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In the last decade, a number of experiments dealt with the problem of measuring the arrival direction distribution of cosmic rays, looking for information on the propagation mechanisms and the identification of their sources. Any deviation…

The detailed modelling of stellar oscillations is a powerful approach to characterising stars. However, poor treatment of systematics in theoretical models leads to misinterpretations of stars. Here we propose a more principled statistical…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

The power density spectrum of a light curve is often calculated as the average of a number of spectra derived on individual time intervals the light curve is divided into. This procedure implicitly assumes that each time interval is a…

Stars exhibit a bewildering variety of variable behaviors ranging from explosive magnetic flares to stochastically changing accretion to periodic pulsations or rotations. The principal LSST surveys will have cadences too sparse and…

I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement…

E-science of photometric data requires automatic procedures and a precise recognition of periodic patterns to perform science as well as possible on large data. Analytical equations that enable us to set the best constraints to properly…

Time-varying non-Euclidean random objects are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of time-varying data. However, quantifying periodicity in general non-Euclidean random objects…

One way of recovering information about the initial conditions of the Universe is by measuring features of the cosmological density field which are preserved during gravitational evolution and galaxy formation. In this paper we study the…

A common feature of Active Galactic Nuclei (AGN) is their random variations in brightness across the whole emission spectrum, from radio to $\gamma$-rays. Studying the nature and origin of these fluctuations is critical to characterising…

We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has…

Temporal analysis of radiation from Astrophysical sources like Active Galactic Nuclei, X-ray Binaries and Gamma-ray bursts provide information on the geometry and sizes of the emitting regions. Establishing that two light-curves in…

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…

Gaussian processes (GPs) are commonly used as a model of stochastic variability in astrophysical time series. In particular, GPs are frequently employed to account for correlated stellar variability in planetary transit light curves. The…

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

We introduce and apply a methodology based on dynamic time warping (DTW) to compare the whole set of gamma-ray light curves reported in the Third Fermi-Large Area Telescope Pulsar Catalogue. Our method allows us to quantitatively measure…

Quasi-periodicity refers to a pattern in a function where it appears periodic but has evolving amplitudes over time. This is often the case in practical settings such as the modeling of case counts of infectious disease or the carbon…

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…

Astronomy is in an era where all-sky surveys are mapping the Galaxy. The plethora of photometric, spectroscopic, asteroseismic and astrometric data allows us to characterise the comprising stars in detail. Here we quantify to what extent…

Pulsars are known to display short-term variability. Recently, examples of longer-term emission variability have emerged that are often correlated with changes in the rotational properties of the pulsar. To further illuminate this…