Related papers: Addressing prior dependence in hierarchical Bayesi…

Pulsar Timing Arrays (PTA) provide a powerful framework to measure low-frequency gravitational waves, but accuracy and robustness of the results are challenged by complex noise processes that must be accurately modeled. Standard PTA…

We present a detailed study of Bayesian inference workflows for pulsar timing array data with a focus on enhancing efficiency, robustness and speed through the use of normalizing flow-based nested sampling. Building on the Enterprise…

The null hypothesis in Pulsar Timing Array (PTA) analyses includes assumptions about ensemble properties of pulsar time-correlated noise. These properties are encoded in prior probabilities for the amplitude and the spectral index of the…

The recent detection of nanohertz stochastic gravitational-wave backgrounds (SGWBs) by pulsar timing arrays (PTAs) promises unique insights into astrophysical and cosmological origins. However, traditional Markov Chain Monte Carlo (MCMC)…

Gaussian Process Regression (GPR) is a powerful tool for nonparametric regression, but its application in a fully Bayesian fashion in high-dimensional settings is hindered by two primary challenges: the difficulty of variable selection and…

Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset,…

Current approximate posteriors in Bayesian neural networks (BNNs) exhibit a crucial limitation: they fail to maintain invariance under reparameterization, i.e. BNNs assign different posterior densities to different parametrizations of…

Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…

Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…

In many real-world scenarios, such as gas leak detection or environmental pollutant tracking, solving the Inverse Source Localization and Characterization problem involves navigating complex, dynamic fields with sparse and noisy…

Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately…

In a bivariate meta-analysis the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Bayesian inference is attractive as informative priors that add small amount of information can…

Pulsar timing arrays (PTAs) perform Bayesian posterior inference with expensive MCMC methods. Given a dataset of ~10-100 pulsars and O(10^3) timing residuals each, producing a posterior distribution for the stochastic gravitational wave…

While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

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…