Management Engineering

The course is basically divided into three parts, each corresponding to about 30 hours of frontal teaching. 1) Descriptive statistics. - Histogram, sample distribution. Characteristics of the first and second-order: mean value, mode, median, standard deviation variance. Characteristics of the III and IV order: skewness, Kurtosis. Rules for plotting a histogram; - Review of probability calculus: mean and variance of affine transformation of a random variable; vector case; - Percentages of a distribution. Box Plot; - Gaussian distribution. Chi2 distribution. T-Student distribution. Fisher distribution. Central limit theorem; - Statistical tests: type 1 and 2 error; more powerful epsilon level test, and uniformly more powerful test. Neyman-Pearson lemma. Q-Q chart. Pearson test. Kolmogorov-Smirnov test. Anderson-Darling test. 2) Inferential statistics. - Point estimate, interval estimate, comparisons between statistics. - Simple and non-independent random sample. Sample estimate of the mean value and the variance of the population, variance of the estimates in the two cases. Gaussian case, cases of asymmetry, fat-tailed distribution; - Confidence interval. Statistical quality control, fault detection; - Comparison test between two groups: between proportions, between means, between variances; - Comparison test between several groups: Bartlett's test, Levene's test; - Analysis of variance (ANOVA). 1-way, two-way Pearson test. Kruskal-Wallis test. Welch Anova; - Outline of non-parametric tests; - Experiment plan. Stratified sampling. 3) Identification of Models. 3.1) Linear regression model. Models of description, models of prediction. Meaning of the linear regression model; - Model parameters: offset, sensitivity, partial correlation; - Estimation of parameters: the normal system of equations. R-square test: variance explained, residual variance; - Data preprocessing: standardization, equalization. Outline PCA, - Complexity of the model: Akaike criterion. Significance of the parameters; - Confidence interval of the regression model. 3.2) Parametric estimation. Introduction, general notions. - Estimates properties: distortion, efficiency. Consistency of the estimate; - Estimation of least squares (LSE): linear model with additive error. Necessary and sufficient conditions of optimum. Properties of model estimation and validation (R2). Weighted least squares estimate; - Outline Maximum likelihood estimation (MLE), and Bayesian estimation; - Estimation of time-varying parameters. Least squares with exponential weights, recursive algorithm. 3.3) Models of historical series. Additive analysis, multiplicative analysis: Decomposition in trend, seasonality, residual. - Trend: global, parametric, and non-parametric models (polynomial model with constant parameters, Prescott-Hodrick filter); local, parametric, and non-parametric models (polynomial model with time-varying parameters, simple moving average, SMA, exponential moving average, EMA). - Seasonality: use of the correlation function, method of estimating the seasonal component; - Residual component: AR, MA, ARMA models, optimal predictor. Model identification: parametric estimation and validation (whiteness test).

The following are indispensable prerequisites: 1) Some basic notions of linear algebra, such as: - linear space, vectors, and linear operations between vectors; - linear dependence and independence between vectors; - matrices and operations between matrices; - rank of a matrix; - determinant of a square matrix; - computation of the inverse of a square matrix; - characteristic polynomial of square matrices; - eigenvalues ​​and eigenvectors of a square matrix - systems of equations. 2) - some basic notions of analytical geometry, such as: - lines and planes in Cartesian space; 3) some basic notions of analysis, such as: - successions and functions; - series of sequences; - concept of limit, continuity of a function and its differentiability; - derivatives and integrals of functions; - maxima and minima of a function; - elements of mathematical programming. 4) Notions of Probability and Statistics, such as: - events and probability of events; - distribution of probability and random variables; - moments of a random variable;

- Lecture notes by the teacher and collection of exam themes. - http://www.itl.nist.gov/div898/handbook/ - http://stattrek.com/

The teaching includes frontal teaching as the main method. The lessons are all problem-oriented in the sense that the importance and significance of the lesson it is stimulated in the student by presenting real case studies and guiding him towards the solution of the problem first through heuristics, drawing on his own intuition, and therefore highlighting the need to have reliable statistical methods of evaluation which, starting from subjective heuristics, develop objective decisional techniques that make the results sharable. In this context, it can be said that the course is practically a reasoned succession of exercises in various economic-managerial fields which determine the application support in which the notions of the theory are triggered. An integral and highly formative part of the course is the weekly receptions in which the learners, spontaneously gathered in small working groups, discuss with the teacher the solutions they propose on the topics of a large and varied collection of exam sessions on an arch time of about 15 years. In the COVID emergency, remote lessons were carried out via the ZOOM platform.

Classes attendance is not mandatory

The elements taken into consideration for the purposes of the assessment are the acquisition by the student of the basic tools introduced in the course and the ability to reason and of using these tools to solve specific problems. The evaluation of the actual learning by the student takes place only through a compulsory written test. The written test is semi-structured, with a closed stimulus and an open answer. It consists of 4 or 5 real case studies taken from the web, in different areas of knowledge. Each theme is decomposed into subproblems for each of which a score is assigned. The vote on each sub-problem depends on the quality and effectiveness of the proposed solution and the correctness of the calculations. The mark for each problem is obtained as the sum of the marks obtained on its subproblems; the sum of the marks on all the case studies of the paper determines the final grade.

Frontal and distance teaching with classes video recording