation procedures and the computational algorithms. Then, we illustrate the use of the package…