# 77093 - Environmental Statistics

## Learning outcomes

By the end of the course, the student has gained basic knowledge about the role of statistical methods for analysing environmental phenomena, mainly from a spatial perspective. The student is led through the fundamentals of the three branches of spatial statistics: areal, geostatistical and point process data are considered, from both a descriptive and modelling point of view. The student is able to apply the statistical methods by using specific R packages.

## Course contents

Analysis of areal data

Global measures of  spatial association. Local Indicators of Spatial Association (LISA). Hypothesis testing for global and local spatial association. Spatial linear regression. Spatial smoothing of mortality rates.

Analysis of geostatistical data

Geostatistics: descriptive measures of spatial dependence, spatial random fields, moments of a spatial random field, variogram, covariogram, kriging.

Analysis of point process data

Introduction to point processes. Descriptive measures for point patterns. Tests for complete spatial randomness and interpoint interaction. Homogeneous Poisson models. Inhomogeneous Poisson models. Point process models evaluation.

Bivand R.S., Pebesma E., Gómez-Rubio V. (2013) Applied Spatial Data Analysis with R. Springer.

Diggle P.J. (2014) Statistical Analysis of Spatial and Spatio-Temporal Point Patterns. Third Edition

## Teaching methods

Lectures and tutorials with the R software in the computer lab

## Assessment methods

The final exam aims at evaluating the achievement of the following educational targets:

- deep knowledge of the topics covered along the course

- ability to analyse spatial data

- ability to implement statistical methods suited for spatial analysis in R.

The exam consists of a test in the computer lab, which lasts 2 hours. The student has to answer some theoretical questions on a paper sheet, and some practical questions using the R software. At the end of the exam, both the paper sheet and an R script must be delivered for evaluation. Optionally, an oral exam can also be taken after the written exam, where the student might increase or decrease her/his grade.

## Office hours

See the website of Fedele Pasquale Greco

See the website of Linda Altieri