FIZ 629E - fizikte istatistiksel yöntemler ve  hata analizi

Dersin Amaçları

1. Introduction to probability
  -Definitions: probability, distribution functions, density functions
  - Common distributions: binomial, Poisson, Gaussian, chi-squared
   - Expectation values &c: mean, mode, variance, covariance
  - Confidence and statistics
  -Bayes' theorem
2. Data simulation techniques; Random variables and probability
densities; The Monte Carlo method
3. Introduction to parameter estimation: least squares minimization ;
Linear and non-linear minimization. Hypothesis testing: Student's "t"
test, chi-squared test, trials
factor
4. 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
5. Method of least squares, Test statistics, multivariate methods;
Goodness-of-fit tests. Nuisance parameters, systematic uncertainties.
6. Bayesian approach: Subjective probability and Bayes' theorem;
Bayesian inference of continuous quantities
7. Comparison of Bayesian and frequentistic statistics: Counting
experiments
8. Asymmetric uncertainties and nonlinear propagation
9. Examples of Bayesian approach; Biased Bayesian estimators and Monte
Carlo checks of Bayesian procedures
10. Applications of Frequentists, combinatorial and Bayesian
evaluation of probability

Dersin Tanımı

Bu ders esas olarak ölçümdeki belirsizliği ileri düzeyde incelemek isteyen fizikçilere, diğer bilim insanlarına ve mühedislere yöneliktir. Olasılık terorilerine kısa bir giriş yaptıktan sonra derste hata analizine, hipotez testlerine ve frekantalist yaklaşım ile Bayescı yaklaşımların karşılaştırılmasına yoğunlaşılacaktır. Ayrıca veri simülasyon teknikleri de incelenecektir.