Applied Multi-Messenger Astronomy 2 (Statistical and Machine Learning Methods in Particle and Astrophysics)

Multi-messenger astronomy is a newly emerging field of astronomy dedicated to the understanding of the high-energy content of our universe. In contrary to classic astronomy, it is focused on neutrinos, gamma rays, and cosmic rays at energies between several MeV and EeV. In order to analyse the enormous amount of data collected from various observatories, it is common practice to apply analysis techniques from statistics, numerics, and data science. We want to broaden the students' understanding for the important results and open questions of multi-messenger astronomy and teach the ability to understand and reproduce some of the most important results of the field by applying basics tools of statistics, data analysis, and software engineering.

The contents of the Lecture comprise:

26.04.2019 (Dr. Matteo Agostini) Statistical models and point estimation Intro do the course , statistical models, toyMC, likelihoods, maximum likelihood estimator

03.05.2019 (Dr. Matteo Agostini) Frequentist hypothesis testing and sensitivity likelihood ratios, test statistics, power and size of the test, p-value, sensitivity (median p-value under an hypothesis)

10.05.2019 (Dr. Matteo Agostini) Frequentist interval estimation from a test to a set of tests (p-value plot a la higgs), asymptotic properties of test statistics

17.05.2019 (Dr. Hans Niederhausen) Frequentist interval estimation (Part 2) / Introduction to IceCube physics confidence intervals via inversion of likelihood ratio tests. pivotal quantities. astrophysical and atmospheric neutrinos. deep inelastic scattering. icecube data.

24.05.2019 (Dr. Hans Niederhausen) A statistical model of the IceCube detection process Building a Monte Carlo Simulation to generate pseudo-IceCube data. understanding importance weights.

31.05.2019 (Dr. Hans Niederhausen) Searching for a needle in the needle stack: the case of neutrino point sources in the sky Implementing a maximum likelihood search for a point source of astrophysical neutrinos in the overwhelming background from atmospheric neutrinos 

07.06.2019 (Dr. J. Michael Burgess) Fitting a line Start with the model that generates the data (simulation)
Least squares, Maximum likelihood (explain that MLE does not give you errors beyond a very very strict assumption), Bayes
Systematics and what they mean for fitting a line

14.06.2019 (Dr. J. Michael Burgess) Fitting a lot of lines A whole lecture on how to build a partial pooling hierarchical bayesian model for fitting correlations from multiple measurements

21.06.2019 (Dr. J. Michael Burgess) Lines, multiple lines, fitting the JLA data set to determine the cosmological parameters Using what we learned, we will build a model to fit the JLA data set for the cosmological parameters while dealing with systematics, malmquist bias, and hierarchal modeling

28.06.2019 (Dr. Patrick Vaudrevange) Basic Introduction to String Theory Just basic ideas, pictures, only very few equations

05.07.2019 (Dr. Patrick Vaudrevange) Cluster analysis Lecture with problem soving with "real" data from string theory

12.07.2019 (Dr. Patrick Vaudrevange) Neural Networks: Basics (basic NN, CNN, autoencoder, ...) Lecture with problem soving with "real" data from string theory

19.07.2019 (Dr. Patrick Vaudrevange) Neural Networks: Reinforcement Learning Lecture with problem soving with "real" data from string theory

After successful completion of the module the students are able to:

• understand the basic concept of multi-messenger astronomy
• iterpret the content of scientific publications in that field
• understand and perform maximum likelihood and chi2 fits
• understand the concept of and use minimizers like Minuit
• understand the concept of and perform Markov-chain Monte Carlo sampling
• understand the basics of Machine Learning and apply it to own problems
• understand and use Bayesian statistics in science
• analyze data from multi-messenger instruments

No preconditions in addition to the requirements for the Master’s program in Physics.

This second part of the course continues the introduction of statistical methods and machine learning techniques. These basic concepts are then linked to actual examples from multi-messenger astronomy. In the last part of the lecture one or two special topics selected by the students can be explored in more depth.

In the exercise, the students get the chance to apply the taught concepts and methods to examples from multi-messenger astronomy, including analyses with real publically available data. The exercises are designed for and will be finally presented in Python. The students are provided with a virtual Linux machine that has all the required software pre-installed.

PowerPoint presentations (recordings also available to students), live coding, text books, complementary literature

• T.K. Gaisser, R. Engel & E. Resoni: Cosmic Rays and Particle Physics, Cambridge University Press, (2016)
• M.A. Wood: Python and Matplotlib Essentials for Scientists and Engineers, Morgan & Claypool, (2015)
• G. Cowan: Statistical Data Analysis, Oxford Science Publications, (1998)

The achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using presentations independently prepared by the students. The exam of 25 minutes consists of the presentation and a subsequent discussion.

For example an assignment in the exam might be:

• Likelihood calculation
• Qualitative description of possible sources of astro-particles
• Basic example of a machine learning application