First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP4063831, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
SC2094, Degree course structure A.Y. 2014/15, A.Y. 2019/20
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination APPLIED STATISTICAL MODELS
Website of the academic structure
Department of reference Department of Statistical Sciences
E-Learning website
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge GIULIANA CORTESE SECS-S/01
Other lecturers GIORGIO CELANT SECS-S/01

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses SECS-S/02 Statistics for Experimental and Technological Research 9.0

Course unit organization
Period Second semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Laboratory 2.5 20 42.5 No turn
Lecture 6.5 44 118.5 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
4 Commissione a.a.2019/20 01/10/2019 30/09/2020 CORTESE GIULIANA (Presidente)
CELANT GIORGIO (Membro Effettivo)
GRIGOLETTO MATTEO (Membro Effettivo)

Prerequisites: The course considers a previous knowledge about:
Foundation of mathematics, Foundation of probability, Linear algebra, Statistics I, Statistics II, Statistical models I.
Target skills and knowledge: The aim of the course is to provide students with an introduction to the design of experiments and basic schemes. Furthermore, the course aims to introduce students to the basic statistical methods and models for the description and analysis of spatial data and time-to-event data (event-history data), coming from environmental, technological and biomedical phenomena.
Through intensive laboratory work, the course also provides the tools necessary for computer analysis of statistical models and methods for spatial data and time-to-event data, using the statistical software R.

Through the laboratory activities, group work and teaching conferences, the student learns to:
1. choose the appropriate experiment plan and apply the relevant methods;
2. describe the real phenomena in statistical terms and to recognize the type of data involved;
3. identify the most appropriate methodology and statistical models for the analysis of each type of data;
4. recognize the limits and the advantages of each method and model, when applied to the analysed real phenomena;
5. carry out statistical analyses in a critical way and with autonomous judgment, also regarding case studies of current interest.
Examination methods: The exam consists of two parts:
1) a written test on the topics covered in the three modules in which the course is divided, containing both some open questions and exercises to be solved analytically.
2) a practical test in the laboratory, consisting in the analysis of data through the software R, related to the topics covered in modules II and III. The result of the test consists of a summary report of the analyses carried out, the results obtained and the responses to the study objectives, accompanied by the R code that has been used.
Assessment criteria: The evaluation criteria are:
- comprehension and acquisition of the arguments carried out in the course;
- ability to apply the acquired knowledge autonomously and consciously, both analytically and through the use of the R software;
- ability to critically choose methods and models based on the type of information present in the data, and the purposes of the study of a real phenomenon;
- ability to interpret the results of a statistical analysis on time-to-event data and spatial data.
Course unit contents: The course provides some statistical methods and models, with particular attention to their applications in the technological, environmental and biomedical fields. It is developed in three distinct modules as follows:

Module I: experimental design.
Introduction and preliminary remarks: factors, experimental units, replications and observations. Modelling of an experimental result, the nature of factors. How to randomize, mathematical expression of randomization.
Notions of additivity and interaction: case of two factors.
Completely randomized design – analysis of variance with one factor: description and example. Estimates of the model parameters, test of the hypothesis of the equivalence between treatments, level and power of the test.
Complete balanced randomized block designs: pattern and example, the estimates of the pattern parameters, testing of the hypothesis of the equivalence of treatments, testing of the hypothesis of the equivalence of blocks, table of analysis of variance, power and level of the associated with the treatments, efficiency of a block design.
Comparison of a complete randomized design and a complete balanced block design.
Incomplete block designs: definitions, pattern and examples, estimates of pattern parameters, estimable functions, laws of estimators, testing of hypothesis.
Generalized inverse of the c information matrix. Classification of B.I.B.S
Row-column designs: latin squares, Greco-latin squares designs.

Module II: models for the analysis of time-to-event data.
Introduction to time-to-event data and their characteristics, fundamental probabilistic functions for the study of such data.
Non-parametric analysis: estimators of the survival function and of the cumulative hazard function.
Comparison of different survival distributions: logarithmic ranks test for two samples, and for more than two samples. Introduction to alternative tests.
Introduction to the likelihood function for right-censored data.
Parametric regression models: multiplicative hazard model, accelerated lifetime models. Inference in exponential and Weibull parametric regression models.
Semi-parametric regression models. Cox model with proportional hazards and stratified Cox model. Inference based on partial likelihood.
Model adequacy and residual analysis.

Module III: models for the analysis of spatial and environmental data.
Introduction to spatial statistics and geostatistics. Introductory examples of case studies and real data.
Key features of geostatistical data and purpose of inference.
The spatial stochastic process. The second-order stationary process and the inherently stationary process.
The variogram and the spatial correlation. The sample variogram. Estimate and estimator of the theoretical variogram.
Parametric models for the variogram and for the correlation function.
The Gaussian spatial model: inference, estimation of the variogram under the model, analysis of residuals.
The Gaussian spatial model in the presence of measurement errors.
Basics of spatial prediction: simple and ordinary kriging.
Planned learning activities and teaching methods: The course contains lectures (module I: 20 hours, modules II and III: 24 hours) and exercises in the computer room (modules II and III: 20 hours).

Possible activities are planned in itinere with exercises to be solved in a group using the software R. The course may possibly include seminar activities by external experts, aimed at illustrating real cases of applications in technologies and sciences.
Additional notes about suggested reading: Lessons and exercises are based on textbooks. During the course, the slides and the R code used in the laboratories will be made available. In addition, where necessary, additional teaching materials and handouts will be available on the site accessible to students.
Textbooks (and optional supplementary readings)
  • Gary W. Oehlert, A First Course in Design and Analysis of Experiments. --: --, 2010.
  • John P. Klein, Melvin L. Moeschberger, Survival analysis: Tecniques for censored and truncated data.. U.S. New York: Springer - Verlag (2nd edition), 2003.
  • Roger S. Bivand, Edzer J. Pebesma, Virgilio Gòmez- Rubio, Applied Spatial Data Analysis with R.. New York: Springer, 2008. Cerca nel catalogo
  • Peter J. Diggle, Paulo J. Ribeiro J., Model-based Geostatistics. U.S. New York: Springer, 2007.
  • Noel Cressie, Statistics for Spatial Data (Revised Edition). --: Wiley-Interscience, 2015.

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Problem based learning
  • Case study
  • Questioning
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Latex
  • Statistical software R

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