Bayesian Statistics

2018/2019

Учебный год

ENG

Обучение ведется на английском языке

4

Кредиты

Кто читает:

Департамент социологии

Статус:

Курс по выбору

Когда читается:

1-й курс, 4 модуль

Преподаватель

Соколов Борис Олегович

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
  You may expect an excellent grade (8-10 on a 0-10 scale) for class work if you actively partici-pate in in-class discussions and other activities, frequently present your homework and progress re-ports, and demonstrate a good performance when responding to the instructor’s conceptual questions and performing simple in-class programming exercises. The general rule is the lower your activity the lower your grade, though it is worth noting that the overall quality of your in-class performance also matters in this respect. If you make mistakes regularly when responding to my questions, performing exercises, or presenting your own work, it will negatively affect your grade. Please notice that attendance is not obligatory, so you can safely miss a few classes. However, if you miss all classes, your grade for class work will be zero. Also keep in mind that if you miss class you are still responsible for everything covered in class, including announcements. Similarly, being absent does not excuse you from obtaining handouts and assignments that you may have missed. It is your responsibility to find out what you have missed and to make arrangements to obtain any handouts, assignments, etc.
• Progress reports and mid-term presentation
  Progress reports are home assignments related to the preparation of your final paper. After each lecture you are expected to apply learned new methods to your own data and statistical model and written a short report describing your results. The most important aspects of progress reports to be graded are: (a) correct application of Bayesian methods to your data and model (0-3 points), (b) specific Bayesian terminology (0-3 points), as well as (c) the ability to interpret the results of your analyses correctly (0-3 points). Notice that (f) style and formatting issues (e.g. correct formatting of tables, figures, in-text cita-tions, and references) also affect the final grade (0-1 points). I do not expect that your style and gram-mar will be perfect, but I should be able, at least, to understand from the text of your assignment what exactly you have done. All students must make at least one mid-term presentation of their progresses. At the presentation, you will be asked to publicly present (with main focus on research design, operationalization, and the sub-stantive interpretation of the results). You will have about 10 minutes to tell the audience about your progress (in English). You will get a higher grade for that presentation if you are able to successfully demonstrate abilities to (a) formulate an original research question, develop a theoretical model, and properly operationalize it; (b) correctly apply Bayesian methods to your data and model; and (c) inter-pret the results properly, as well as (d) good presentation skills.
• Exam
  The most important aspects of your final papers to be graded are: (a) ability to formulate an original research question which at the same time is related to ongoing theoretical debates (0-2 points); (b) ability to operationalize your theoretical/conceptual model using relevant data (0-2 points); (c) ap-propriate use of Bayesian methods (0-2 points) and (d) specific Bayesian terminology (0-1 points), as well as (e) the ability to interpret the results of your analyses correctly (0-2 points). Notice that (f) style and formatting issues (e.g. correct formatting of tables, figures, in-text cita-tions, and references) also affect the final grade (0-1 points). I do not expect that your style and gram-mar will be perfect, but I should be able, at least, to understand from the text of your assignment what exactly you have done, Final project paper can be written alone or in collaboration with another student (three-author papers are not allowed). If you are working together, please indicate clearly in your reports and presen-tations, who did what part of the work. Notice that unless a group project deserves an excellent grade (8-10), it will get a final grade one point lower than an individual project of equivalent quality. If you plagiarize, you will fail. The deadline for submitting final papers is noon of March 24th, 2018. Late submissions will be graded down (one point on a 1-10 scale per day of delay; papers submitted with a delay of three days or more will be penalized by 3 points, irrespective of the length of delay)

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

Bibliography

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

Recommended Additional Bibliography

• Kruschke, J. K. . V. (DE-588)143634666, (DE-627)662785142, (DE-576)346169313, aut. (2015). Doing Bayesian data analysis a tutorial with R, JAGS, and Stan John K. Kruschke, Dept. of Psychological and Brain Sciences, Indiana University, Bloomington. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edswao&AN=edswao.415512638