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.
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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 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.
Course 4 of 5 in the Statistics with R Specialization.
Syllabus
WEEK 1
The Basics of Bayesian Statistics
Welcome! Over the next several weeks, we will together explore Bayesian statistics. In this module, we will work with conditional probabilities, which is the probability of event B given event A. Conditional probabilities are very important in medical decisions. By the end of the week, you will be able to solve problems using Bayes' rule, and update prior probabilities. Please use the learning objectives and practice quiz to help you learn about Bayes' Rule, and apply what you have learned in the lab and on the quiz.
WEEK 2
Bayesian Inference
In this week, we will discuss the continuous version of Bayes' rule and show you how to use it in a conjugate family, and discuss credible intervals. By the end of this week, you will be able to understand and define the concepts of prior, likelihood, and posterior probability and identify how they relate to one another.
WEEK 3
Decision Making
In this module, we will discuss Bayesian decision making, hypothesis testing, and Bayesian testing. By the end of this week, you will be able to make optimal decisions based on Bayesian statistics and compare multiple hypotheses using Bayes Factors.
WEEK 4
Bayesian Regression
This week, we will look at Bayesian linear regressions and model averaging, which allows you to make inferences and predictions using several models. By the end of this week, you will be able to implement Bayesian model averaging, interpret Bayesian multiple linear regression and understand its relationship to the frequentist linear regression approach.
WEEK 5
Perspectives on Bayesian Applications
This week consists of interviews with statisticians on how they use Bayesian statistics in their work, as well as the final project in the course.
Data Analysis Project
In this module you will use the data set provided to complete and report on a data analysis question. Please read the background information, review the report template (downloaded from the link in Lesson Project Information), and then complete the peer review assignment.
