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Regular version of the site
Master 2019/2020

Bayesian Statistics: From Concept to Data Analysis

Area of studies: Applied Mathematics and Informatics
When: 2 year, 3 module
Mode of studies: Blended
Instructors: Evgeny Vybornyi
Master’s programme: Mathematical Methods of Modelling and Computer Technologies
Language: English
ECTS credits: 3

Course Syllabus

Abstract

This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. Wewill compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses.
Learning Objectives

Learning Objectives

  • The objective of this course is to form a foundation of Bayesian Statisticsand its application.
Expected Learning Outcomes

Expected Learning Outcomes

  • To ger knowledge about the philosophy of the Bayesian approach as well as how to implement it for common types of data
  • Apply Bayesian methods to the analysis of real data sets
  • Properly report the results of Bayesian analysis in research papers
Course Contents

Course Contents

  • Week 1: Probability and Bayes' Theorem
    In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.
  • Week 2: Statistical Inference
    This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives. Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data. Lesson 5 introduces the fundamentals of Bayesian inference. Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayes’ theorem to update the prior with data to obtain posterior probabilities. This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals
  • Week 3: Priors and Models for Discrete Data
    In this module, you will learn methods for selecting prior distributions and building models for discrete data. Lesson 6 introduces prior selection and predictive distributions as a means of evaluating priors. Lesson 7 demonstrates Bayesian analysis of Bernoulli data and introduces the computationally convenient concept of conjugate priors. Lesson 8 builds a conjugate model for Poisson data and discusses strategies for selection of prior hyperparameters
  • Week 4: Models for Continuous Data
    This module covers conjugate and objective Bayesian analysis for continuous data. Lesson 9 presents the conjugate model for exponentially distributed data. Lesson 10 discusses models for normally distributed data, which play a central role in statistics. In Lesson 11, we return to prior selection and discuss ‘objective’ or ‘non-informative’ priors. Lesson 12 presents Bayesian linear regression with non-informative priors, which yield results comparable to those of classical regression
Assessment Elements

Assessment Elements

  • non-blocking Exam
  • non-blocking Assessment obtained on the platform https://www.coursera.org/learn/bayesian-statistics
Interim Assessment

Interim Assessment

  • Interim assessment (3 module)
    0.5 * Assessment obtained on the platform https://www.coursera.org/learn/bayesian-statistics + 0.5 * Exam
Bibliography

Bibliography

Recommended Core Bibliography

  • Bolstad, W. M. (2017). Introduction to Bayesian Statistics (Vol. Third edition). Hoboken, N.J.: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1342637
  • Harney, H. L. (2016). Bayesian Inference : Data Evaluation and Decisions (Vol. 2nd ed). Switzerland: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1301176

Recommended Additional Bibliography

  • Donovan, T. M., & Mickey, R. M. (2019). Bayesian Statistics for Beginners : A Step-by-step Approach. Oxford: OUP Oxford. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2139683
  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2014). Bayesian Data Analysis (Vol. Third edition). Boca Raton: Chapman and Hall/CRC. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=1763244
  • Li, K., & Principe, J. C. (2019). Functional Bayesian Filter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.10606