Introduction to Bayesian Statistics

Dr. William M. 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:

1. 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.



2. 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.



3. Bayesian statistics uses a single tool, Bayes' theorem. Frequentist procedures require many different tools.



4. Bayesian methods often out perform the corresponding frequentist methods even when evaluated using frequentist criteria.



5. 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.



6. 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.

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.

For those enrolled in Professional Advancement Programs, this is a required or elective course in the following Programs:

• Biostatistics (epidemiology) - elective
• Biostatistics (controlled trials) - elective

Course Program:

The course is structured as follows

The Instructor:

Dr. William M. Bolstad has 25 years of teaching experience at the University of Waikato (New Zealand), where he currently serves in the Dept. of Statistics. Dr. Bolstad is the author of Introduction to Bayesian Statistics (the course text), and has pioneered the use of Bayesian methods in teaching the first year statistics course.

Organization of the Course:

The course takes place over the internet, at statistics.com. 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. The course is scheduled to take place over 4 weeks, and typically requires 10-15 hours per week. 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 and work through exercises. Discussion among participants is encouraged. The instructor will provide answers and comments.

Certificates and Grades:

You may be interested only in learning the material presented, and not be concerned with grades or certificates. Or you may be enrolled in a statistics.com Professional Advancement Program that requires demonstration of proficiency in the subject, in which case your work will be assessed for purposes of issuing a grade. Or you may require only a "Certificate of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). As you begin the class, you will be asked to specify your category.

Credit:

This course offers continuing education units (CEU's). For those successfully completing the course (generally this means marks of 50% or better on the homework), 5.0 CEU's and a certificate will be issued by statistics.com, upon request.

Dates:

Oct. 24 - Nov. 21, 2008
Click here to be notified of future course offerings.

Participants gain access to the online materials on the first day of the course, and typically spend about 10-15 hours per week (at their convenience). You retain full access to course materials, including discussion board, for two weeks after the course closing date.

Level:

Intermediate

Prerequisite:

The equivalent of Introduction to Statistics I: Inference for a Single Variable, and Introduction to Statistics II: Working with Bivariate Data (and, if necessary before these courses, Introduction to Statistics for Beginners or Survey of Statistics for Beginners). Bayesian statistics relies on a direct application of the rules of probability, so being able to manipulate formulae is a necessary skill. A knowledge of calculus would be helpful, but is not absolutely necessary. Those interested in more than a cursory treatment of Bayesian modeling (session 4) would benefit from familiarity with Introduction to Regression and Logistic Regression. For additional information about course prerequisites, click here.

Course Text:

The required text is Introduction to Bayesian Statistics by W. M. Bolstad. This text can be purchased directly from Wiley here. Wiley typically offers statistics.com customers discounts of up to 15%. 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.

Registration:

Register Online - $449
Register Online (academic) - $349 (you must be affiliated with a college, university or high school)

Add $50 service fee if you require a prior invoice, or if you need to submit a purchase order or voucher, pay by wire transfer or EFT, or refund and reprocess a prior payment. Please use this printed registration form, for these and other special orders.

Note: Courses may fill up at any time and registrations are processed in the order in which they are received. Your registration will be confirmed for the first available course date, unless you specify otherwise.