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The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…

We introduce and test several novel approaches for periodicity detection in unevenly-spaced sparse datasets. Specifically, we examine five different kinds of periodicity metrics, which are based on non-parametric measures of serial…

Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…

Survey observations of the three-dimensional locations of galaxies are a powerful approach to measure the distribution of matter in the universe, which can be used to learn about the nature of dark energy, physics of inflation, neutrino…

Anomaly detection for time-series data has been an important research field for a long time. Seminal work on anomaly detection methods has been focussing on statistical approaches. In recent years an increasing number of machine learning…

Many astronomical phenomena, including Fast Radio Bursts and Soft Gamma Repeaters, consist of brief, separated, seemingly aperiodic events. The intervals between these events vary randomly, but there are epochs of greater activity, with…

Change detection in multivariate time series has applications in many domains, including health care and network monitoring. A common approach to detect changes is to compare the divergence between the distributions of a reference window…

Astronomy has been at the forefront of the development of the techniques and methodologies of data intensive science for over a decade with large sky surveys and distributed efforts such as the Virtual Observatory. However, it faces a new…

I describe ongoing work on development of Bayesian methods for exploring periodically varying phenomena in astronomy, addressing two classes of sources: pulsars, and extrasolar planets (exoplanets). For pulsars, the methods aim to detect…

We use data from a recent long ASCA observation of the Narrow Line Seyfert 1 Ark 564 to investigate in detail its timing properties. We show that a thorough analysis of the time series, employing techniques not generally applied to AGN…

Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to…

Robust state estimation in coupled dynamical systems depends critically not only on sensor quality but on the structural alignment between observation channels and the system's intrinsic dynamics. This paper develops a rigorous framework…

In this paper, we develop a complete methodology for detecting time-varying/non time-varying parameters in ARCH processes. For this purpose, we estimate and test various semiparametric versions of the time-varying ARCH model (tv-ARCH) which…

The first step when investigating time varying data is the detection of any reliable changes in star brightness. This step is crucial to decreasing the processing time by reducing the number of sources processed in later, slower steps.…

We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…

Telescopes are much more expensive than astronomers, so it is essential to minimize required sample sizes by using the most data-efficient statistical methods possible. However, the most commonly used model-independent techniques for…

An important challenge in big data is identification of important variables. In this paper, we propose methods of discovering variables with non-standard univariate marginal distributions. The conventional moments-based summary statistics…

A method for testing nonlinearity in time series is described based on information-theoretic functionals -- redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique,…