21002063-3 - MATHEMATICAL AND STATISTICAL METHODS

The development of a project on an urban scale (masterplan) with particular attention to the themes of the resilience to the climate change and to the relationship between physical and social form. Among the topics discussed: use of space; temporality of movement of the inhabitants; open and built spaces; design of soil and infrastructure; places of social life, of living and working. In addition, they analyze the models of urban development and demographic, land use, traffic, food sustainability, social interactions and urban spaces, the economy and the metabolism of the city.
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Programme

Part 1: Statistical survey and types of data
Types of data: nominal and ordinal. Frequencies and distributions.
Mean, weighted mean, median, rank, range, variance, standard deviation, interquartile range, percentiles. Chebyshev's Theorem.
Dependent and independent variables, chi-square, correlation and covariance, Pearson's coefficient, linear regression model, data fitting.

Part 2: Probability of Events and Probability Distributions
Probability and events. Types of events. Conditional probabilities and independence, Bayes' theorem.
Random variables and probability distributions. Discrete and continuous variables.
Distributions of interest:
Uniform, binomial and Poisson distributions for discrete variables.
Uniform, normal and standardised normal distributions for continuous variables.
Central limit theorem. Sampling. Point and interval estimation.

Part 3: Statistical Inference
Statistical test theory, test for rejection of hypotheses (TRI), p-value, standardised variables. Z-test, T-test and Chi-square test.

Excel exercises: The Excel spreadsheet, importing data, basic functions.
Calculating frequencies for different types of data, histogram. Calculating frequency tables, histograms, distributions, cumulative distributions, averages, medians, percentiles. Conditional frequencies, chi-square, covariance, Pearson's coefficient, linear regression.
Probability exercises.
Analysis and processing of statistical surveys of urban interest.

Core Documentation

The material to be studied will be indicated by the lecturer during the class.
Books:
Statistica – Metodologie per le Scienze economiche e sociali, Simone Borra e Agostino Di Ciaccio. Mc Graw Hill​
Analisi Statistica dei dati biologici; M. Whitlock, D. Schluter. Zanichelli​

Reference Bibliography

R, P. Abelson, Statistics As Principled Argument doi: https://doi.org/10.4324/9781410601155 M. Krzywinski, N. Altman Importance of being uncertain, Nature Methods, 10, 809-810 (2013) doi: https://doi.org/10.1038/nmeth.2613 Navarrete MS. Common statistical misconceptions-plainly explained. Medwave. 2019 Jul 2;19(6):e7660. doi: 10.5867/medwave.2019.06.7660.

Type of delivery of the course

Lectures, exercises