相关论文: Deep Bayesian Filter for Bayes-faithful Data Assim…
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…
Distributed Lag Models (DLMs) and similar regression approaches such as MIDAS have been used for many decades in econometrics and more recently to investigate how poor air quality adversely affects human health. In this paper we describe…
We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…
We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…
This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…
Many recent advances in sequential assimilation of data into nonlinear high-dimensional models are modifications to particle filters which employ efficient searches of a high-dimensional state space. In this work, we present a complementary…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
The structure of the nonlinear inverse problem arising from capillarity-driven imbibition in porous media is investigated, considering a degenerate parabolic PDE with compactly supported diffusivity and boundary-driven fluxes as the…
Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…
We propose an approximation to the forward-filter-backward-sampler (FFBS) algorithm for large-scale spatio-temporal smoothing. FFBS is commonly used in Bayesian statistics when working with linear Gaussian state-space models, but it…
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
This paper deals with the state estimation of non-linear and non-Gaussian systems with an emphasis on the numerical solution to the Bayesian recursive relations. In particular, this paper builds upon the Lagrangian grid-based filter (GbF)…
We introduce a deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling. As telescopes and simulations rapidly expand the volume and resolution of astrophysical data, fast simulation-based…
Bayesian experimental design (BED) provides a principled framework for optimizing data collection by choosing experiments that are maximally informative about unknown parameters. However, existing methods cannot deal with the joint…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…
We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…