相关论文: Numerical validation of probabilistic laws to eval…
Context: Software engineering has a problem in that when we empirically evaluate competing prediction systems we obtain conflicting results. Objective: To reduce the inconsistency amongst validation study results and provide a more formal…
Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating…
A probabilistic approach for estimating sample qualities for stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the distance between the invariant probability measure of a…
We study finite element approximations of second-order elliptic problems with measure-valued right-hand sides supported on lower-dimensional sets. The exact solution generally lacks $H^1$-regularity due to the source singularity, which…
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that…
Researchers have employed variations of the Smoluchowski coagulation equation to model a wide variety of both organic and inorganic phenomena and with relatively few known analytical solutions, numerical solutions play an important role in…
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
This paper studies theoretically and empirically a method of turning machine-learning algorithms into probabilistic predictors that automatically enjoys a property of validity (perfect calibration) and is computationally efficient. The…
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical…
The aim of this paper is the numerical study of a class of nonlinear nonlocal degenerate parabolic equations. The convergence and error bounds of the solutions are proved for a linearized Crank-Nicolson-Galerkin finite element method with…
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.
Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have…
This chapter demystifies P-values, hypothesis tests and significance tests, and introduces the concepts of local evidence and global error rates. The local evidence is embodied in \textit{this} data and concerns the hypotheses of interest…
Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are,…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…
In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when…
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be…