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Course name
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Error
Analysis and statistical methods in physics
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code
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FIZ633
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credit
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Hour/week
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semester
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spring
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3
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3
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-
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Lecturer
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Assoc. Prof. Kerem Cankoçak
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Course Description
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This course
is primarily addressed to physicists and other scientists
and
engineers
who need to evaluate uncertainty in measurement.
After
a short introduction to the probability theory, the course
will focus on the error analysis, hypothesis testing and
the
comparison
of the frequentalist and Bayesian approach. Data simulation
techniques will be examined as well.
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Course Objectives
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1-) To
calculate uncertainties, mean and standard deviation and
errors in measurements
2-) To
introduce probability, Bayes theorem, mode,
variance,confidence and statistics
3-) To
analyze common probability distributions, such as binomial,
Poisson, Gaussian, chi-squared
4-) To
understand error analysis, instrumental and statistical
uncertainties; propagation of errors
5-)
To
learn least square method, minimization techniques,
parameter estimation, statistical tests, hypothesis
testing, Monte Carlo
method
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Course Learning Outcomes
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I.
Uncertainties and erros in measurements, mean and
standard deviation of distributions
II.
Probability theory, distribution functions, Bayes'
theorem
III.
Probability
distributions; Common distributions (binomial, Poisson,
Gaussian, chi-squared)
IV
Error analysis: instrumental and statistical
uncertainties; propagation of errors, specific error
formulas
V.
Least square method, probability tests, Data simulation
techniques, Monte Carlo method
VI.
Parameter estimation, minimization techniques, hypothesis
testing, Student's "t" and chi-squared test
VII.
Statistical tests, error propagation, statistical vs
systematic uncertainty
VIII
Advanced parameter estimation: maximum likelihood
IX.
Comparison of Bayesian/non-Bayesian methods
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Weekly schedule
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Uncertainties in Measurements, measuring errors,
parent and sample distributions, mean and standard
deviation of distributions
Introduction to probability, Definitions:
probability, distribution functions, density functions,
Expectation values, mean, mode, variance, covariance;
Confidence and statistics, Bayes' theorem
Probability distributions; Common distributions:
binomial, Poisson, Gaussian, chi-squared
Error analysis: instrumental and statistical
uncertainties; propagation of errors, specific error
formulas
Estimates of mean and errors; least square method,
statistical fluctuations, probability tests
Data simulation techniques; Random variables and
probability densities; The Monte Carlo method; random
numbers from probability distributions
Introduction to parameter estimation: least squares
minimization ;
Linear and non-linear minimization
Least square fit to an arbitrary function
Hypothesis testing: Student's "t" test,
chi-squared test, trials factor
Statistical tests: general concepts, error
propagation, statistical vs systematic uncertainty
Confidence intervals: definitions, estimation, the
role of assumptions
Advanced parameter estimation: maximum likelihood,
robust
estimators
Examples of Bayesian approach
Comparison of Bayesian/non-Bayesian methods; Monte
Carlo tests
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Course literature
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Data Reduction and Error Analysis for the Physical Sciences,
Philip Bevington, D. Keith Robinson, Mc Graw Hill, 2003
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Statistical Data Analysis, Glen Cowan , Oxford 1998
Giulio D'Agostini,"Bayesian Reasoning in Data Analysis",World Scientific, 2003
Christian Walck, “Hand-Book on Statistical Distributions For
Experimentalists”, SUF-PFY/96-01,2007
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