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An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
We developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to…
We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problems; this refers to the study of how to estimate unknown model…
The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar…
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
We review the available atomic data used for interpreting and modeling X-ray observations. The applications for these data can be divided into several levels of detail, ranging from compilations which can be used with direct inspection of…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
We consider the application of high-pass Fourier filters to remove periodic systematic fluctuations from full-sky survey CMB datasets. We compare the filter performance with destriping codes commonly used to remove the effect of residual…
This presentation describes the Bayesian Block algorithm in the context of its application to analysis of time series data from the Fermi Gamma Ray Space Telescope. More generally this algorithm performs optimal segmentation analysis on…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
In the next decade, high energy physicists will use very sophisticated equipment to record unprecedented amounts of data in the hope of making major advances in our understanding of particle phenomena. Some of the signals of new physics…
The following working document summarizes our work on the clustering of financial time series. It was written for a workshop on information geometry and its application for image and signal processing. This workshop brought several experts…
Mining Time Series data has a tremendous growth of interest in today's world. To provide an indication various implementations are studied and summarized to identify the different problems in existing applications. Clustering time series is…
Time series forecasting with limited data is a challenging yet critical task. While transformers have achieved outstanding performances in time series forecasting, they often require many training samples due to the large number of…
Physics analysis in astroparticle experiments requires the capability of recognizing new phenomena; in order to establish what is new, it is important to develop tools for automatic classification, able to compare the final result with data…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
Asteroseismology is a unique tool that can be used to study the interior of stars and hence deliver unique information for the studiy of stellar physics, stellar evolution, and Galactic archaeology. We aim to develop a simple model of the…
Nowadays there is no field research which is not flooded with data. Among the sciences, Astrophysics has always been driven by the analysis of massive amounts of data. The development of new and more sophisticated observation facilities,…