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We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…

Statistics Theory · Mathematics 2013-08-05 Sergios Agapiou , Stig Larsson , Andrew M. Stuart

A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…

Optimization and Control · Mathematics 2024-01-05 William Fife , Pradipto Ghosh , Kyle DeMars

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

Machine Learning · Computer Science 2020-03-03 Xuan Su , Wee Sun Lee , Zhen Zhang

In real applications, the construction of prior and acceleration of sampling for posterior are usually two key points of Bayesian inversion algorithm for engineers. In this paper, q-analogy of Gaussian distribution, q-Gaussian distribution,…

Numerical Analysis · Mathematics 2018-08-06 Zhiliang Deng , Xiaomei Yang

We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to…

Statistical Mechanics · Physics 2013-11-25 Rudro R. Biswas , Pabitra N. Sen

This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…

Methodology · Statistics 2013-02-05 Simo Särkkä Jouni Hartikainen

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Computer Science 2014-08-12 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Statistics 2013-05-27 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…

Machine Learning · Statistics 2025-02-11 Alessandro Micheli , Mélodie Monod , Samir Bhatt

Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…

Instrumentation and Methods for Astrophysics · Physics 2026-02-06 Sébastien Pierre , Erwan Allys , Pablo Richard , Roman Soletskyi , Alexandros Tsouros

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

Methodology · Statistics 2017-05-31 Yunbo Ouyang , Feng Liang

Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…

Robotics · Computer Science 2026-01-29 Muzaffar Qureshi , Tochukwu Elijah Ogri , Kyle Volle , Rushikesh Kamalapurkar

Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…

Machine Learning · Computer Science 2021-11-17 Farzaneh Mahdisoltani

Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…

Methodology · Statistics 2023-11-21 Paul F. V. Wiemann , Matthias Katzfuss

We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…

Statistics Theory · Mathematics 2025-10-28 Mara Daniels

Reparameterizable densities are an important way to learn probability distributions in a deep learning setting. For many distributions it is possible to create low-variance gradient estimators by utilizing a `reparameterization trick'. Due…

Machine Learning · Statistics 2019-03-13 Luca Falorsi , Pim de Haan , Tim R. Davidson , Patrick Forré

In this paper we present Poisson mixture approaches for origin-destination (OD) modeling in transportation analysis. We introduce covariate-based models which incorporate different transport modeling phases and also allow for direct…

Methodology · Statistics 2020-11-13 Konstantinos Perrakis , Dimitris Karlis , Mario Cools , Davy Janssens

We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first…

Statistics Theory · Mathematics 2026-04-09 Giuseppe Carere , Han Cheng Lie

Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which can be viewed as a deficiency because the exact likelihood is permutation-invariant. This article takes the alternative…

Computation · Statistics 2018-02-20 Joseph Guinness

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

Methodology · Statistics 2019-07-04 Peyman Jalali , Kshitij Khare , George Michailidis