Insegnamento a.a. 2024-2025

20231 - BAYESIAN STATISTICAL METHODS

Department of Decision Sciences

Course taught in English

Class timetable
Exam timetable
Go to class group/s: 31
CLMG (6 credits - I sem. - OP  |  SECS-S/01) - M (6 credits - I sem. - OP  |  SECS-S/01) - IM (6 credits - I sem. - OP  |  12 credits SECS-S/01) - MM (6 credits - I sem. - OP  |  SECS-S/01) - AFC (6 credits - I sem. - OP  |  SECS-S/01) - CLELI (6 credits - I sem. - OP  |  SECS-S/01) - ACME (6 credits - I sem. - OP  |  SECS-S/01) - DES-ESS (6 credits - I sem. - OP  |  SECS-S/01) - EMIT (6 credits - I sem. - OP  |  SECS-S/01) - GIO (6 credits - I sem. - OP  |  SECS-S/01) - DSBA (6 credits - I sem. - OP  |  SECS-S/01) - PPA (6 credits - I sem. - OP  |  SECS-S/01) - FIN (6 credits - I sem. - OP  |  SECS-S/01) - AI (6 credits - I sem. - OP  |  SECS-S/01)
Course Director:
BEATRICE FRANZOLINI

Classes: 31 (I sem.)
Instructors:
Class 31: BEATRICE FRANZOLINI


Suggested background knowledge

Elementary probability and statistics background is needed.

Mission & Content Summary

MISSION

Bayesian statistical methods have advanced significantly in the past 20 years, thanks to their flexibility, ability to integrate diverse information, and effectiveness in handling complex data structures. They are now widely used across various scientific disciplines, including economics, finance, econometrics, marketing, biostatistics, image processing, and network analysis. This course provides an introductory exploration of Bayesian statistics, covering theoretical principles, computational techniques, and practical applications. By the course's conclusion, students will have acquired a robust understanding of Bayesian hierarchical models, techniques for model selection, clustering, and regression, as well as a comprehension of the general principles for modeling complex data structures. Throughout the course, we will maintain a balance between theoretical concepts and applications. By exploring practical examples employing the statistical software R, students will not only gain an understanding of theoretical frameworks but also the ability to select and implement Bayesian statistical models tailored to real-world scenarios. This course equips students with a distinctive skill set in statistics and data analysis, valuable for pursuing a quantitative career path in both academia and industry.

CONTENT SUMMARY

  • Thinking like a Bayesian: subjective probability.
  • Statistical inference as the update of belief: Bayes' Theorem.
  • Predictive approach to statistical inference: exchangeability and de Finetti's representation theorem.
  • Selection of prior distributions: conjugate families.
  • Parametric inference: point estimation, interval estimation, hypothesis testing, model selection.
  • Stochastic simulation methods: Monte Carlo, Gibbs sampler, and Metropolis-Hastings.
  • Posterior prediction and validation.
  • Bayesian hierarchical models and partial exchangeability.
  • Bayesian regression and classification: linear regression, regularization, bias-variance tradeoff, Gaussian processes, and naïve Bayes.
  • Bayesian clustering: mixture models and random partitions.

Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Illustrate the concept of subjective probability and its role in Bayesian inference.
  • Comprehend the logical foundations of Bayesian data analysis.
  • Explain the theoretical basis of Bayesian parameter estimation, hypothesis testing, interval estimation, and model selection.
  • Identify appropriate prior distributions and the most effective computational techniques based on the statistical problem.

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Select suitable Bayesian statistical models for a given problem.
  • Compute posterior distributions using analytical methods and computational techniques.
  • Interpret and communicate the results obtained from Bayesian analysis.
  • Apply Bayesian statistical methods to real-world problems.
  • Critically evaluate the strengths and limitations of Bayesian approaches in different contexts.

Teaching methods

  • Lectures
  • Practical Exercises
  • Collaborative Works / Assignments

DETAILS

The teaching and learning activities are based on lectures that present Bayesian statistics with a main attention to methodology, theory, and computational methods. Furthermore, these aspects are illustrated through R code "scripts" explained during lectures and available on the Bboard platform, which students can upload to their own computers and use/modify directly to better understand the actual role of various models and proposed initial distributions. The group work, which contributes to the final evaluation, allows students to delve into a topic of their interest (theoretical or applied).


Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
  x x
  • Individual Works/ Assignment (report, exercise, presentation, project work etc.)
x    
  • Collaborative Works / Assignment (report, exercise, presentation, project work etc.)
x    

ATTENDING AND NOT ATTENDING STUDENTS

Student evaluations is based on:

 

  • One between group or individual assignment, to verify the student's ability to use and understand the methodologies and techniques presented in class in situations other than those explicitly considered in the course. [optional]
  • Written exam (either a single general or midterm and end of semester exams), consisting of exercises, multiple-choice, and theory questions, which aim to evaluate both the understanding of the proposed methodologies and the student's ability to apply the analytical tools illustrated during the course.

 

Grading rule: Let X denote the grade of the written individual exam and let Y be the grade of the group assignment. Then, if Y is greater than or equal to X, the final grade is 0.3*Y+0.7*X. Otherwise, if Y is less than X, the final grade is X.


Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

Lecture notes are provided via BBoard.

 

The course relies, mostly, on the books:

  • A. A. JOHNSON, et al., Bayes Rules! An introduction to applied Bayesian modeling2022 by Chapman & Hall.
  • P.D. HOFF, A first course in Bayesian statistical Methods, New York, Springer-Verlag, 2009.   
  • A. GELMAN, et al., Bayesian Data Analysis, Third Edition, CRC Press, 2013.

 

Students who are interested in deepening, individually, specific concepts are provided with additional reading materials upon request. These additional materials are not object of final evaluation.

Last change 22/04/2024 15:46