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1
Uncertainties in Measurements, measuring errors, parent and sample distributions, mean and standard deviation of distributions
2
Introduction to probability, Definitions: probability, distribution functions, density functions, Expectation values, mean, mode, variance, covariance; Confidence and statistics, Bayes' theorem
3
Probability distributions; Common distributions: binomial, Poisson, Gaussian, chi-squared
4
Error analysis: instrumental and statistical uncertainties; propagation of errors, specific error formulas
5
Estimates of mean and errors; least square method, statistical fluctuations, probability tests
6
Data simulation techniques; Random variables and probability
densities; The Monte Carlo method; random numbers from probability distributions
7
Introduction to parameter estimation: least squares minimization ;
Linear and non-linear minimization
8
Least square fit to an arbitrary function
9
Hypothesis testing: Student's "t" test, chi-squared test, trials
factor
10
Statistical tests: general concepts, error propagation, statistical
vs systematic uncertainty
11
Confidence intervals: definitions, estimation, the role of
assumptions
12
Advanced parameter estimation: maximum likelihood, robust
estimators
13
Examples of Bayesian approach
14
Comparison of Bayesian/non-Bayesian methods; Monte Carlo tests |