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We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
Distributed estimation methods have recently been used to compute the maximum likelihood estimate of the precision matrix for large graphical Gaussian models. Our aim, in this paper, is to give a Bayesian estimate of the precision matrix…
In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
This work deals with a novel Gaussian filter-based pressure correction technique with a super compact higher order finite difference scheme for solving unsteady three-dimensional (3D) incompressible, viscous flows. This pressure correction…
We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…
Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely-quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…
This paper describes the most accurate analytical frequentist assessment to date of the uncertainties in the estimation of physical parameters from gravitational waves generated by non spinning binary systems and Earth-based networks of…
Astronomical data often suffer from noise and incompleteness. We extend the common mixtures-of-Gaussians density estimation approach to account for situations with a known sample incompleteness by simultaneous imputation from the current…
Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input…
This paper studies how to learn parameters in diagonal Gaussian mixture models. The problem can be formulated as computing incomplete symmetric tensor decompositions. We use generating polynomials to compute incomplete symmetric tensor…
In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…
A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
Antenna array calibration is necessary to maintain the high fidelity of beam patterns across a wide range of advanced antenna systems and to ensure channel reciprocity in time division duplexing schemes. Despite the continuous development…
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
In gravitational wave astronomy, non-Gaussian noise, such as scattered light noise disturbs stable interferometer operation, limiting the interferometer's sensitivity, and reducing the reliability of the analyses. In scattered light noise,…