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We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous…
The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
We present a novel procedure to solve the Schr\"odinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
This paper proposes multi-target filtering algorithms in which target dynamics are given in continuous time and measurements are obtained at discrete time instants. In particular, targets appear according to a Poisson point process (PPP) in…
In this work we develop the Gaussian quadrature rule for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. Besides the computation based on the use of the standard and the modified Chebyshev…
Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the…
Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman-Bucy…
Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…
By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further…
This paper studies the optimal points in the capacity region of Gaussian multiple access channels (GMACs) with constant fading, multiple antennas and various power constraints. The points of interest maximize general rate objectives that…
The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential L\'evy processes are calibrated using regularized weighted…
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type and its application to the smoothing problem in the case when noise is…
This paper explores Barenblatt solutions of the time-fractional porous medium equation, characterized by a Caputo-type time derivative. Employing an integral equation approach, we rigorously prove the existence of these solutions and…
We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…
Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…
Canonical correlation analysis (CCA) is a standard tool for studying associations between two data sources; however, it is not designed for data with count or proportion measurement types. In addition, while CCA uncovers common signals, it…