Academic year 2015/2016
- Course ID
- Teaching staff
- Prof. Stefano Favaro
- 1st year
- Teaching period
- First semester
- D.M. 270 TAF C - Related or integrative
- Course disciplinary sector (SSD)
- SECS-S/01 - statistica
- Class Lecture
- Type of examination
- Mathematical, probabilistic and statistical tools acquired in the three-year undergraduate program. A detailed list of the required backgroud will be provided during the first lecture.
Sommario del corso
Ability to apply statistical concepts and statistical techniques, from a classical and Bayesian perspective, with respect to the point estimation, hyphotesis testing and confidence sets.
Results of learning outcomes
Knowledge and understanding
Advances knowledge of statistical modeling via point estimation, hypothesis testing and confidence intervals.
Applying knowledge and understanding
Ability to convert various problems of practical interest into statistical models and make inference on it.
Students will be able to discern the different aspects of statistical modeling.
Students will properly use statistical and probabilistic language arising from the classical statistics.
The skills acquired will give students the opportunity of improving and deepening their knowledge of the different aspects of statistical modeling.
Main lectures are devoted to the theorerical aspects of statistical inference from the classical and the Bayesian perspective. Exercises will be assigned during these lectures. Lecture devoted to exercises are included in the course.
Learning assessment methods
The exam consists of two parts: the first part is a formal discussion of one of the main topics of statistical infence; the second part consists of two exercises, typically with more than two questions.
ProgramClassical Statistics• Random samples and their distributions, the statistical model, the likelihood function, exponential families.• Sufficient statistics and minimal sufficient statistics, finite properties for estimators, asymptotic properties for estimators, methods for evaluatingestimators.• Methods for constructing point estimators: method of moments and generalizations, method of the least square errors, method of maximumlikelihood, methods of minimum distance.• Hypothesis testing: probabilistic structure of hypothesis testing, Neyman-Pearson lemma, likelihood ration tests, asymptotic tests, confidence sets.Bayesian statsitics• exchangeability, de Finetti’s representation theorem• prior and posterior distributions• conjugate priors• the Gaussian model
Suggested readings and bibliography
Casella, G. and Berger, R.L. (2001). Statistical inference. Duxbury Press
Hoff, P.D. (2009). A first course in Bayesian statistical methods. Springer Texts in Statistics
Days Time Classroom