TIME-DOMAIN ASTROPHYSICS
No prerequisites are needed, apart from a basic knowledge of analysis and statistics.
The final examination is an oral one. Students must interact with the teacher in advance of the examination and a science case obtained by the modern literature will be selected. The student will be asked to properly describe the main formal aspects of the study and discuss critically the reliability and limits of the presented results.
The goal of the examination is to:
1. verify the proper knowledge of the mathematical foundations and limitations of the tools adopted to solve the specific problem suggested by the teacher. It is expected that the discussion is carried out in a full Bayesian framework;
2. show the ability to evaluate the stationarity or non-stationarity of the time series under analysis, and derive inferences about short- and long-term noise affecting the data;
3. know how to search for and compute the statistical significance of possible periodicities hidden in the data applying, depending on the specific case, the most reliable technique(s) in the frequency or time domains, for regularly or irregularly spaced data, affected or non affected by correlated noise, etc.
4. Discuss the most effective solutions of analogous problems with data coming from future instruments and surveys in a “For any question, discussion, concern, etc, students are invited to contact the teacher at the following email: stefano.covino@uninsubria.itbig data” scenario.
Item 1-3 contribute for 30% each to the final grade, items 4 for the remaining 10%. The final grade is derived by a weighed average of the scores of each above-mentioned item. The optional exercises, if properly solved and discussed during the lecture period, will allow a student to obtain full marks with laude if the previous item scores are already at the maximum level in the adopted scale. Otherwise, they could improve the grade by a 10%.
Time series are ubiquitous in astrophysics. This course is aimed at providing students the main capabilities to extract physical information with state-of-the-art statistical inferences from the available datasets. We will refer to real science cases developed in the astrophysical literature, yet the discussed methodologies could be of definite interest to anyone involved in quantitative analysis of data in a temporal (or spatial) sequence in any field of modern physics, economy, engineering and social sciences.
At the end of the course students will be able to:
• carry out analysis of any statistical problem in a full Bayesian framework;
• properly model time series to derive meaningful statistical inferences about stationarity, short- and long-term memory behavior;
• know how to search for and compute the statistical significance of possible periodicities hidden in the data;
• carry out the analysis both in the frequency and time domains;
• deal with data irregularly spaced and/or affected by correlated noise;
• look for specific patterns in highly noisy datasets.
• apply big-data techniques to carry out the analyses of typical large datasets obtained by modern astrophysical facilities.
• Introduction to time series
• Time (and spatial) variability in astrophysics
• Fourier analysis and noise characterization
◦ Case study: stellar variability
◦ Case study: exo-planet transits
◦ Case study: pulsars
• Time-domain analysis and auto-regressive processes
• Irregular sampling, Lomb-Scargle periodograms
◦ Case studies: AGN variability
• Advanced topics: non-parametric analysis
• Matching filters
◦ Case study: LIGO/Virgo gravitational wave signals
• Data exploration
◦ Case study: SETI data analysis
• Big-data, machine learning and “intelligent” systems for time-series analysis
◦ Case studies: spatial variability (CMB, large scale structure)
• Final topics: forecasting
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The course is organized in regular frontal lectures with formal introductions followed by real research life examples fully described during the lectures. Optional exercises will be proposed to improve the knowledge of the various topics to the most interested students based on publicly available data.
These exercises will not be part of the final examination but if properly executed will contribute to the final grade. They will be executed privately by the students beyond the standard lectures. It is expected that the interested students contact the teacher for discussions about these additional problems.