First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
PHYSICS OF DATA
Course unit
ASTRO-STATISTICS AND COSMOLOGY
SCP8082722, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
PHYSICS OF DATA
SC2443, Degree course structure A.Y. 2018/19, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination ASTRO-STATISTICS AND COSMOLOGY
Website of the academic structure http://physicsofdata.scienze.unipd.it/2019/laurea_magistrale
Department of reference Department of Physics and Astronomy
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge MICHELE LIGUORI FIS/05

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2018 course timetable

Examination board
Examination board not defined

Syllabus
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, Robertson-Walker metric, Friedmann-Robertson-Walker 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. Metropolis-Hastings, 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): Metropolis-Hastings, 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. Cerca nel catalogo
  • Sivia, Devinder S.; Skilling, John, Data analysisa Bayesian tutorialD. S. Sivia with J. Skilling. Oxford: O xford University press, 2006. Cerca nel catalogo

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, ...)

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