### Bayesian Statistics

Introduction to Bayesian Statistics

taught by William Bolstad

Aim of Course:

This course will introduce you to the basic ideas of Bayesian Statistics. In Bayesian statistics, population parameters are considered random variables having probability distributions. These probabilities measure "degree of belief". The rules of probability (Bayes' theorem) are used to revise our belief, given the observed data. You will learn how to perform Bayesian analysis for a binomial proportion, a normal mean, the difference between normal means, the difference between proportions, and for a simple linear regression model. Bayesian methods will be contrasted with the comparable frequentist methods, demonstrating the advantages this approach offers. These include:

- Bayesian statistics uses both prior and sample information. Usually something is known about possible parameter values before the experiment is performed, and it is wasteful not to use this prior information.
- The Bayesian approach allows direct probability interpretations of the parameters, given the observed data. All probability statements in the frequentist approach are about possible data that could have been observed, but were not. These statements aren't of much scientific use.
- Bayesian statistics uses a single tool, Bayes' theorem. Frequentist procedures require many different tools.
- Bayesian methods often out perform the corresponding frequentist methods even when evaluated using frequentist criteria.
- Bayesian statistics has a straightforward method for dealing with nuisance parameters. It integrates them out of the joint posterior distribution. There is no single corresponding method in frequentist statistics, and nuisance parameters are harder to deal with.
- Bayes' theorem gives the general way to find the predictive distribution of future observations. There is no such general method in frequentist statistics, only a collection of methods that sometimes work.

This course may be taken individually (one-off) or as part of a certificate program.

Course Program:

## WEEK 1: Introduction to Bayesian Statistics

- Logic probability & uncertainty
- Discrete random variables
- Bayesian inference for discrete random variables

## WEEK 2: Bayesian Inference For Binomial Proportion and Poisson Mean

- Continuous random variables
- Bayesian inference for binomial proportion
- Comparing Bayesian and frequentist inferences for proportion
- Bayesian inference on Poisson mean

## WEEK 3: Bayesian Inference For Normal Mean

- Bayesian inference for normal mean
- Comparing Bayesian and Frequentist inferences for mean
- Bayesian inference for difference between means

## WEEK 4: Modeling

- Bayesian Inference for Simple Linear Regression Model
- Robust Bayesian methods
- Bayesian inference for normal standard deviation

HOMEWORK:

Homework in this course consists of short answer questions to test concepts and guided data analysis problems using software.

In addition to assigned readings, this course also has supplemental readings available online, and an end of course data modeling project.

# Introduction to Bayesian Statistics

Who Should Take This Course:

Biostatisticians, those designing and analyzing clinical trials, social science statisticians, environmental and geophysical scientists; nearly all fields of statistical analysis are amenable to a Bayesian approach.

Level:

Intermediate

You should be familiar with introductory statistics. Try these self tests to check your knowledge.

Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement:

About 15 hours per week, at times of your choosing.

This course has supplemental readings that are available online, and an end of course modeling project.

Credit:

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

- You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
- You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
- You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). For those successfully completing the course, CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

The required text for this course is *Introduction to Bayesian Statistics*, 2nd edition, by W. M. Bolstad.

PLEASE ORDER YOUR COPY IN TIME FOR THE COURSE STARTING DATE.

Software:

The instructor will offer illustrations in Minitab and R, and exercises can be done using these two packages.

Click here for information on obtaining free or trial versions of Minitab and R.

# Introduction to Bayesian Statistics

July 07, 2017 to August 04, 2017January 12, 2018 to February 09, 2018July 06, 2018 to August 03, 2018