The course in Statistical Treatment and Analysis of the Data is intended to review the standard data analysis techniques that should already be known to the student and provide new insight in this discipline by means of a more rigorous treatment of the subject and by a number of examples tailored to specific applications in Experimental Physics.
Statistical Treatment and Analysis of the Data
Prof. T.Del Prete
PROGRAM of the course ( 20 hours total )
A review of undergraduate statistics with examples and enhancements
Discrete Distributions
A review of the Normal distribution
A review of the Binomial distribution
A review of the Poisson distribution
The Poisson distribution Measured by Inefficient Counters
The Compound Poisson distribution
The Multinomial distribution
Continuous Distributions
A review of the c2 distribution
The Gamma distribution
Linearized Approximation and the "Propagation of Errors"
The Least Square Method
The simplest case : a review
The linear model in the General Case
The Gauss-Markoff theorem
Using Orthogonal Polynomials
Normal Regression with Linear Constraints
The General Least Square Fit
Hyphotesis Testing
Examples of hypothesis testing
The Smirnov-Cramer-Von Mises w2 Test
The Kolmogorov-Smirnov Test
The Run Test
Combining different tests
Errors in Hypothesis Testing
The Normality Test
The t ( Student - Gosset ) distribution
The F ( Fisher - Snedecor ) distribution
The Maximum of Likelihood Method
ML in the case of Normal Distributed Variables
The likelihood principle
Confidence Intervals of ML estimates
General Properties of the Estimators
The Cramers-Rao inequality
The Minimum Variance Bound (MVB)
Properties of ML estimators
Confidence Intervals for the Least Square estimates
The least square method when s is known
The least square method when s is unknown
Confidence Intervals
Classical Confidence Intervals
Upper and Lower Limits in Poisson Processes
Upper and Lower Limits in Poisson Processes with Background