Related papers: Bayesian Statistical Inversion for High-Dimensiona…
The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting…
Optimal design facilitates intelligent data collection. In this paper, we introduce a fully Bayesian design approach for spatial processes with complex covariance structures, like those typically exhibited in natural ecosystems. Coordinate…
Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of…
Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…
Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…
We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…
In this contribution we present an accelerated optimization-based approach for combined state and parameter reduction of a parametrized linear control system which is then used as a surrogate model in a Bayesian inverse setting. Following…
Gravitational wave astrophysics relies heavily on the use of matched filtering both to detect signals in noisy data from detectors, and to perform parameter estimation on those signals. Matched filtering relies upon prior knowledge of the…
Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…
In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…
Exoplanet research is carried out at the limits of the capabilities of current telescopes and instruments. The studied signals are weak, and often embedded in complex systematics from instrumental, telluric, and astrophysical sources.…
We consider optimal experimental design (OED) for nonlinear inverse problems within the Bayesian framework. Optimizing the data acquisition process for large-scale nonlinear Bayesian inverse problems is a computationally challenging task…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…