Statistical Decision Theory

Course objectives

Learning goals Introduction to problems and methods of Statistical decision theory and to its main approaches (Bayesian and frequentist). Students acquire the ability: - to formalize statistical problems as decision problems, - to compare different solutions - to apply decisional methods to real data Knowledge and understanding knowledge and understanding of: - general decision problems - statistical problems as decision problems - different approaches to statistical decision problems (Bayesian and frequentist) Applying knowledge and understanding At the end of the course students are able to: - formalize statistical problems as decision problems - apply and compare different decisional method to the most important models - apply decision theory to new models - interpret the results of their analysis Making judgements Students develop judgement skills by: - applying and comparing different decisional methods to a wide range of statistical models - interpreting the results from the use of alternative decision methods on real data Communication skills Students develop communication skills by: - solving and presenting problems in written and oral form - group activity Learning skills The comparative-analytical methodology used in the course provides students with a learning capacity that is an important basis to approach following courses in the statistical area of the master program and of more advanced programs (PhD in Statistics)."

Channel 1
FULVIO DE SANTIS Lecturers' profile

Program - Frequency - Exams

Course program
Part 1. Introduction to Bayesian inference (1/3 of the course) Prior and posterior distributions. Inference. Prediction. Part 2. General decision theory (1/6 of the course) Decisions and loss functions. Pre-optimal analysis: completeness, admissibility. Optimality criteria. Randomization. Bayesian decisions. Optimality and admissibility. Part 3. Statistical decisions (1/2 of the course) Bayesian statistical decision theory. Frequentist statistical decision theory. Relationships.
Prerequisites
- Calculus (real functions of a real variable and of more than one variable, differentiation, integration) - Probability (random variables, convergence concepts) - Statistical inference (likelihood theory and frequentist inference)
Books
Books - De Santis F. (2024). Basic Bayes - Introduzione all'inferenza bayesiana. (Available on-line, sito elearning2 Sapienza). - Lesaffre E. Lawson B.L. (2012). Bayesian Biostatistics. Wiley. - Piccinato L. (2009). Metodi per la decisioni statistiche. Springer. Additional texts - De Santis F. et al. (2024). Inferenza statistica. (Available on-line, sito elearning2 Sapienza). - De Santis F. et al. (2017). Esercizi svolti di Inferenza statistica. (Available on-line, sito elearning2 Sapienza). - Problems and notes (in Italian, available on-line, sito elearning2 Sapienza).
Teaching mode
Lectures will be a mix of theory and practical sessions. Lecture will be given in presence, unless sanitary restrictions will be adopted.
Frequency
Attendance of the lectures is advised. Students who cannot attend the lectures must get in touch with the instructor.
Exam mode
The exam is split in 2 parts: a) a written test (either a unique test at the end of the semester or intermediate tests during the semester) b) an oral exam If necessary the above tests can be reunited
Bibliography
Additional texts - De Santis F. et al. (2021). Inferenza statistica. (Available on-line, sito elearning2 Sapienza) - De Santis F. et al. (2017). Esercizi svolti di Inferenza statistica. (Available on-line, sito elearning2 Sapienza) - Problems and notes (in Italian, available on-line, sito elearning2 Sapienza) Furthermore - Berger J.O (1985) - Statistical decision theory and Bayesian analysis - Wiley.
Lesson mode
Lectures will be a mix of theory and practical sessions. Lecture will be given in presence, unless sanitary restrictions will be adopted.
FULVIO DE SANTIS Lecturers' profile

Program - Frequency - Exams

Course program
Part 1. Introduction to Bayesian inference (1/3 of the course) Prior and posterior distributions. Inference. Prediction. Part 2. General decision theory (1/6 of the course) Decisions and loss functions. Pre-optimal analysis: completeness, admissibility. Optimality criteria. Randomization. Bayesian decisions. Optimality and admissibility. Part 3. Statistical decisions (1/2 of the course) Bayesian statistical decision theory. Frequentist statistical decision theory. Relationships.
Prerequisites
- Calculus (real functions of a real variable and of more than one variable, differentiation, integration) - Probability (random variables, convergence concepts) - Statistical inference (likelihood theory and frequentist inference)
Books
Books - De Santis F. (2024). Basic Bayes - Introduzione all'inferenza bayesiana. (Available on-line, sito elearning2 Sapienza). - Lesaffre E. Lawson B.L. (2012). Bayesian Biostatistics. Wiley. - Piccinato L. (2009). Metodi per la decisioni statistiche. Springer. Additional texts - De Santis F. et al. (2024). Inferenza statistica. (Available on-line, sito elearning2 Sapienza). - De Santis F. et al. (2017). Esercizi svolti di Inferenza statistica. (Available on-line, sito elearning2 Sapienza). - Problems and notes (in Italian, available on-line, sito elearning2 Sapienza).
Teaching mode
Lectures will be a mix of theory and practical sessions. Lecture will be given in presence, unless sanitary restrictions will be adopted.
Frequency
Attendance of the lectures is advised. Students who cannot attend the lectures must get in touch with the instructor.
Exam mode
The exam is split in 2 parts: a) a written test (either a unique test at the end of the semester or intermediate tests during the semester) b) an oral exam If necessary the above tests can be reunited
Bibliography
Additional texts - De Santis F. et al. (2021). Inferenza statistica. (Available on-line, sito elearning2 Sapienza) - De Santis F. et al. (2017). Esercizi svolti di Inferenza statistica. (Available on-line, sito elearning2 Sapienza) - Problems and notes (in Italian, available on-line, sito elearning2 Sapienza) Furthermore - Berger J.O (1985) - Statistical decision theory and Bayesian analysis - Wiley.
Lesson mode
Lectures will be a mix of theory and practical sessions. Lecture will be given in presence, unless sanitary restrictions will be adopted.
  • Lesson code1018629
  • Academic year/1
  • CurriculumDemografico sociale
  • Year1st year
  • Semester1st semester
  • SSDSECS-S/01
  • CFU9