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Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple…
Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…
In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…
The paper considers direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty due to the noisy data and data scarcity is less discussed in…
Standard Bayesian retrievals for exoplanet atmospheric parameters from transmission spectroscopy, while well understood and widely used, are generally computationally expensive. In the era of the JWST and other upcoming observatories,…
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…
Radio occultations are commonly used to assess remotely the thermodynamic properties of planets or satellites' atmospheres within the solar system. The data processing usually involves the so-called Abel inversion method or the numerical…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
We consider the problem of estimating a temperature-dependent thermal conductivity model (curve) from temperature measurements. We apply a Bayesian estimation approach that takes into account measurement errors and limited prior information…
Bleed Air System (BAS) is critical for maintaining flight safety and operational efficiency, supporting functions such as cabin pressurization, air conditioning, and engine anti-icing. However, BAS malfunctions, including overpressure, low…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
Argo floats measure seawater temperature and salinity in the upper 2,000 m of the global ocean. Statistical analysis of the resulting spatio-temporal dataset is challenging due to its nonstationary structure and large size. We propose…
In electromyogram (EMG)-based motion recognition, a subject-specific classifier is typically trained with sufficient labeled data. However, this process demands extensive data collection over extended periods, burdening the subject. To…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
Accurate prediction of fragmentation cross sections is essential for rare-isotope beam production, planning new-isotope searches, and designing experiments to study the most exotic regions of the nuclear chart. However, existing reaction…
Bayesian learning aided massive antenna array based THz MIMO systems are designed for spatial-wideband and frequency-wideband scenarios, collectively termed as the dual-wideband channels. Essentially, numerous antenna modules of the THz…
The appropriateness of the Poisson model is frequently challenged when examining spatial count data marked by unbalanced distributions, over-dispersion, or under-dispersion. Moreover, traditional parametric models may inadequately capture…
The conventional FL methods face critical challenges in realistic wireless edge networks, where training data is both limited and heterogeneous, often leading to unstable training and poor generalization. To address these challenges in a…