Sciences and Teaching of Natural Systems

FEDERICO MARINI
FEDERICO MARINI

Chemometrics is the branch of chemistry that uses mathematics and statistics to extract useful information from experimental data.

Students will acquire knowledge of the main data analysis techniques, in particular of multivariate data, produced in the chemical field and will be able to perform a rational design of experiments, an exploratory analysis of the collected data and the formulation of predictive models. Students will also be able to critically evaluate the results they have obtained, also in light of the definition of a rigorous validation strategy for the results.

There are no particular prerequisites for attending the course

Introduction: What is chemometrics and how it fits within the analytical chemistry disciplines. Recalls of statistics and probability theory: The measurement error as a result of random and systematic contributions.

Statistical inference: from the sample to the population. Parameters characterizing a statistical distribution (mean and standard deviation). The Normal and standardized Normal (Z) statistical distributions. Student's t and Fisher's F distributions and their use. Statistical tests.

Univariate Regression: The need for building a regression model. The least squares method. Calculation of the parameters of the interpolating line (intercept and slope) and of the respective uncertainties. Uncertainty on x and y predictions and confidence bands. Figures of merit to evaluate the regression (R2, RMSE, bias). Residual analysis.

Principal component analysis (PCA): What principal components are and how to calculate them. Importance of the experimental variables in the definition of the principal components. Some criteria to select the appropriate number of principal components. Examples of application of the PCA method. PCA for the identification of anomalous data and outliers.

Multivariate Regression: Direct and Inverse Calibration. The least squares method for multivariate data (multiple linear regression, MLR) in the case of one or more responses. Principal component regression (PCR). PLS regression for one or more responses. Interpretation of multivariate regression models.

Classification: Discriminant classification methods and class-modeling techniques. Linear (LDA) and quadratic (QDA) discriminant analysis. Nonparametric classification: the kNN method. Using abstract variables for classification: the PLS-DA method. Class-modeling techniques: SIMCA.

Validation: The use of predictive multivariate methods and the need for a more accurate estimate of their predictive ability.

Slides of the course.

As a support, the following textbooks are recommended:
Michele Forina, Fondamenta per la Chemiometria, Edizioni SISNIR, Lodi, 2012. Freely downloadable from: http://www.sisnir.org/index.php/edsisnir/10-fondamenti-di-chemiometria
Roberto Todeschini, Introduzione alla chemiometria, EdiSES, Napoli, 1998.
D.L. Massart et. al., Chemometrics. A textbook, Elsevier, Amsterdam, 1988.
F. Marini (ed.), Chemometrics in food chemistry, Elsevier, Oxford, 2013.

The course consists of classroom lectures where the topics will be addressed from the theoretical point of view and through critically discussed application examples.

Course attendance is optional. Students can prepare the exam also only by studying the teaching material provided.

The students will be assessed based on the outcome of an oral examination to check the knowledge of the topics under consideration.

The exam questions will focus on the entire program of the course. In particular, students will be asked to describe the main chemometric models seen during the lessons, with particular attention to the information they can provide and their interpretation.