STATISTICAL MODELS

Second cycle degree in STATISTICAL SCIENCES

Campus: PADOVA

Language: English

Teaching period: Second Semester

Lecturer: LUISA BISAGLIA

Number of ECTS credits allocated: 9


Syllabus
Prerequisites: First year Unipd Master of Statistics courses,
especially Calcolo delle probabilità, Statistica
progredito
Examination methods: A written exam for each parts of the course.
Each exam will be marked independently by the corresponding instructor.
At the end of the course, students will receive a final mark based on all 3 exams results.
Course unit contents: Generalized linear mixed models
o Introduction to the course: basic ideas
o Generalized linear models: structure and inference
o Extending GLMs: First instances of models for hierarchical data
o Generalized linear mixed models
o Introduction to hierarchical models and to GLMMs
o Likelihood inference in GLMMs
o Bayesian Hierarchical Models
o Practical sessions with R and R-Bugs

Time series analysis
o Introduction. Linear time series models.
o Linear time series models: model specification.
o Linear time series models: parameter estimation and forecasting.
o Introduction to spectral analysis
o Nonlinear models: an introduction
o Nonlinear models: Markov-Switching Models and Threshold Autoregression Models
o Long-memory models. Integer AutoRegressive models

Spatial statistics
1. Introduction to spatial statistics:
2. Estimation and modeling of spatial correlations:
3. Prediction and Interpolation (kriging):
4. Spatio-temporal modeling:
5. Second order spatial models for network data:
6. Gibbs-Markov random fields on networks:
7. Simulation and estimation of a Markov random field on a network:
8. Hierarchical spatial models and Bayesian statistics: