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We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…
The estimation of phase errors from digital-holography data is critical for applications such as imaging or wave-front sensing. Conventional techniques require multiple i.i.d. data and perform poorly in the presence of high noise or large…
We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observation is often hard to…
We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…
Transmission spectroscopy, which consists of measuring the wavelength-dependent absorption of starlight by a planet's atmosphere during a transit, is a powerful probe of atmospheric composition. However, the expected signal is typically…
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…
Position and frequency switching techniques used for the removal of the bandpass dependence of radio astronomical spectra are presented and discussed in detail. Both methods are widely used, although the frequency dependence of the system…
The ionosphere critically influences Global Navigation Satellite Systems (GNSS), satellite communications, and Low Earth Orbit (LEO) operations, yet accurate prediction of its variability remains challenging due to nonlinear couplings…
A unified, Bayesian inference of midplane electron temperature and density profiles using both Thompson scattering (TS) and interferometric data is presented. Beyond the Bayesian nature of the analysis, novel features of the inference are…
Interferometric observations of the low-frequency radio sky (< 1 GHz) are largely limited by systematic effects introduced by the ionosphere. Here, we analyse a ten-hour nighttime uGMRT Band-4 observation of 3C48 to characterise ionospheric…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…
Ion-acoustic modes propagating in unmagnetized dusty plasmas are studied by applying a generic collisionless fluid model. An Eulerian-to-Lagrangean variable transformation leads to a new system of evolution equations, which may be combined…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
Gaussian processes provide a method for extracting cosmological information from observations without assuming a cosmological model. We carry out cosmography -- mapping the time evolution of the cosmic expansion -- in a model-independent…
Many astronomical questions require deep, wide-field observations at low radio frequencies. Phased arrays like LOFAR and SKA-low are designed for this, but have inherently unstable element gains, leading to time, frequency and…
We analyze deterministic and random temporal variations in dispersion measure (DM) from the full three-dimensional velocities of pulsars with respect to the solar system, combined with electron-density variations on a wide range of length…