Introduction to Bayesian Statistics

taught by Bill Bolstad

Brief Description:

This course will introduce you to the basic ideas of Bayesian Statistics. 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.

Instructor(s):
Level: Intermediate

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.

Dates:
August 17, 2012 to September 14, 2012February 01, 2013 to March 01, 2013
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Registration:
Please read the syllabus tab, noting the prerequisites, text and software requirements.

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Introduction to Bayesian Statistics

taught by Bill 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.

This course is a core requirement or elective in the following Program(s) in Analytics and Statistical Studies (PASS):

• Biostatistics - Controlled Trials

• Biostatistics - Epidemiology

• Environmental Science

Prerequisite(s):

• Calculus Review

Course Program:

SESSION 1: Introduction to Bayesian Statistics

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

SESSION 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

SESSION 3: Bayesian Inference For Normal Mean

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

SESSION 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.

Organization of the Course:

This course takes place over the internet 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.

The course typically requires 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, 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.

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

1. You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
2. 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.
3. 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, 5.0 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, and it can be ordered from Wiley by clicking here. Wiley typically offers statistics.com customers up to 15% discount on this book (and all other statistics titles): enter the code aff15 in the Promotion Code field when prompted during checkout and click the Apply Discount button. (If you are located in Asia, the web procedure for your location may not accept this discount – try calling your regional Wiley representative.).

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.

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Introduction to Bayesian Statistics

taught by Bill Bolstad

Instructor(s):
Dates:
August 17, 2012 to September 14, 2012February 01, 2013 to March 01, 2013
Course Fee: $499
Academic Rate: $399

Before registering, please read the syllabus tab, noting the prerequisites, text and software requirements. When you click the register button, you will be taken to our secure transaction page.

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