Related papers: High-Pass Filtering and Gaussian Process Regulariz…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
Doppler spectroscopy has uncovered or confirmed all the known planets orbiting nearby stars. Two main techniques are used to obtain precision Doppler measurements at optical wavelengths. The first approach is the gas cell method, which…
Starspots, plages, and activity cycles cause radial velocity variations that can either mimic planets or hide their existence. To verify the authenticity of newly discovered planets, observers may search for periodicity in spectroscopic…
To date, only 18 exoplanets with radial velocity (RV) semi-amplitudes $<2$ m/s have had their masses directly constrained. The biggest obstacle to RV detection of such exoplanets is variability intrinsic to stars themselves, e.g. nuisance…
A new apodized Keplerian (AK) model is proposed for the analysis of precision radial velocity (RV) data to model both planetary and stellar activity (SA) induced RV signals. A symmetrical Gaussian apodization function with unknown width and…
With the unprecedented photometric precision of the Kepler Spacecraft, significant systematic and stochastic errors on transit signal levels are observable in the Kepler photometric data. These errors, which include discontinuities,…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…
Gaussian process (GP) models have been used in a wide range of battery applications, in which different kernels were manually selected with considerable expertise. However, to capture complex relationships in the ever-growing amount of…
The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…
Since it has become possible to discovery planets orbiting nearby solar-type stars through very precise Doppler-shift measurements, the role of methods used to analyze such observations has grown significantly. The widely employed…
Atmospheric retrievals are essential tools for interpreting exoplanet transmission and eclipse spectra, enabling quantitative constraints on the chemical composition, aerosol properties, and thermal structure of planetary atmospheres. The…
Precision radial velocity (RV) measurements continue to be a key tool to detect and characterise extrasolar planets. While instrumental precision keeps improving, stellar activity remains a barrier to obtain reliable measurements below 1-2…
Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…
Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with…
Approximate Bayesian computation (ABC) can be used for model fitting when the likelihood function is intractable but simulating from the model is feasible. However, even a single evaluation of a complex model may take several hours,…
Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by…
Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…
Relativistic binary pulsars orbiting white dwarfs and neutron stars have already provided excellent tests of gravity. However, despite observational efforts, a pulsar orbiting a black hole has remained elusive. One possible explanation is…
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…