Course detail

Empiric Models

FSI-9EMMAcad. year: 2023/2024

If the important variables for a process are known or sought but the process model is unknown, an empirical approach to model building is required. The development of empirical models represents a continuous process that involves postulation of a model, experimentation to collect empirical data, "fitting" of the model, i.e. estimation of the model coefficients, and evaluation of results. The strategy of empirical model building is described in the course.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

Ing. Josef Bednář, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Populations, samples, binomial and Poisson distributions, distributions of averages, distributions of a continuous probability, testing of hypothesis

Rules for evaluation and completion of the course

Oral exam

Aims

If the important variables for a process are known or sought but the process model is unknown, an empirical approach to model building is required. The development of empirical models represents a continuous process that involves postulation of a model, experimentation to collect empirical data, "fitting" of the model, i.e. estimation of the model coefficients, and evaluation of results. The strategy of empirical model building is described in the course.
Empiric model, fitting, residuum, adequate model

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

B. Maroš: Empirické modely I, Brno, 1989
D. M. Himmelblau: Process Analysis by Statistical Methods. John Wiley&Sons,New York 1969
K. Zvára: Regresní analýza. Academia, Praha 1989
Vícerozměrné statistické metody: Vícerozměrné statistické metody. SNTL/ALFA, Praha 1987

Recommended reading

B. Maroš: Empirické modely I. PC-DIR, Brno 1998
J. Anděl_: Matematická statistika. SNTL/ALFA, Praha 1978
K. Zvára: Vícerozměrné statistické metody. SNTL/ALFA, Praha 1987

Classification of course in study plans

  • Programme D-APM-P Doctoral 1 year of study, winter semester, recommended course
  • Programme D-KPI-P Doctoral 1 year of study, winter semester, recommended course
  • Programme D-APM-K Doctoral 1 year of study, winter semester, recommended course
  • Programme D-KPI-K Doctoral 1 year of study, winter semester, recommended course

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

Ing. Josef Bednář, Ph.D.

Syllabus

1. Linear models. Linearization of the nonlinear model.
2. Linear models with one independent variable. Least squares estimation.
3. Analysis of variance. Variances of parameters.
4. Variances of predicted values.
5. ANOVA about the adequate model.
6. Confidence intervals for parameters.
7. Locus of confidence limits.
8. Locus of tolerance limits.
9. Confidence region.
10.Linear models with several independent variables.
11.Reziduals.