C6780 Fyzikálně organická chemometrie

Přírodovědecká fakulta
jaro 2006
Rozsah
2/0/0. 2 kr. (příf plus uk plus > 4). Doporučované ukončení: zk. Jiná možná ukončení: k.
Vyučující
prof. RNDr. Miroslav Holík, CSc. (přednášející)
Garance
prof. RNDr. Miroslav Holík, CSc.
Ústav chemie – Chemická sekce – Přírodovědecká fakulta
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
předmět má 25 mateřských oborů, zobrazit
Cíle předmětu
Introduction to probability and statistics, random sampling, point and interval estimates, outlier detection, statistical hypotheses. Matrix calculations in chemistry, matrix decomposition by SVD, PCA, PLS methods. Correlation and regression, correlation coefficients (single, multiple, partial), multivariable regression, multicollinearity, non-linear regression (relaxation, derivative and simplex methods), weighted least squares, confluential analysis. Design and optimization of experiments, analysis of variance, Plackett-Burman plan. Cluster and discrimination analysis.
Osnova
  • 1. Random sampling, point and interval estimate, tests. Sample and population quantities (mean-average, variance, standard deviation), large and small sets of data, probability distribution and density function (the normal and Student's distributions), degrees of freedom, tests for outliers, null hypothesis, errors of the 1st and 2nd kind. 2. Two random variables and the tests of their similarity. Testing the difference of the means (independent variables and paired, with equal and unequal variances, Euclidean distance, agreement factor, angle between vectors, coefficient of determination, correlation coefficient and its transformations. 3. Linear regression like a proportionality relation Standard deviation of variables and standard error of estimate, standard deviations of regressions parameters, tests for confidence intervals, standard error of prediction, 'hat' matrix and influential points, tests of linearity, analysis of residuals. 4. Analysis of variance - additivity and nonadditivity Single-way, two-ways, and two-ways with interaction variance, experiment planning. 5. Multivariable regression, multicollinearity Bias of estimate due to inproper model, parcial F test, stepwise regression, suppression of multicollinearity (ridge regression). 6. Nonlinear and weighted regression, confluential analysis. Linearization of nonlinear regression, use of weighted regression, orthogonal regression with errors in both variables, nonlinear regressions and conditionality tests. 7. Principal component analysis Pretreatment of data (normalization, standardization). SVD -singular value decomposition; principal component scores and loadings, number of significant principal conpoments, reproduction of data from reduced components and loadings. Factor analysis and other variant methods. 8. SVD in regression and correlation analysis Principal component regression (PCR), suppression of the multicollinearity, transformation matrices, target testing, missing data calculation, methods NIPALS and PLS. 9. Planning and optimization of experiments Multiparameter analysis of variance, metods with repetition and separation into groups, latin and graecolatin squares, faktorial designs, Box-Hunter scheme, Plackett-Burman method. 10. Optimization with simplex, relaxation and derivation methods. Modified and supermodified simplex, weighted and two-site simplex, testing criteria for end of optimization. Single dimension optimization, relaxation methods, derivation metods for optimizing of parameters of nonlinear equations.
Metody hodnocení
Ústní zkouška buď v angličtině nebo v češtině.
Informace učitele
Krosval-Validace kalibrační přímky (učební text ve formátu MS-Word)
Další komentáře
Předmět je vyučován každoročně.
Výuka probíhá každý týden.
Předmět je zařazen také v obdobích jaro 2008 - akreditace, jaro 2000, jaro 2003, jaro 2004, jaro 2005, jaro 2007, jaro 2008.