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Advanced Topics of Statistics

Objectives

The objective of Advanced Topics in Statistics is to provide students with the most current knowledge of these areas in development. By the end of the CU students must know: the principles of Bayesian inference and apply them (exact, numeric and simulated methods); hierarchical modelling; estimation and predicting methods for the various types of spatial data; to choose from a set of alternatives with consequences an action according to some optimality criterium.

General characterization

Code

12991

Credits

9.0

Responsible teacher

Isabel Cristina Maciel Natário

Hours

Weekly - 4

Total - 140

Teaching language

Português

Prerequisites

Available soon

Bibliography

- Turkman MAA, Paulino CD, Müller P (2019). Computational Bayesian Statistics, An Introduction. Cambridge UP
- Bernardo JM, Smith AFM (1994). Bayesian theory. Wiley
- Gelman A, Carlin JB, Stern HB, Dunson DB, Vehtari A, Rubin DB (2013). Bayesian Data Analysis, 3rd Edition. CRC Press
- Blangiardo M, Cameletti M (2013). Bayesian Spatio and Spatio-Temporal Models with R-INLA. Wiley
- Carvalho ML, Natário I (2008). Análise de Dados Espaciais. INE
- Cressie N, Wikle CK (2011). Statistics for Spatio-Temporal Data. Wiley
- Gelfand AE, Diggle PJ, Fuentes M, Guttorp P, Eds (2010). Handbook of Spatial Statistics. CRC Press
- Berger J. (1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag
- DeGroot MH (2004). Optimal Statistical Decisions - 2nd edition. Wiley
- Pratt JW, Raiffa R, Schlaifer R (1995). Introduction to Statistical Decision Theory. MIT Press

Teaching method

 Lecture-lab classes are the adequate way to convey the course contents to students as, together with the explanation of the main concepts and results, illustrative examples are given, being students supposed to take active part in their resolution. Consequently, students acquire the basic expertise not only of the adequate implementation of the methodologies learned in each concrete situation but may also contact with different relevant statistic software.

Evaluation method

The evaluation consists on the resolution of three assignments with written reports, that may be presented and discussed by the students in classroom.

Subject matter

• Bayesian Statistics: Foundations. Prior and posterior distributions. Bayesian inference. Bayesian computation - simulation and approximation methods. Bayesian modelling - generalized linear models, hierarchical models, model evaluation and comparison.
• Spatial statistics: Geostatistics - stationary gaussian model and extensions, parametric estimation, kriging; covariance and variogram functions, families of covariance functions; Point processes - exploratory and empirical analyses and pattern modelling, complete spatial randomness hypothesis, stationarity and isotropy, point and marked point processes, homogeneous and non-homogeneous Poisson processes, Cox process; Areal models: spatial
association measures, spatial independence tests, smoothing, Markov Gaussian random fields, auto-regressive models.
• Decision theory: basic concepts; utility and loss; Bayesian decision theory; minimax analysis; sequential decisions.