
Course unit
APPLIED STATISTICAL MODELS
SCP4063831, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
SECSS/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 
Hours of Individual study 
Shifts 
Laboratory 
2.5 
20 
42.5 
No turn 
Lecture 
6.5 
44 
118.5 
No turn 
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 timetoevent data (eventhistory 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 timetoevent 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 timetoevent 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
Rowcolumn designs: latin squares, Grecolatin squares designs.
Module II: models for the analysis of timetoevent data.
Introduction to timetoevent data and their characteristics, fundamental probabilistic functions for the study of such data.
Nonparametric 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 rightcensored data.
Parametric regression models: multiplicative hazard model, accelerated lifetime models. Inference in exponential and Weibull parametric regression models.
Semiparametric 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 secondorder 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. http://users.stat.umn.edu/~gary/book/fcdae.pdf

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.

Peter J. Diggle, Paulo J. Ribeiro J., Modelbased Geostatistics. U.S. New York: Springer, 2007.

Noel Cressie, Statistics for Spatial Data (Revised Edition). : WileyInterscience, 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
Sustainable Development Goals (SDGs)

