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.,
Richard A. Johnson, Dean W. Wichern (2013.), Applied Multivariate Statistical Analysis: Pearson New International Edition, Pearson Higher Ed
George A. F. Seber, Alan J. Lee (2012.), Linear Regression Analysis, John Wiley & Sons
Rik Pintelon, Johan Schoukens (2004.), System Identification, John Wiley & Sons
Irwin Miller, Marylees Miller (2004.), John E. Freund's Mathematical Statistics with Applications, 7th ed., Prentice Hall
Robert V. Hogg, Joseph W. McKean, Allen T. Craig (2013.), Introduction to Mathematical Statistics, 7th ed., Pearson
Theodore W. Anderson (2009.), An Introduction to Multivariate Statistical Analysis, 3rd Ed., John Wiley & Sons
Lennart Ljung (1999.), System Identification, Prentice Hall
Philip Bevington, D. Keith Robinson (2003.), Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill Science Engineering

For students

General

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