Introduction to Bayesian Statistics

# Introduction to Bayesian Statisticstaught 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:

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 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
Prerequisite:

You should be familiar with introductory statistics.  Try these self tests to check your knowledge.  Also, you should be familiar with what an integral is (in calculus), though extensive preparation in calculus is not needed (most integration calculations will be done by software).
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:

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

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

1. No credit - You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
2. Certificate - 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. CEUs and/or proof of completion - 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.
4. Digital Badge - Courses evaluated by the American Council on Education have a digital badge available for successful completion of the course.
5. Other options - Statistics.com Specializations, INFORMS CAP recognition, and academic (college) credit are available for some Statistics.com courses

Specialization:
Specializations are an easy way for you to demonstrate mastery of a specific skill in statistics and analytics. This course is part of the Bayesian Statistics Specialization which uses Bayes' Theorem to perform analyses and computations, and learn what makes it so popular.

INFORMS CAP:
This course is also recognized by the Institute for Operations Research and the Management Sciences (INFORMS) as helpful preparation for the Certified Analytics Professional (CAP®) exam, and can help CAP® analysts accrue Professional Development Units to maintain their certification .
Course Text:

The required text for this course is Introduction to Bayesian Statistics, 3rd edition, by W. M. Bolstad.

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.

Instructor(s):

Dates:

January 10, 2020 to February 07, 2020 July 03, 2020 to July 31, 2020

# Introduction to Bayesian Statistics

Instructor(s):

Dates:
January 10, 2020 to February 07, 2020 July 03, 2020 to July 31, 2020

Course Fee: \$589

We have flexible policies to transfer to another course, or withdraw if necessary (modest fee applies)

Group rates: Email jdobbins "at" statistics.com to get information on group rates.

First time student or academic? Click here for an introductory offer on select courses. Academic affiliation?  You may be eligible for a discount at checkout.

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