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Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty -- from uncertain input parameters to uncertain output quantities -- in high resolution mathematical models of brain physiology. Advanced…

We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties…

An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential…

Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as…

Subsurface remediation often involves reconstruction of contaminant release history from sparse observations of solute concentration. Markov Chain Monte Carlo (MCMC), the most accurate and general method for this task, is rarely used in…

Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…

Regularized Maximum Likelihood (RML) techniques are a class of image synthesis methods that achieve better angular resolution and image fidelity than traditional methods like CLEAN for sub-mm interferometric observations. To identify best…

Deep learning has been extensively applied in medical image reconstruction, where Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) represent the predominant paradigms, each possessing distinct advantages and inherent…

The performance of land surface models (LSMs) significantly affects the understanding of atmospheric and related processes. Many of the LSMs' soil and vegetation parameters were unknown so that it is crucially important to efficiently…

Monte Carlo (MC) method has been recognized the most accurate dose calculation method for radiotherapy. However, its extremely long computation time impedes clinical applications. Recently, a lot of efforts have been made to realize fast MC…

We developed a three-dimensional radiative transfer code for an ultra-relativistic background flow-field by using the Monte Carlo (MC) method in the context of gamma-ray burst (GRB) emission. For obtaining reliable simulation results in the…

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy.…

Precise radial velocity measurements have led to the discovery of ~170 extrasolar planetary systems. Understanding the uncertainties in the orbital solutions will become increasingly important as the discovery space for extrasolar planets…

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…

Markov Chain Monte Carlo (MCMC) is one of the most powerful methods to sample from a given probability distribution, of which the Metropolis Adjusted Langevin Algorithm (MALA) is a variant wherein the gradient of the distribution is used…

Compact gamma cameras with a square-shaped monolithic scintillator crystal and an array of silicon photomultipliers (SiPMs) are actively being developed for applications in areas such as small animal imaging, cancer diagnostics and…

We introduce a new micro-macro Markov chain Monte Carlo method (mM-MCMC) with indirect reconstruction to sample invariant distributions of molecular dynamics systems that exhibit a time-scale separation between the microscopic (fast)…

Monte Carlo rendering algorithms are widely used to produce photorealistic computer graphics images. However, these algorithms need to sample a substantial amount of rays per pixel to enable proper global illumination and thus require an…

Monte-Carlo (MC) Dropout provides a practical solution for estimating predictive distributions in deterministic neural networks. Traditional dropout, applied within the signal space, may fail to account for frequency-related noise common in…