Lecture 9

26 Novembro 2013, 18:00 • Rui Paulo

The Bayesian approach to statistics. Bayes' theorem as an inferential tool, and the prior to posterior updating process. Properties and examples. Inference within the Bayesian paradigm.

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Lecture 8

19 Novembro 2013, 18:00 • Rui Paulo

UMVU estimators - conclusion.

Mean squared error. Consistency.

Methods of estimation: method of moments and method of maximum likelihood. Properties, including large sample properties. Examples.

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Lecture 7

12 Novembro 2013, 18:00 • Rui Paulo

Fisher information: conclusion.

Parametric point estimation: general considerations, unbiasedness, most efficient estimator, UMVUE (to be continued).

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Lecture 6

5 Novembro 2013, 18:00 • Rui Paulo

Completeness. Sufficient and complete statistics are minimal sufficient, the reciprocal is not valid, Basu's theorem.

The exponential family of distributions. Sufficient and complete statistics in this family.

The likelihood and score functions. Fisher information and its properties under regularity conditions.

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Lecture 5

29 Outubro 2013, 18:00 • Rui Paulo

Sufficiency: definition and the factorization criterion.

Statistics and induced partition. Minimal sufficient statistics; the Lehmann-Scheffe theorem.

Ancillary statistics. The location-scale family of distributions and ancillarity in the context of this family.

Minimal sufficient and ancillary statistics are not always independent.

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