Bi7490 Introduction to Stochastic Modelling

Faculty of Science
Spring 2008
Extent and Intensity
2/0/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Ladislav Dušek, Ph.D. (lecturer)
RNDr. Jiří Jarkovský, Ph.D. (lecturer)
RNDr. Eva Gelnarová (seminar tutor)
Mgr. Klára Komprdová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ladislav Dušek, Ph.D.
RECETOX – Faculty of Science
Contact Person: prof. RNDr. Ladislav Dušek, Ph.D.
Timetable
Tue 8:00–11:50 Kontaktujte učitele
Prerequisites
Knowledge on basic unidimensional exploratory statistical techniques, analysis of variance, correlation analysis, regression analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Basic mathematical procedures with vectors and matrices, linear equations. Introduction to modelling.
Markov chains.
Leslie matrix.
Simple applications of regression analysis.
Estimation of optimum of environmental parameters.
Logistic regression.
Multivariate linear regression.
Generalized multivariate linear model.
Role of correlation analysis in multivariate regression.
Nonlinear regression.
Introduction to time series analysis.
Application of regression in trend analysis.
Forecasting from time series.
Syllabus
  • Basic mathematical procedures with vectors and matrices, linear equations. Introduction to modelling.
  • Markov chains. Applications in modelling of succession of ecosystem, structure of biological populations.
  • Non - homogeneous Markov chains in ecology. Leslie matrix.
  • Simple applications of regression analysis.
  • Estimation of optimum of environmental parameters. Gaussian curves. Indicator species values.
  • Logistic regression - one- and multivariate model.
  • Multivariate linear regression. The least square method. The maximum likehood method.
  • Generalized multivariate linear model. Analysis of residuals - homoscedacity. Autocorrelation.
  • Role of correlation analysis in multivariate regression. Multicolinearity.
  • Nonlinear regression.
  • Modelling using contingency tables in ecology.
  • Introduction to time series analysis. Autocorrelation. Trend analysis. Non-parametric methods for estimation of trends.
  • Application of regression in trend analysis. Polynomial regression.
  • Box-Jwenkins modelling. Spline methods. Forecasting from time series.
Literature
  • MELOUN, Milan and Jiří MILITKÝ. Statistické zpracování experimentálních dat. [1. vyd.]. Praha: Plus, 1994, 839 s. ISBN 80-85297-56-6. info
  • Statistické zpracování experimentálních dat :v chonometrii, biometrii, ekonometrii a v dalších oborech přírodních , technických a společenských věd. Edited by Milan Meloun. 2. vyd. Praha: East Publishing, 1998, xxi, 839 s. ISBN 80-7219-003-2. info
  • HEBÁK, Petr and Jiří HUSTOPECKÝ. Vícerozměrné statistické metody s aplikacemi. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1987, 452 s. URL info
  • MCCULLAGH, P. and John A. NELDER. Generalized linear models. 2nd ed. London: Chapman & Hall, 1989, xix, 511. ISBN 0412317605. info
  • Cajo J.F. ter Braak, (1996). Unimodal models to relace species to environment. DLO-Agricultural Mathematics Group, Wageningen
  • SOKAL, Robert R. and James F. ROHLF. Biometry :the principles and practice of statistics in biological research. 3rd ed. New York: W.H. Freeman and Company, 1995, xix, 887 s. ISBN 0-7167-2411-1. info
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Teacher's information
http://www.cba.muni.cz/vyuka/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Autumn 2014, Autumn 2015, Autumn 2019, Autumn 2020, autumn 2021.
  • Enrolment Statistics (Spring 2008, recent)
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