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Regular version of the site
Master 2018/2019

## Bayesian Statistics

Type: Elective course (Comparative Social Research)
Area of studies: Sociology
When: 1 year, 4 module
Mode of studies: offline
Instructors: Boris Sokolov
Master’s programme: Comparative Soсial Research
Language: English
ECTS credits: 4

### Course Syllabus

#### Abstract

Bayesian data analysis is a rapidly developing field of statistics, which has many useful applications in various areas of political science, sociology, and international relations. The course begins with the basic concepts of Bayesian statistics (e.g., Bayes’s rule. priors, likelihood, and posterior distribution). Then we consider various approaches to the estimation and assessment of Bayesian models (with most attention to the MCMC-based methods) in the context of generalized linear models. Next we learn about main Bayesian approaches to model selection, including Bayes factors, DIC, and cross-validation methods. We conclude by discussing Bayesian model averaging (BMA), a powerful Bayesian approach to reducing model specification uncertainty. Students are assumed to have basic knowledge of statistics and be familiar with several conventional statistical methods, most importantly regression analysis. Knowledge of advanced topics, such as multilevel regression analysis and maximum-likelihood estimation, is helpful, but not critical. In addition, for practical exercises we will use R programming environment, so another major prerequisite is a basic knowledge of R.

#### Learning Objectives

• to provide a brief and “mostly harmless” (that is, as informal as possible) introduction to the theory and application of Bayesian statistical methods

#### Expected Learning Outcomes

• Understand the basic principles of Bayesian analysis, the opportunities which this statistical method offers for social scientists, and its limitations
• Apply Bayesian methods to the analysis of real data sets
• Properly report the results of Bayesian analysis in research papers

#### Course Contents

• Introduction. Basic concepts of Bayesian analysis
Content: frequentist vs. epistemic concepts of probability, Bayes’s rule, prior and posterior dis-tributions, likelihood, discrete probability examples, simple continuous distributions examples, popular R packages for Bayesian analysis. Bayesian linear regression, choice of priors, interpretation of model parameters, Bayesian inference, credibility intervals, Bayesian generalized regression modeling, ex-amples in MCMCpack and rstanarm. Reading: Gelman et al. 2014, Chapters 14 and 16 (optionally – also Ch. 15); Kruschke 2015, Chapter 2; Western 1999.
• General principles of Bayesian inference. Priors and likelihood
Content: MCMC estimation, Gibbs sampling, Hamiltonian Monte-Carlo, main convergence diagnostics, INLA, variational inference. Reading: Gelman et al. 2014, Chapters 11 and 12
• Bayesian model estimation: Gibbs sampling and Hamiltonian Monte Carlo
Content: Posterior predictive distribution, posterior predictive checks, posterior predictive P-value, visual checks. Reading: Gelman et al. 2014, Chapter 7, Sections 7.1-7.2; Lynch and Western 2004.
• Bayesian model evaluation. Posterior predictive checks.
Content: Posterior predictive distribution, posterior predictive checks, posterior predictive P-value, visual checks. Reading: Gelman et al. 2014, Chapter 7, Sections 7.1-7.2; Lynch and Western 2004.
• Bayesian model comparison
Content: Bayes factors, Bayesian Information Criterion (BIC) and Deviance Information Crite-rion (DIC), WAIC, leave-one-out cross-validation. Reading: Gelman et al. 2014, Chapter 7, Sections 7.3-7.7; Raftery 1995; Vehtari et al. 2017.
• Bayesian model averaging
Content: What is BMA, why it can be useful for social scientists, model priors selection, most popular BMA algorithms and their implementation in R. Reading: Bartels 1997; Montgomery and Nyhan 2010

#### Assessment Elements

• Home assignments
Half of your written home assignments will be conceptual assignments and the other half will be related to preparation of your final paper. You may expect an excellent grade (8-10 on a 0-10 scale) for conceptual assignments if you are able to (a) give correct answers to the stated questions, (b) write (if necessary) correct R code, and (c) interpret properly the results of Bayesian analyses done by other researchers, and also (d) demonstrate a proper understanding (and usage) of relevant Bayesian terminology. As to conceptual assignments, I encourage you to work in groups on the homework, but you always need to write your own solutions including your computer code. Also, it is hugely beneficial to attempt the problems sets on your own before working in groups.
• Class work
• Progress reports and mid-term presentation
• Exam

#### Interim Assessment

• Interim assessment (4 module)
0.26 * Class work + 0.35 * Exam + 0.325 * Home assignments + 0.065 * Progress reports and mid-term presentation

#### Recommended Core Bibliography

• 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