Basics

Detector & statistics in a nutshell

1. Statistical data analysis in a nutshell
   
2. Probability
   One of the central concepts of statistical data analysis is probability. Probability is either interpreted as limiting relative frequency: This definition is the basis of so-called frequentist or classical statistics and assumes that an experiment is at least in principle repeatable.
   Or it is interpreted in a more general sense as the degree of belief (subjective or Bayesian probability).
   Ex. 1: P(Morgen geht die Sonne auf) = 1
   Ex. 2: is understood as the (a-posteriori) probability that a certain theory is true after having measured a certain set of data. According to Bayes theorem it is given by the (a-priori) probability (degree of believe) that the theory is true times the (conditional) probability to observe this set of data if the theory is indeed true.
   In the following we will make use only of classical statistics if not stated otherwise.
   
   
3. Probability Distributions
   
4. Cumulative Distributions
   
5. Expectation Values
   
6. Functions of random variables
   
7. Specific Probability Distributions
   
8. Parameter Estimation from Data
   
9. Statistical Tests
   
10. Basic detector concepts
    
11. Problems