School on Bayesian Analysis in Physics and Astronomy

Stellenbosch, South Africa, 23-26 November 2013.

Material related to the lectures by Giulio D'Agostini

• Slides and more
  • bayes2013a.pdf
  • bayes2013b.pdf
  • bayes2013c.pdf, with related matter:
    • Slides 17-28 from Lecture 4 of 2005 CERN Academic Training ('uncertainty propagations')
    • Section 8.3 of Ref.[3] ('conjugate priors')
    • beta_distribution.pdf, from Ref.[1] (further details on the Wiki)
    • common_systematics.pdf, from Ref.[1], sects 6.8-6.10
  • Concerning frequentistic confidence levels and confidence intervals (that do not tell us how much we should be confident on something):
    • Chapter 1 of Ref.[1], plus sec. 10.7 there ('Frequentistic coverage')
    • Neyman's recommandation to practitioners ("If you are asked whether you `believe' that c belongs to the confidence interval you must refuse to answer", etc.) can be found in note 61, p.50, of Ref.[4].
    • The ultimate confidence intervals calculator (strictly adhering to Neyman's prescriptions!)
    • For the vitious reasoning leading 'confidence intervals': Ref.[5]
  • Error Vs Uncertainty: → GUM
    • Ref.[1], sects. 1.2-1.3, 8.7-8.8
    • GUM: Guide to the Expression of Uncertainty in Measurement from ISO web site
      [→ fundamental reference document]
    • Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results
  • Asymmetric uncertainties: see Ref.[6]
  • About Jaynes/MaxEnt 'followers':
    • Footnote 43 in Ref.[4]
    • Sec. 5.4.2 in Ref.[1] (the school of thought mentioned there refers to Jaynes and followers).
    • Sec. 10.5.2 in Ref.[1], pp. 222-224.
    • 'Role and meaning of subjective probability: some comments on common misconceptions'
  • About de Finetti's verifiability:
    • Sec. 10.5.2 in Ref.[1], pp. 224-225.
  • About the biased Bayesian estimators and Monte Carlo checks of Bayesian procedures:
    • Sec. 10.6 in Ref.[1].
• Problems
  • texts
  • bare answers
  • detailed solutions (also as ps, since the pdf has got some convertion problems)
   
• References
  1. Bayesian Reasoning in data analysis
  2. Probably a discovery: Bad mathematics means rough scientific communication
  3. Bayesian inference in processing experimental data: principles and basic applications
  4. A defense of Columbo (and of the use of Bayesian inference in forensics): A multilevel introduction to probabilistic reasoning
  5. About the proof of the so called exact classical confidence intervals. Where is the trick?
  6. Asymmetric uncertainties: sources, treatment and possible dangers
  
    → Much more here
   
• An extra reference
  • Daniel Kahneman, Thinking, Fast and Slow,
    an enlighting book about 'priors and reasoning' in everyday life (with insights even in Bayesian reasoning)
  
   

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• Software for the examples of my lectures
  (Not scrictly needed! This info is provided just in the case someone wants to reproduce some of my examples, expecially if he/she comes with the software already installed on laptops.)
   
  • R
    
    • For info, documentation and installation see the R web site
      (to Ubuntu users: sudo apt-get install r-base; then R to execute it)
    • For those who already know Mathlab/Octave: R-and-octave.txt
    • As first sessions you can esecute by cut/paste the commands contained in the following files from my web page dedicated to R (don't care of Italian comments: just execute the commands and in case of doubt use the help, eg. '?rnorm', '?hist', etc )
      • basi.R (simple operations; functions)
      • vettori.R (handling vectors)
      • prob.R (probability functions, with some plotting)
      • plots.R (a bit more on plotting)
      • Animated Metropolis algorithm (recommended introductions: short; long)
    
     
  • Hugin
    
    • Download and install the FREE Hugin Lite
    • tutorials and examples
    • Example discussed in Appendix J of Ref.[4]:
      
      • box_testimony.oobn
    • Particle identification:
      • particle_id.oobn
      • particle_id_comp.oobn
      • particle_id_comp_8.oobn
    
     
  • OpenBUGS
    (Note: in the examples only the Windows version, with GUI, will be used):
    • Download OpenBUGS322setup.exe from the downloads page (local copy, since in the past weeks I experienced instability of the OpenBUGS site) and install it.
      → to Linux users: it runs rather well under the latest versions of Wine: in case of error try to upgrade Wine and it should go.
    • Documentation
    • Particle identification
      • Preliminary tests (no inference!)
        • test_beta.txt (model)
        • mu_id_test.txt (model),  
          mu_id_test_data.txt (data)
        • mu_id_test_uncertain_beam.txt (model),  
          mu_id_test_uncertain_beam_data.txt (data)
      • Particle inference
        • mu_id_1_obs.txt (model),  
          mu_id_1_obs_data.txt
      • Beam composition inference
        • generate_events.R
        • mu_id_N_obs.txt (model)
        • beam_priors.txt (to be loaded as data too)
        • data_pmu0.15_N100.txt
        • data_pmu0.15_N1000.txt
        • data_pmu0.15_N10000.txt
        • data_pmu0.80_N10000.txt
    • Why OpenBUGS?
      • You begin focusing on modelling instead of fooling around with the technical details of MCMC (needed at a certain point).
        
      • The package contains many examples ready to be run, which include the underlying graphical model and detailed explanation, and you might learn probability distribution you never tought about them and that perhaps might be suited to your problem, instead of trying to do everithing with binomial, Poisson and normal distributions that unfortunatly are the only pdf physicists know about.
      • Many tutorials and books available, which include example code. Search e.g. the following key words on http://www.amazon.com:
        • bayesian winbugs
        • bayesian openbugs
        (OpenBUGS is the opensource continuation of WinBUGS, but the underlying ideas are the same)
   

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• Other software
  Note: in this section I just show how I managed to install root and then BAT on a laptop with Ubuntu 12.04 LTS, where I had already installed compilers and cernlib (some preinstallation would be needed in other cases).
  I hope this information would be useful to somebody, but no garantee is given, because installing root might be not that simple, unfortunatly Ubuntu binaries seems unavailable and the instructions at CERN are quite long and discourage non computer experts.
  [11 November 2013]
   
  1. Root
     1. Install packages required to compile root with the required options.
        In my install, only GLS was missing. Then:
           sudo apt-get install libgsl0-dev
     2. Download latest version of root from this site
        (in date 11 November 2013 I downloaded root_v5.34.11.source.tar.gz, so in the following I'll refer to that file).
        → I saved it in /usr/local/src, but you can place alsewhere alse, e.g. in your home directory
        (in the following the dir name will be highlighted so that you can replace with the directory name you choose)
        [note: in my laptop I made this directory writable by 'all' users, which means only me...
        If this is not the case in your computer, you need to 'sudo' the following commands]
     3. Uncompress, configure and compile:
        • tar -xzf root_v5.34.11.source.tar.gz
        • cd root
        • ./configure
          • Resulting message:
            Enabled support for asimage, astiff, builtin_afterimage, builtin_ftgl, builtin_glew, builtin_lzma, cintex, explicitlink, genvector, krb5, ldap, mathmore, memstat, mysql, opengl, python, reflex, shadowpw, shared, ssl, tmva, x11, xft, xml
            → check the presence of mathmore, needed by BAT (and mathmore requires GLS -- see above)
        • make
          [... it takes MUCH time: in my case about 40 minutes on a i7 quad-core with 8GB RAM and solid state disk !!]
     4. Prepare to execute:
        • add the following line
              source /usr/local/src/root/bin/thisroot.sh
          at the end of the following files
              ~/.bashrc       [this is only for you -- that's enough if are the only user]
              /etc/.bashrc    [this is for all users]
        • then
              source ~/.bashrc
          or just open a new bash shell [users of csh should use /usr/local/src/root/bin/thisroot.csh]
     5. Execute:
            root
        [type '.q' to quit]
      
  2. BAT
     1. Download BAT from the BAT web site
        (in date 11 November 2013 I downloaded BAT-0.9.3.tar.gz).
        → which I also saved in /usr/local/src
     2. Uncompress, configure and compile
        • tar -xzf BAT-0.9.3.tar.gz
        • cd BAT-0.9.3
        • ./configure
        • make
        • sudo make install
        OK
     3. Set path:
        • issue the command
               export LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:/usr/local/lib
        • and for future sessions insert the coommand at the end of .bashrc or of /etc/bash.bashrc
     4. Run an example from the ad hoc dir myBAT (in order to leave the original dir untouched)
        • cd
        • mkdir myBAT
        • cd myBAT
        • cp -r /usr/local/src/BAT-0.9.3/examples .
        • cd examples/basic/poisson
        • make
        • ./runPoissonCounting
        • acroread PoissonModel_plots.pdf &
        Wow!!
     5. What else? I will try to learn it during the school