相关论文: Analytical approximation for Landau's constants by…

Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…

We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…

This paper studies numerical methods for the approximation of elliptic PDEs with lognormal coefficients of the form $-{\rm div}(a\nabla u)=f$ where $a=\exp(b)$ and $b$ is a Gaussian random field. The approximant of the solution $u$ is an…

In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.

Model checking is a technique to automatically assess whether a model of the behaviour of a system meets its requirements. Evidence explaining why the behaviour does (not) meet its requirements is essential for the user to understand the…

This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…

An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of generalized…

The Gaussian expansion method (GEM) is extensively applied to the calculations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that has been tested in the mean-field calculations. By comparing the RPA…

We consider the optimal quantization of compressive sensing measurements following the work on generalization of relaxed belief propagation (BP) for arbitrary measurement channels. Relaxed BP is an iterative reconstruction scheme inspired…

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the…

Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number of methods for estimating ratios of…

We study numerical methods for solving a system of quasilinear stochastic partial differential equations known as the stochastic Landau-Lifshitz-Bloch (LLB) equation on a bounded domain in $\mathbb R^d$ for $d=1,2$. Our main results are…

The determination of low-energy constants from data is an important component of most effective field theory programs, including that of chiral perturbation theory. We propose a novel method based on Bayesian probability theory which allows…

This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…

We propose a gradient flow perspective to the spatially homogeneous Landau equation for soft potentials. We construct a tailored metric on the space of probability measures based on the entropy dissipation of the Landau equation. Under this…

We provide two methods for computation of continuum backstepping kernels that arise in control of continua (ensembles) of linear hyperbolic PDEs and which can approximate backstepping kernels arising in control of a large-scale, PDE system…

In this work we address the problem of uniform approximation of differential forms starting from weak data defined by integration on rectifiable sets. We study approximation schemes defined by the projection operator L given by either…

In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model…