Lectures from a course for graduate students in astronomy at UBC, SepNov 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  PowerLaw
4. RANDOM NUMBER TOOLBOX
 why generate pseudorandom 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/nonparam) 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 / NeymanPearson  tests for means and variances (classical/Bayesian)  nonGaussian parametric testing  model choice / Bayes Factor
9. HYPOTHESIS TESTING THE NONPARAMETRIC WAY
 power and Type 1 error rate  the basis of nonparametric (classical) tests  chisquare test  Fisher exact probability test  KolmogorovSmirnov test  runs test  U test  summary tables of tests
10. DATA MODELLING / PARAMETER ESTIMATION
 framework, concept, formalism  maximum likelihood  leastsquares  regression analysis  linear models  minimum chisquare
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  MetropolisHasting 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 crosscorrelation
18. SEQUENTIAL DATA / 1D CONTINUED
 filtering  lowpass  highpass  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  twopoint angular correlation function  countsincells  angular power spectrum  Wilkinson Microwave Anisotropy Probe (WMAP) Cosmic Microwave Background (CMB) angular power spectrum
21. REVIEW OF PREVIOUS POINTS and PROBLEMS
 more on twopoint correlation function  plotting power laws  s/n for an optical telescope  Principle Compenent Analysis results  runs test  AndersonDarling 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 6parameter `concordance' universe (despite `tension')