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A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each…

We introduce Accelerated Sequential Posterior Inference via Reuse (ASPIRE), a broadly applicable framework that transforms existing posterior samples and Bayesian evidence estimates into unbiased results under alternative models without…

This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

We propose GS-IR, a novel inverse rendering approach based on 3D Gaussian Splatting (GS) that leverages forward mapping volume rendering to achieve photorealistic novel view synthesis and relighting results. Unlike previous works that use…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

Recent advances in Gaussian Splatting-based inverse rendering extend Gaussian primitives with shading parameters and physically grounded light transport, enabling high-quality material recovery from dense multi-view captures. However, these…

Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…

Following the advent of NeRFs, 3D Gaussian Splatting (3D-GS) has paved the way to real-time neural rendering overcoming the computational burden of volumetric methods. Following the pioneering work of 3D-GS, several methods have attempted…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

3D Gaussian Splatting (3DGS) has emerged as a powerful representation for high-quality rendering across a wide range of applications.However, its high computational demands and large storage costs pose significant challenges for deployment…

Recent advances in 3D Gaussian splatting have significantly improved real-time novel view synthesis, yet insufficient geometric constraints during scene optimization often result in blurred reconstructions of fine-grained details,…

The globalised cascaded scattering matrix technique is a well proven, practical method that can be used to simulate large accelerating RF structures in which realistic fabrication errors to be incorporated in an efficient manner without the…

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…

We study the problem of proper discretizing and sampling issues related to geodesic X-ray transforms on simple surfaces, and illustrate the theory on simple geodesic disks of constant curvature. Given a notion of band limit on a function,…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…

In inverse rendering, accurately modeling visibility and indirect radiance for incident light is essential for capturing secondary effects. Due to the absence of a powerful Gaussian ray tracer, previous 3DGS-based methods have either…