
Course unit
ASTROSTATISTICS AND COSMOLOGY
SCP8082722, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
FIS/05 
Astronomy and Astrophysics 
6.0 
Course unit organization
Period 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Examination board not defined
Prerequisites:

Probability and statistics: definition of probability, probability distributions, mean value, variance and covariance, Bayes Theorem, basics of statistical estimation theory, maximum likelihood, confidence intervals, hypthesis testing.
Cosmology: Hubble law, RobertsonWalker metric, FriedmannRobertsonWalker equations. Cosmological perturbations: Jeans instability, power spectrum, growth factor. 
Target skills and knowledge:

At the end of the course, the student should have a clear understanding of basic concepts in Bayesian statistics and be able to apply such concepts to the resolution of actual data analysis problems in astrophysics and cosmology.
More specifically, the acquired knowledge should enable the student to:
1) Build optimal statistical estimators of astrophysical and cosmological parameter in a variety of practical situations.
2) Apply Monte Carlo Markov Chain (MCMC) algorithms for Bayesian inference, choosing from different approaches (e.g. MetropolisHastings, Gibbs sampling, Hamiltonian sampling).
3) Implement Bayesian model selection algorithms in practical contexts.
4) Have a practical approach to the problem of estimation of experimental uncertainties, considering limitations and issues of different statistical methods which can be applied in specific situations. Evaluate the impact of systematic effects, in simple cases, and produce strategies for their mitigation. 
Examination methods:

The exam is comprised of three phases.
1) Resolution of assigned homework during the course, eventually to undertake in group.
2) Written examination, structured in 1 or 2 exercises  where the concepts discussed in class are applied  and theoretical questions.
3) Optional: oral examination with discussion of the course topics. 
Assessment criteria:

The evaluation criteria can be summarized as follows:
1) Comprehensive understanding of the course topics.
2) Critical thinking and ability connect different subjects discussed in the course.
3) Exhaustive knowledge of the course topics.
4) Synthesis skills and exposition clarity.
5) Correct use of technical terminology.
6) Ability to apply theoretical concepts, as well as analytical and comptational techniques discussed in class to the resolution of realistic problems in forecasting, data analysis and parameter estimation in astrophysics and cosmology. 
Course unit contents:

Bayes theorem and bayesian probability. Choice of prior. Bayesian inference and Monte Carlo Markov Chain (MCMC): MetropolisHastings, Gibbs and Hamiltonian sampling. Joint likelihood. Parameter marginalization. Bayesian evidence: model selection and comparison, information criteria. Fisher matrix for experimental design and forecasting.
Applications: power spectrum estimation in cosmological datasets (Cosmic Microwave Background and Large Scale Structure), MCMC for cosmological parameter estimation, component separation, Gravitational Wave data analysis, Fisher matrix forecasting for future cosmological surveys.
Parts of the program might undergo changes, according to the composition and the competences of the class. 
Planned learning activities and teaching methods:

The course is structured as a series of lectures, presented at the blackboard. Slides and additional visual material will be used as an aid. The course is characterized by an interactive approach, with discussions and open questions asked in class to the students. Emphasis is given the the presentation of case studies, applications and concrete examples. 
Additional notes about suggested reading:

Besides the suggested textbooks, additional study material will be made available on moodle (notes, exercises, relevant scientific articles and reviews). 
Textbooks (and optional supplementary readings) 

Hobson, M.P.; Jaffe, Andrew H., Bayesian methods in cosmologyMichael P. Hobson, Andrew H. Jaffe, Andrew R. Liddle, David Parkinson. Cambridge: Cambridge University Press, 2010.

Sivia, Devinder S.; Skilling, John, Data analysisa Bayesian tutorialD. S. Sivia with J. Skilling. Oxford: O xford University press, 2006.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Case study
 Interactive lecturing
 Working in group
 Questioning
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
Sustainable Development Goals (SDGs)

