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We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using non-stationary Gaussian processes. The Gaussian process prior mean and…
In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…
We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…
Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…
For the finite element solution of Poisson's equation, a local a posteriori error estimation based on the Hypercircle method is proposed. Even for the solution of Poisson's equation without the $H^2$ regularity, this method can provide…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…
We construct a family of estimators for a regression function based on a sample following a qdistribution. Our approach is nonparametric, using kernel methods built from operations that leverage the properties of q-calculus. Furthermore,…
In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…
We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm…
We establish a general Bernstein--von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for…
Stochastic expansion-based methods of uncertainty quantification, such as polynomial chaos and separated representations, require basis functions orthogonal with respect to the density of random inputs. Many modern engineering problems…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
abridged] A method to rapidly estimate the Fourier power spectrum of a point distribution is presented. This method relies on a Taylor expansion of the trigonometric functions. It yields the Fourier modes from a number of FFTs, which is…
In this work, we use the Belief Function Theory which extends the probabilistic framework in order to provide uncertainty bounds to different categories of crowd density estimators. Our method allows us to compare the multi-scale…