Spacial statistics and modeling

The goal of this course is to make the students familiar with basic modeling statistica techniques, focusing on regression models and spatial statistics methods. In addition, the application of these methods to Marine Biology will be also encourage. Besides, the students will also learn how to work with a statistical package for data analysis.

The contents of this course are organized in two parts. The first part will be devoted to regression models. The second part concerns spatial statistical methods. Along the different sessions, the statistical software R will be used for data analysis and illustration of the proposed methods. The first session of the course will be an introduction to the R package.

Parte 1. An introduction to R.
1.1 Presentation and installation.
1.2 Data structures: vectors, matrices, lists and dataframes.
1.3 Import/export data.
1.4 Graphical tools.


Part 2. Regression models.
2.1 An introduction to linear regression models: estimation, prediction and inference
2.2 Simple linear regression: estimation, prediction and inference.
2.3 Model diagnosis: outliers and/or influential observations; homocedasticity and normality.
2.4 Other regression models: polynomial regression, linearized models, non linear models and nonparametric regression.
2.5 Multiple linear regression: variable selection, colinearity, randomness and independence.
2.6 Applications in Marine Biology.


Part 3. Spatial statistics
3.1 Basics of spatial statistics. Spatial processes.
3.2 Introduction to geostatistics: stationarity and isotropy.
3.3 Spatial dependence modeling: variography.
3.4 Kriging prediction.
3.5 Aplications in Marine Biology.

BASIC BIBLIOGRAPHY
[1] Bivand, R.S., Pebesma, E.J. and Gómez-Rubio, V. (2008). Applied Spatial Data Analysis with R. Springer.
[2] Diggle, P. and Ribeiro, P.J. (2007) Model-based Geostatistics. Springer.
[3] Schabenberger, O. and Gotway, C.A. (2005) Statistical Methods for Spatial Data Analysis. Chapman and Hall.

COMPLEMENTARY BIBLIOGRAPHY
[1] Chilès, J.P. and P. Delfiner (1999) Geostatistics: modeling spatial uncertainty. Wiley
[2] Cressie, N.A. (1993) Statistics for Spatial Data. John Wiley.

In this course, we will try to enhance the general competencies collected in the report of the Master in Marine Biology: CG1, CG2, CG4, CG5, CG6, CG8, CG9, CG10, CG11, CG12, CG13, CG14, CG15, as well as those specific competencies CEC7, CEC17, CEC18 (knowledge) and CEH4, CEH5,. CEH6, CEH7, CEH8, CEH30, CEH31, CEH32 and CEH46.

Teaching methodology involves on-site and autonomous activities. On-site activities collect lectures, interactive sessions and tutorship hours, as well as the examen and project presentations. As autonomous activities, we include the study time (also reflected in the ECTS score for each session type) and project preparation.

Lectures (1.25 ECTS): during lecture hours, the professors will introduce the main concepts, using presentations. Some standard problems will be also solved, in order to enable the students to work on the exercise assigments. With respect to the course material, apart from the recommended bibliography, the students will also access some handouts prepared by the professors.

Interactive sessions (1.25 ECTS): during interactive sessions, the students will work with the statistical package R, focusing on practical cases in the Marine Biology context. For these sessions, students will have an outline of each practical lab.

Tutorship hours (0.05 ECTS): tutorship hours are devoted to the supervision of the students learning process, as well as to the advisory on the course projects

The assessment of the course will be mainly based on the continued work of the students. This work will entail the solution of exercises and reports and/or presentations. These activities may be carried out individually or in groups.

Individual work is about one hour and a half for each on-site hour (lectures and interactive sessions), with 2.5 ECTS in total. Students will take 0.4 ECTS for preparing the different assignments (individually and in working groups) proposed during the course.

Basic knowledge on probability and statistics are recommended. Students should also be able to read scientific texts in English.

Teaching platforms on the web will be used during the course, as a mean for uploading material.