Related papers: A non-parametric consistency test of the $\Lambda$…
This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…
We present a new approach for statistical inference on noise properties of CMB anisotropy data. We consider a Maximum Likelihood parametric estimator to recover the full dependence structure of the noise process. We also consider a…
We present a joint cosmological analysis combining data from the Planck satellite, the Atacama Cosmology Telescope, and the South Pole Telescope. We construct a unified likelihood that reproduces the measured temperature and polarisation…
We adapt the smooth tests of goodness of fit developed by Rayner and Best to the study of the non-Gaussianity of interferometric observations of the cosmic microwave background (CMB). The interferometric measurements (visibilities) are…
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…
The measurements of the statistical properties of the Cosmic Microwave Background (CMB) fluctuations enable us to probe the physics of the very early Universe especially at the epoch of inflation. A particular interest lays on the detection…
Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force…
Machine learning has become widely used in astronomy. Gaussian Process (GP) regression in particular has been employed a number of times to fit or re-sample supernova (SN) light-curves, however by their nature typical GP models are not…
The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…
The canonical technique for nonlinear modeling of spatial/point-referenced data is known as kriging in geostatistics, and as Gaussian Process (GP) regression for surrogate modeling and statistical learning. This article reviews many…
This work proposes a nonparametric method to compare the underlying mean functions given two noisy datasets. The motivation for the work stems from an application of comparing wind turbine power curves. Comparing wind turbine data presents…
In this article, we extend previous studies based on CMB spherical harmonic phases (SHP) to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field (GRF). The null hypothesis…
Much focus was on the possible slowing down of cosmic acceleration under the dark energy parametrization. In the present paper, we investigate this subject using the Gaussian processes (GP), without resorting to a particular template of…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…
We present a Gaussian regression method for time series with missing data and stationary residuals of unknown power spectral density (PSD). The missing data are efficiently estimated by their conditional expectation as in universal Kriging,…
In astrophysical (inverse) regression problems it is an important task to decide whether a given parametric model describes the observational data sufficiently well or whether a non-parametric modelling becomes necessary. However, in…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
We test the consistency between Planck temperature and polarization power spectra and the concordance model of $\Lambda$ Cold Dark Matter cosmology ($\Lambda$CDM) within the framework of Crossing statistics. We find that Planck TT best fit…
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…
Weakly stationary Gaussian processes (GPs) are the principal tool in the statistical approaches to the design and analysis of computer experiments (or Uncertainty Quantification). Such processes are fitted to computer model output using a…