- Docente: Elena Bandini
- Credits: 6
- SSD: MAT/06
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
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from Feb 18, 2025 to May 30, 2025
Learning outcomes
The aim of the course is to give students the basic knowledge of statistics for data-analysis and of statistical elementary methods that can be applied to other mathematical areas. In the end of the course, the student possesses the ability to study the behavior of samples of a random variable and to apply statistical elementary methods to some problems of analysis, number theory and mathematical physics.
Course contents
Statistical models. The exponential family.
Estimators and their properties: consistency, bias, asymptotic normality.
Different methods for finding estimators.
Confidence intervals.
Hypothesis testing.
Other properties of estimators.
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Sufficiency.
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Completeness.
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The Rao-Blackwell and Lehmann-Scheffé theorems.
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The Cramer-Rao theorem.
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Efficiency and Fisher's information.
Properties of maximum likelihood estimators.
The Poisson process: properties and inference.
Elements of Bayesian statistics.
Readings/Bibliography
Lectures notes and sheets of exercises prepared by the teacher (available on virtuale.unibo.it in Italian).
Supplementary textbook:
G. Casella, R.L. Berger. Statistical Inference. Second edition. 2001.
Teaching methods
Lectures and exercises will be alternated in order to explain theoretical concepts through examples.
Lectures are in Italian.
Assessment methods
Oral examination.
Teaching tools
Website of the course available on virtuale.unibo.it, where the student can find: lecture notes, sheets of exercises, as well as other useful material for the course.
Office hours
See the website of Elena Bandini