Bachelor
2021/2022
Bayesian Statistics
Type:
Elective course (Fundamental and Computational Linguistics)
Area of studies:
Fundamental and Applied Linguistics
Delivered by:
School of Linguistics
Where:
Faculty of Humanities
When:
3 year, 3 module
Mode of studies:
distance learning
Open to:
students of one campus
Language:
English
ECTS credits:
3
Contact hours:
2
Course Syllabus
Abstract
This course describes Bayesian statistics, in which one's inferences about parameters or hypotheses are updated as evidence accumulates. You will learn to use Bayes’ rule to transform prior probabilities into posterior probabilities, and be introduced to the underlying theory and perspective of the Bayesian paradigm. The course will apply Bayesian methods to several practical problems, to show end-to-end Bayesian analyses that move from framing the question to building models to eliciting prior probabilities to implementing in R (free statistical software) the final posterior distribution. Additionally, the course will introduce credible regions, Bayesian comparisons of means and proportions, Bayesian regression and inference using multiple models, and discussion of Bayesian prediction. We assume learners in this course have background knowledge equivalent to what is covered in the earlier three courses in this specialization: "Introduction to Probability and Data," "Inferential Statistics," and "Linear Regression and Modeling." https://www.coursera.org/learn/bayesian
Learning Objectives
- The goal of this course is to teach students about Bayesian Statistics, Bayesian Linear Regression, Bayesian Inference, R Programming, teach them to use Bayes’ rule to transform prior probabilities into posterior probabilities, and introduce them to the underlying theory and perspective of the Bayesian paradigm.
Expected Learning Outcomes
- Can implement Bayesian model averaging, interpret Bayesian multiple linear regression and understand its relationship to the frequentist linear regression approach.
- Can understand and define the concepts of prior, likelihood, and posterior probability and identify how they relate to one another, knows what Bayesian inference, non-conjugate priors, credible intervals and predictive inference module learning objectives are.
- Can use the data set provided to complete and report on a data analysis question.
- Knows how Bayesian methods can be used when working with big data, in biostatistics and public health.
- Knows how to work with loss functions, how to minimize expected loss for hypothesis testing, how to work with mixtures of conjugate priors and MCMC, how to compare two paired means using Bayes' factors. Knows what posterior probabilities of hypotheses and Bayes factors, the Normal-Gamma Conjugate Family, predictive distributions are.
- Knows the basics of Bayesian statistics, understands conditional probabilities, Bayes' rule, Bayesian vs. frequentist definitions of probability, frequentist and Bayesian approaches to inference for a proportion, effect of sample size on the posterior, frequentist vs. Bayesian inference, can solve problems using Bayes' rule
Course Contents
- About the Specialization and the Course
- The Basics of Bayesian Statistics
- Bayesian Inference
- Decision Making
- Bayesian Regression
- Perspectives on Bayesian Applications
- Data Analysis Project
Bibliography
Recommended Core Bibliography
- Rohatgi, V. K., & Saleh, A. K. M. E. (2001). An Introduction to Probability and Statistics (Vol. 2nd ed. Vijay K. Rohatgi, A.K. Md. Ehsanes Saleh). New York: Wiley-Interscience. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=396326
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