Related papers: A Multivariate Non-Gaussian Bayesian Filter Using …

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

The real-world applications in signal processing generally involve estimating the system state or parameters in nonlinear, non-Gaussian dynamic systems. The estimation problem may get even more challenging when there are physical…

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…

We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…

Data assimilation is widely used to improve flood forecasting capability, especially through parameter inference requiring statistical information on the uncertain input parameters (upstream discharge, friction coefficient) as well as on…

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…

In this paper we consider the continuous--time nonlinear filtering problem, which has an infinite--dimensional solution in general, as proved by Chaleyat--Maurel and Michel. There are few examples of nonlinear systems for which the optimal…

Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is…

Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and…

We propose a Bayesian nonparametric method for low-pass filtering that can naturally handle unevenly-sampled and noise-corrupted observations. The proposed model is constructed as a latent-factor model for time series, where the latent…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

The paper provides simple formulas of Bayesian filtering for the exact recursive computation of state conditional probability density functions given quantized innovations signal measurements of a linear stochastic system. This is a topic…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

In the present paper we consider the problem of estimating the multidimensional power spectral density which describes a second-order stationary random field from a finite number of covariance and generalized cepstral coefficients. The…

We examine an experimental setup implementing a family of quantum non-Gaussian filters. The filters can be applied to an arbitrary two-mode input state. We assume realistic photodetection in the filtering process and explore two different…

State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…