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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…

Developing reliable interatomic potential models with quantified predictive accuracy is crucial for atomistic simulations. Commonly used potentials, such as those constructed through the embedded atom method (EAM), are derived from…

This work introduces a novel Fourier phase retrieval model, called polarimetric phase retrieval that enables a systematic use of polarization information in Fourier phase retrieval problems. We provide a complete characterization of…

Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…

A simulation is useful when the phenomenon of interest is either expensive to regenerate or irreproducible with the same context. Recently, Bayesian inference on the distribution of the simulation input parameter has been implemented…

Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the nonresponse weighting adjustment is complicated because the effect of estimating the…

We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…

We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…

We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the…

We propose a Bayesian approach to the problem of multi-reference alignment -- the recovery of signals from noisy, randomly shifted observations. While existing frequentist methods accurately recover the signal at arbitrarily low…

In robotics, simulation has the potential to reduce design time and costs, and lead to a more robust engineered solution and a safer development process. However, the use of simulators is predicated on the availability of good models. This…

Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature…

Identifying parameters of computational models from experimental data, or model calibration, is fundamental for assessing and improving the predictability and reliability of computer simulations. In this work, we propose a method for…

Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

Precise polarisation measurements of the cosmic microwave background (CMB) require accurate knowledge of the instrument orientation relative to the sky frame used to define the cosmological Stokes parameters. Suitable celestial calibration…

Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…