Statistical Methods and Applications

GIOVANNA JONA LASINIO

Learning goals
The student at the end of the course should be able to use with knowledge advanced modeling and exploratory techniques specifically developed for spatially dependent data. This is achieved by assigning several homeworks on real data. Practical sessions with the R software are part of each lecture, so to allow students to implement what is taught in the theoretical part. Among the expected results, ability to elaborate environmental data using R software, ability to interpret the results obtained, ability to choose the most suitable statistical models according to the hypotheses they are founded on and to their compatibility with the data available.

Knowledge and understanding
The student will be able to understand the main tools for the analysis of spatial and spatio-temporal data. Also an introductory knowledge of extreme value estimation and modeling will be part of his cultural heritage

Applying knowledge and understanding
Students will be involved in the discussion and analysis of case studies using the open source statistical software R. Students will be asked prepare and discuss a presentation of the results of their homeworks. The presentation will be given on front of the class and discussed.

Making judgements
Through the homeworks and the final presentations discussions, tudente will develop judgements capacity in terms of theoretical choices in representation of real worls phenomena.

Communication skills
Students will be asked prepare and discuss a presentation of the results of their homeworks. The presentation will be given on front of the class and discussed.
This procedure will help the student to develop his/her ability to communicate the results of its work.

Learning skills
One of the aims of the course is to build a statistical glossary and a dictionary of specific statistical concepts that will allow the student to read and understand scientific papers using advanced statistical tools in the analysis of environmental data.

After completing this course, students will be able to:
- map geographic data
- create descriptive spatial statistics
- interpolate continuous spatial processes
- analyze discrete spatial processes
- model extreme event data
- estimate nonhomogenous point processes (spatial point processes)

The students are expected to have a good knowledge of statistical inference. It is suggested to acquire a good knowledge of linear and nonlinear models (generalized additive models) and some basic knowledge on mixed-effects models. It is also recommended to be familiar with the software environment R.

The course addresses the following topics:
Introduction to Spatial Statistic
- Exploratory Data Analysis using R
- Non stochastic approaches to spatial interpolation
Geostatistical Models
- Spatial Interpolation under a stochastic model: mixed effect spatial model
- Estimation in the likelihood paradigm
- Bayesian Estimation (with a brief introduction to general Bayesian statistics)
Computational issues in spatial statistics
- The big N problem and some way to deal with it
Lattice Models
- Spatial glm and automodels

Extreme Value theory
- Generalized extreme value distribution
- Genralized Pareto distribution

Spatio temporal modeling of environmental data: some examples

The evaluation of the acquired skills is done through a series of homeworks that will be assigned during classes and posted on the course web page so that they can be developed by not attending students, and a final report based on the homeworks results.

Slides of the lectures and other teaching material are available online in the DSS elearning web page.
Suggested text books:

- Handbook of Spatial Statistics Editors Alan E. Gelfand, Peter Diggle, Peter Guttorp, Montserrat Fuentes. CRCpress
- Stuart Coles Introduction to Extreme Value theory Springer

A more advanced text books is

Sudipto Banerjee, Bradley P. Carlin, Alan E. Gelfand Hierarchical Modeling and Analysis for Spatial Data, Second Edition CRCpress

- Handbook of Spatial Statistics Editors Alan E. Gelfand, Peter Diggle, Peter Guttorp, Montserrat Fuentes. CRCpress
- Stuart Coles Introduction to Extreme Value theory Springer
- Sudipto Banerjee, Bradley P. Carlin, Alan E. Gelfand Hierarchical Modeling and Analysis for Spatial Data, Second Edition CRCpress

The class will be developed according to University and government direction. it is not the choice of the teacher.
Every lecture is organized in a theoretical part and a practical one on real data.
First week:
Introduction to Spatial Statistic
- Exploratory Data Analysis using R
- Non-stochastic approaches to spatial interpolation
Month of October:
Geostatistical Models
- Spatial Interpolation under a stochastic model: mixed effect spatial model
- Estimation in the likelihood paradigm
- Bayesian Estimation (with a brief introduction to general Bayesian statistics)
Computational issues in spatial statistics
- The big N problem and some way to deal with it

Month of November
Lattice Models
- Spatial glm and automodels

Extreme Value theory
- Generalized extreme value distribution
- Genralized Pareto distribution
Month of december
Spatiotemporal modeling of environmental data: some examples

Students can physically attend class or not as per their availability, attendance is suggested because there are many activities of general use in the classroom. All the information is available on the teacher's dashboard.
Lectures recordings are available.

The final score is computed on the basis of returned homework and a report (individual and in English) summarizing the elaborations developed in the homeworks.

No oral exam is required

• Spatial Statistics
  • Books: Slides of the lectures and other teaching material are available online in the  elearning web page.Handbook of Spatial Statistics Editors Alan E. Gelfand, Peter Diggle, Peter Guttorp, Montserrat Fuentes. CRCpress


• Advanced Spatial Statistics
  • Books: Sudipto Banerjee, Bradley P. Carlin, Alan E. Gelfand Hierarchical Modeling and Analysis for Spatial Data, Second Edition


• Exyreme value theory
  • Books: Stuart Coles Introduction to Extreme Value theory Springer