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We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…

Computation · Statistics 2026-03-16 Daniel Sharp , Bart van Bloemen Waanders , Youssef Marzouk

Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…

Computation · Statistics 2025-07-14 Fuqun Han , Stanley Osher , Wuchen Li

For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational…

Methodology · Statistics 2023-07-14 Wyatt Bridgman , Reese Jones , Mohammad Khalil

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…

Machine Learning · Statistics 2013-12-18 Roger Frigola , Fredrik Lindsten , Thomas B. Schön , Carl E. Rasmussen

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

We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo (MCMC) algorithms for Bayesian inverse problems. Here four examples of information metrics are…

Optimization and Control · Mathematics 2022-06-27 Yifei Wang , Wuchen Li

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

Machine Learning · Statistics 2026-05-19 George Whittle , Juliusz Ziomek , Jacob Rawling , Maike A. Osborne

The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…

Dynamical Systems · Mathematics 2016-04-05 Juha Ala-Luhtala , Simo Särkkä , Robert Piché

Bayesian inference in complex generative models is often obstructed by the absence of tractable likelihoods and the infeasibility of computing gradients of high-dimensional simulators. Existing likelihood-free methods for generalized…

Applications · Statistics 2026-01-05 Diksha Bhandari , Sebastian Reich

Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…

Dynamical Systems · Mathematics 2019-10-17 Alfredo Garbuno-Inigo , Franca Hoffmann , Wuchen Li , Andrew M. Stuart

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…

Computation · Statistics 2023-06-21 Adrien Corenflos , Hany Abdulsamad

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…

Methodology · Statistics 2015-06-22 Clément Gilavert , Saïd Moussaoui , Jérôme Idier

Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…

Optimization and Control · Mathematics 2017-10-31 Abhishek Halder , Tryphon T. Georgiou

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…

Computational Engineering, Finance, and Science · Computer Science 2025-10-30 G. Robalo Rei , C. P. Schmidt , J. Nitzler , M. Dinkel , W. A. Wall

We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…

Image and Video Processing · Electrical Eng. & Systems 2026-04-16 Muhamed Kuric , Martin Zach , Andreas Habring , Michael Unser , Thomas Pock

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…

Computation · Statistics 2019-04-03 Jaewoo Park , Murali Haran

Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…

Machine Learning · Statistics 2021-06-10 William J. Wilkinson , Arno Solin , Vincent Adam

With extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating probabilistic (high-resolution…

Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…

Statistics Theory · Mathematics 2009-11-13 François Caron , Manuel Davy , Arnaud Doucet , Emmanuel Duflos , Philippe Vanheeghe

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…

Numerical Analysis · Mathematics 2016-11-03 Felix Lucka