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Subjective probability and Bayes'
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Bayesian Reasoning in High
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Approximate methods
Contents
``Bayesian primer''
- slightly reviewed version of the 1995 DESY/Rome report -
Subsections
Subjective probability and Bayes' theorem
Orig inal abstract of the ``primer''
Introduction to the ``primer''
Probability
What is probability?
Subjective definition of probability
Rules of probability
Subjective probability and ``objective'' description of the physical world
Conditional probability and Bayes' theorem
Dependence of the probability on the state of information
Conditional probability
Bayes' theorem
Conventional use of Bayes' theorem
Bayesian statistics: learning by experience
Hypothesis test (discrete case)
Choice of the initial probabilities (discrete case)
General criteria
Insufficient reason and maximum entropy
Distributions (a concise reminder)
Random variables
Discrete variables
Continuous variables: probability and density function
Distribution of several random variables
Central limit theorem
Terms and role
Distribution of a sample average
Normal approximation of the binomial and of the Poisson distribution
Normal distribution of measurement errors
Caution
Bayesian inference applied to measurements
Measurement errors and measurement uncertainty
Statistical inference
Bayesian inference
Bayesian inference and maximum likelihood
The dog, the hunter and the biased Bayesian estimators
Choice of the initial probability density function
Difference with respect to the discrete case
Bertrand paradox and angels' sex
Normally distributed observables
Final distribution, prevision and credibility intervals of the true value
Combination of several measurements
Measurements close to the edge of the physical region
Counting experiments
Binomially distributed observables
Poisson distributed quantities
Uncertainty due to systematic errors of unknown size
Example: uncertainty of the instrument scale offset
Correction for known systematic errors
Measuring two quantities with the same instrument having an uncertainty of the scale offset
Indirect calibration
Counting measurements in the presence of background
Bypassing the Bayes' theorem for routine applications
Approximate methods
Linearization
BIPM and ISO recommendations
Evaluation of type B uncertainties
Examples of type B uncertainties
Caveat concerning the blind use of approximate methods
Indirect measurements
Covariance matrix of experimental results
Building the covariance matrix of experimental data
Offset uncertainty
Normalization uncertainty
General case
Use and misuse of the covariance matrix to fit correlated data
Best estimate of the true value from two correlated values.
Offset uncertainty
Normalization uncertainty
Peelle's Pertinent Puzzle
Bayesian unfolding
Problem and typical solutions
Bayes' theorem stated in terms of causes and effects
Unfolding an experimental distribution
Giulio D'Agostini 2003-05-15
