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Surface reconstruction is a vital tool in a wide range of areas of medical image analysis and clinical research. Despite the fact that many methods have proposed solutions to the reconstruction problem, most, due to their deterministic…

A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve…

One of the tasks of the Bayesian inverse problem is to find a good estimate based on the posterior probability density. The most common point estimators are the conditional mean (CM) and maximum a posteriori (MAP) estimates, which…

This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex probability…

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…

In this paper, we provide a novel method for the estimation of unknown parameters of the Gaussian Mixture Model (GMM) in Positron Emission Tomography (PET). A vast majority of PET imaging methods are based on reconstruction model that is…

Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET…

Estimation of small failure probabilities is one of the most important and challenging computational problems in reliability engineering. The failure probability is usually given by an integral over a high-dimensional uncertain parameter…

We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

An analytical solution for the posterior estimate in Bayesian tomography of the unknown quantum state of an arbitrary quantum system (with a finite-dimensional Hilbert space) is found. First, we derive the Bayesian estimate for a pure…

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, choosing an appropriate prior distribution is an important task. In…

Markov chain Monte Carlo (MCMC) methods form one of the algorithmic foundations of Bayesian inverse problems. The recent development of likelihood-informed subspace (LIS) methods offers a viable route to designing efficient MCMC methods for…

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…