Statistical Modeling and Identification

Course Description

The role of statistical modeling and identification in modern science (an example). Descriptive statistics and data visualization (histogram, scatter graph, box plots). Goodness of fit tests. Description and evaluation of statistical properties of an estimate: biasness, efficiency, consistency, sufficiency and completeness (Neyman-Fisher factorization theorem, Rao-Blackwell-Lehmann-Scheffe theorem). Methods for finding the estimate: minimum variance unbiased criterion (MVU estimate), maximum likelihood estimation (ML) and CR lower bound, BLUE, method of moments, Bayesian methods. Departures from assumptions (errors-in-variables, instrumental variables). Comparison and selection of methods. Model evaluation and selection (F-test and normal-plot, Akaike information criterion, Mallows Cp). Regression and correlation. Factor analysis and principal component analysis (PCA; scree plot).

Study Programmes

Postgraduate doctoral study programme

Literature

(.), S. M. Kay: Fundamentals of Statistical Signal Processing, Estimation Theory; Prentice-Hall 1993.,
(.), N. R. Draper, H. Smith: Applied Regression Analysis, 3rd ed., John Wiley & Sons 1998.,
(.), R. A. Johnson, D. W. Wichern: Applied Multivariate Statistical Analysis, 6th ed., Pearson Prentice Hall 2008.,
(.), G. A. F. Seber, A. J. Lee: Linear Regression Analysis, 2nd edition, Wiley 2003.,
(.), R. Pintelon, J. Schoukens: System Identification, A Frequency Domain Approach; IEEE Press 2001.,
(.), I. Miller, M. Miller: John E. Freund's Mathematical Statistics with Applications, 7th ed., Prentice Hall 2004.,
(.), R. V. Hogg, J. W. McKean, A. T. Craig: Introduction to Mathematical Statistics, 6th ed., Prentice Hall 2005.,
(.), T. W. Anderson: An Introduction to Multivariate Statistical Analysis, 3rd Edition, Wiley 2003.,
(.), L. Ljung: System Identification: Theory for the User, 2nd edition, Prentice Hall 1997.,
(.), P. R. Bevington, D. K. Robinson: Data Reduction and Error Analysis for the Physical Sciences, 3rd ed., McGraw Hill 2003.,

General

ID 154763
  Summer semester
6 ECTS
L0 English Level
L1 e-Learning