ASTR 530B Practical Statistics for Astronomers
3 credit
Prereqs: None, beyond meeting the admission requirements for UBC graduate
astronomy programme
Evaluation: Continuous assessment via weekly assignments. Heavy homework.
The course is presented through data-analysis examples, with minimum time
spent on discussion of statistical / probability theory. Bayesian, classical
and non-parametric methods are covered. The goal is for students to obtain
an analytical tool-box for astronomy data.
Unit: Basics - decision and the way science works; how probability and
statistical analysis developed in astronomy; the nature of probability;
probability distributions, with emphasis on those most frequently
encountered in astronomy; statistics versus expectation values.
Unit: Random-number toolbox - how to generate random numbers uniformly
or following a prescribed distribution; simulation of a model via random
numbers; an example of a toy model universe.
Unit: Correlation - the pitfalls; the tests, parametric, non-parametric,
and Bayesian; partial correlation; Principle Component Analysis.
Unit: Hypothesis-testing, data-modelling, and parameter estimation -
use of classical, non-parametric and Bayesian methods; Bayesian model
choice, and Markov-Chain Monte Carlo methods in integration and simulation.
Unit: Detection, sky surveys and luminosity functions - the nature of
detection; Malmquist and Eddington bias; luminosity functions and their
evaluation, including analysis of censored data (survival analysis).
Unit: Astronomical analyses - treatment of 1D data such as spectral
scans; 2D (surface distribution) analysis including 2-point correlation,
counts-in-cells, and power-spectrum analysis; recent astronomy and
cosmology results from statistical analysis, including galaxy clustering
and its cosmic evolution, and derivation of cosmological parameters from
Cosmic Microwave Background data.