Many spatial processes in environmental applications, such as climate variables and climate model errors on a global scale, exhibit complex nonstationary dependence structure, in not only their marginal covariance but also their cross-covariance. Flexible crosscovariance models for processes on a global scale are critical for an accurate description of each spatial process as well as the cross-...

Neurons in primary visual cortex are commonly characterized using linear models, or simple extensions of linear models. Specifically, V1 simple cell responses are often characterized using a rectified linear receptive field, and complex cell responses are often described as the sum of squared responses of two linear subunits. We examined this class of model directly by applying spike-triggered ...

This paper addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the paper. The member in this family having minimal trace is said to be “family-optimal”. When...

This manuscript presents valuable data on CH4 fluxes from the understudied permafrost region of NE Europe. CH4 fluxes were measured on the plot scale by closed chambers and on the landscape scale by the eddy covariance approach. The combination of these two approaches is a particular strength of this study. Furthermore, the authors present interesting data on stable carbon signatures of pore wa...

Environmental spatial data often show complex spatial-temporal dependency structures that are difficult to model and estimate due to the lack of symmetry and other standard assumptions of the covariance function. In this study, we introduce certain types of symmetry in spatialtemporal processes: axial symmetry in time, axial symmetry in space, and diagonal symmetry in space, and propose new cla...

We study algorithms for approximation of the mild solution of stochastic heat equations on the spatial domain ]0, 1[. The error of an algorithm is defined in L2-sense. We derive lower bounds for the error of every algorithm that uses a total of N evaluations of one-dimensional components of the driving Wiener process W . For equations with additive noise we derive matching upper bounds and we c...

One of main issues in point matching is the choice of the mapping function and the computation of its optimal hyperparameters. In this paper, we propose an attractive approach to determine the mapping function based on Gaussian processes (GPs) model. The mapping function is assumed to belong to a GPs model specified by a mean and a covariance function. Meanwhile, hyperparameters optimization of...

We propose, in maximum likelihood sense, an optimal method for the affine fundamental matrix estimation in the presence of both Gaussian noise and outliers. It is based on weighting the squared residuals by the iteratively computed, residual posterior probabilities to be relevant. The proposed principle is also used for the covariance matrix estimation of the affine F-matrix where the novelty i...

Interest has rapidly increased in studies that randomly assign classrooms or schools to interventions. When well implemented, such studies eliminate selection bias, providing strong evidence about the impact of the interventions. However, unless expected impacts are large, the number of units to be randomized needs to be quite large to achieve adequate statistical power, making these studies po...