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The radio astronomy community is adopting deep learning techniques to deal with the huge data volumes expected from the next-generation of radio observatories. Bayesian neural networks (BNNs) provide a principled way to model uncertainty in…

Bayesian profile regression mixture models (BPRM) allow to assess a health risk in a multi-exposed population. These mixture models cluster individuals according to their exposure profile and their health risk. However, their results, based…

Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…

In cohort studies binary outcomes are very often analyzed by logistic regression. However, it is well-known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a…

Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources…

This is a course project report with complete methodology, experiments, references and mathematical derivations. Matrix factorization [1] is a widely used technique in recommendation systems. Probabilistic Matrix Factorization (PMF) [2]…

In the era of Big Data, Markov chain Monte Carlo (MCMC) methods, which are currently essential for Bayesian estimation, face significant computational challenges owing to their sequential nature. To achieve a faster and more effective…

Approximate Bayesian computation (ABC) is a class of Bayesian inference algorithms that targets for problems with intractable or {unavailable} likelihood function. It uses synthetic data drawn from the simulation model to approximate the…

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior…

Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for…

If the conclusion of a data analysis is sensitive to dropping very few data points, that conclusion might hinge on the particular data at hand rather than representing a more broadly applicable truth. How could we check whether this…

In Markov Chain Monte Carlo (MCMC) simulations, the thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the…

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…

Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…

In this work, we propose a hybrid Bayesian approach towards clock offset and skew estimation, thereby synchronizing large scale networks. In particular, we demonstrate the advantage of Bayesian Recursive Filtering (BRF) in alleviating…

A system to update estimates from a sequence of probability distributions is presented. The aim of the system is to quickly produce estimates with a user-specified bound on the Monte Carlo error. The estimates are based upon weighted…

We develop a computationally efficient framework for quasi-Bayesian inference based on linear moment conditions. The approach employs a delayed acceptance Markov chain Monte Carlo (DA-MCMC) algorithm that uses a surrogate target kernel and…

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

This paper concerns the Bayesian approach to inverse acoustic scattering problems of inferring the position and shape of a sound-soft obstacle from phaseless far-field data generated by point source waves. To improve the convergence rate,…

In this paper we propose to numerically assess the performance of standard Gaussian approximations to probe the posterior distribution that arises from Bayesian data assimilation in petroleum reservoirs. In particular we assess the…