28174 - Inference

Learning outcomes

By the end of the course the student should know the basic theory of likelihood-based and Bayesian statistical inference. In particular the student should be able: - to derive maximum likelihood and Bayesian estimators and their properties - to derive interval estimates - to test statistical hypotheses according to Neyman and Pearson’s approach and the GLR criterion.

Course contents

Introduction to the statistical inference.The Likelihood function. Sufficient statistics.

Estimation theory.

Moments and maximum likelihood estimation method. Point estimation: finite and asymptotic properties of estimators. Interval estimation: the pivotal quantity method and asymptotical confidence intervals.

Hypothesis testing.

Neyman-Pearson theory. Null hypothesis and alternative hypothesis; Type I and Type II errors; power of a test. Rejection Region. Simple hypothesis and composite hypothesis. Simple null and alternative hypothesis: Neyman-Pearson's lemma. Generalized Likelihood Ratio Test.

Bayesian inference.

Subjective approach to probability. Bayesian estimation. Loss function appraoch. Conjugate prior distributions.

 

Readings/Bibliography

Larsen R.J. and Marx M.L. "An introduction to mathematical statistics and its applications", Prentice Hall, 2012.

Azzalini A. "Statistical infernece based on the likelihood", Chapman & Hall/CRC, 2002.

Hoff P.D. "A First Course in Bayesian Statistical Methods", Springer, 2009.

Teaching methods

Lectures and tutorials

Assessment methods

The exam consists of a mandatory written exam (lasting two hours).

The exam paper consists of questions concerning the theoretical parts of the course and exercises aiming at evaluating if the students are able to solve statistical inference problems. The final grade is given by the sum of the partial grades obtained in each exercise and is expressed out of thirty.

During the exam the use of textbooks, notes and computers tools are not allowed.

Teaching tools

Slides available at https://virtuale.unibo.it

 

All students who attend the planned practical activities in computer lab must also attend the Modules 1 (General training) and 2 (Specific training) of an online course for training on Health and Safety in study and research areas (https://www.unibo.it/en/services-and-opportunities/health-and-assistance/health-and-safety/online-course-on-health-and-safety-in-study-and-internship-areas ). Please note that such modules are compulsory for all students who are involved in any activities which take place in IT laboratories and other work places that present specific risks.

Office hours

See the website of Silvia Cagnone