Lectures from a course for graduate students in astronomy at UBC, Sep-Nov 2013

All lectures copyright J V Wall. Please contact JVW (jvw@phas.ubc.ca) to use all or part.

Click on each LECTURE LABEL to download:

1. DECISION - the nature of science - deciding - what is or are statistics? Why?

2. PROBABILITY - what is it and why we need it - conditionality and independence - Bayes' Theorem - priors - posterior distribution

3. PROBABILITY DISTRIBUTIONS - what they are and how defined - quantifiers - Binomial and Poisson - Central Limit Theorem - Gaussian - Power-Law

4. RANDOM NUMBER TOOLBOX - why generate pseudo-random numbers - pitfalls - random numbers from a given distribution - toy universe - sorting and indexing

5. STATISTICS AND EXPECTATIONS - nature of statistics - Bayesian contrast - expectation values - error propagation - order statistics

6. CORRELATION - why? - pitfalls - standard model - bivariate randoms - Bayesian+classical (param/non-param) testing - DIY testing

7. PARTIAL CORRELATION AND PRINCIPAL COMPONENT ANALYSIS - bootstrap and jackknife - partial correlation - bivariate Gaussian again - PCA - geometric and matrix approaches - examples

8. HYPOTHESIS TESTING - rejection/elimination - classical testing / Neyman-Pearson - tests for means and variances (classical/Bayesian) - non-Gaussian parametric testing - model choice / Bayes Factor

9. HYPOTHESIS TESTING THE NON-PARAMETRIC WAY - power and Type 1 error rate - the basis of non-parametric (classical) tests - chi-square test - Fisher exact probability test - Kolmogorov-Smirnov test - runs test - U test - summary tables of tests

10. DATA MODELLING / PARAMETER ESTIMATION - framework, concept, formalism - maximum likelihood - least-squares - regression analysis - linear models - minimum chi-square

11. DATA MODELLING THE BAYESIAN WAY - concept/framework - Bayesian Likelihood Analysis (BLA) - marginalization - BLA evidence - Bayesian models of models - hierarchical models - hyperparameters

12. MODEL CHOICE - choosing the model - use of Bayesian evidence - model simplicity / `Ockham factor' - avoiding the integrations - emphasis on Bayes factor as a statistic - Akaike and Bayesian information criteria

13. DOING BAYESIAN INTEGRALS - Monte Carlo integration - importance sampling - Metropolis-Hasting algorithm - proposal function - Markov chains - evidence via MCMC computation

14. DETECTION - more on MCMC - meaning of detection - classical approach - Bayesian detection / examples - detection summary

15. MALMQUIST AND EDDINGTON BIAS / LUMINOSITY FUNCTIONS - catalogues and selection effects - Malmquist bias and forced correlations - Eddington bias - luminosity function and V/Vmax - examples

16. SURVEYS - LUMINOSITY FUNCTION LIKELIHOOD, CENSORSHIP AND CONFUSION - likelihood and space density - survival analysis / censored data and examples - censored data and hypothesis testing - the confusion limit - examples

17. SEQUENTIAL DATA / 1D - the multitude of occurrences - data transformations - Fourier analysis and its properties - the Fast Fourier Transform (FFT) - example - redshifts from cross-correlation

18. SEQUENTIAL DATA / 1D CONTINUED - filtering - low-pass - high-pass - coherence function and example

19. SEQUENTIAL DATA / 1D CONTINUED FURTHER - digital correlator - unevenly -sampled data / periodogram - wavelets - detection difficulties and 1/f noise

20. DATA ON A SURFACE - 2D sky projections - measures of distribution - two-point angular correlation function - counts-in-cells - angular power spectrum - Wilkinson Microwave Anisotropy Probe (WMAP) Cosmic Microwave Background (CMB) angular power spectrum

21. REVIEW OF PREVIOUS POINTS and PROBLEMS - more on two-point correlation function - plotting power laws - s/n for an optical telescope - Principle Compenent Analysis results - runs test - Anderson-Darling test

22. THE GREAT GALAXY REDSHIFT SURVEYS - historical understanding of our unviverse at 1990 - the change with SNIa Hubble diagrasm and with CMB fluctuations - how the 2dF galaxy survey was done - 3D correlation function - 2dF and cosmological parameters - how the SDSS galaxy survey was done - baryon acoustic oscillations and significance - summary of 2dF and SDSS accomplishments

23. THE CMB SINCE 1990 / WMAP - finding the CMB in 1965 - COBE and the first fluctuations - BOOMERanG and MAXIMA and the angular power spectrum at last - WMAP and its data reduction, including `removal' of the Galaxy - WMAP angular power spectrum and the tools used to obtain it - from the power spectrum to our 6-parameter `concordance' universe (despite `tension')