625.665.82 - Bayesian Statistics
Description
In Bayesian statistics, inference about a population parameter or hypothesis is achieved by merging prior knowledge, represented as a prior probability distribution, with data. This prior distribution and data are merged mathematically using Bayes’ rule to produce a posterior distribution, and this course focuses on the ways in which the posterior distribution is used in practice and on the details of how the calculation of the posterior is done. In this course, we discuss specific types of prior and posterior distributions, prior/posterior conjugate pairs, decision theory, Bayesian prediction, Bayesian parameter estimation and estimation uncertainty, and Monte Carlo methods commonly used in Bayesian statistical inference. Students will apply Bayesian methods to analyze and interpret several real-world data sets and will investigate some of the theoretical issues underlying Bayesian statistical analysis. R is the software that will be used to illustrate the concepts discussed in class. Course Note(s): Prior experience with R is not required; students not familiar with R will be directed to an online tutorial.
Instructor
Carsten Botts
Course Structure
The course materials are divided into modules which can be accessed by clicking Modules on the course menu. A module will have several sections including the overview, content, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.
Course Topics
- Review – Calculus Based Probability and Stats 1
- Review – Calculus Based Probability and Stats 2
- Basics of Bayesian Inference
- Picking the Prior Distribution
- Decision Theory
- Approximate Posterior Inference 1
- Approximate Posterior Inference 2
- Regression
- Models for Multivariate and Missing Data
- Hierarchical Models
- Hypothesis Testing and the Two-Sample Problem
- Nonparametric Models
Course Goals
At the end of this course, you will be able to solve complicated statistical problems using (computational) Bayesian methods. You will be able to understand and list the possible benefits and pitfalls of using Bayesian statistics (as opposed to classical statistics) to solve such problems.
Course Learning Outcomes (CLOs)
- Apply and interpret the most important and fundamental principles and mathematics of Bayesian analysis.
- Formulate the relationship between prior and posterior distributions.
- Obtain inference from a posterior distribution, whether it be analytically or through Monte Carlo methods.
- Apply Bayesian methods to solve problems which are traditionally solved using classical statistics.
Textbooks
Lee, Peter. (2012). Bayesian Statistics. Wiley & Sons, United Kingdom.
- Available online through Sheridan Library and from the course menu as an eReserve.
Required Software
R Application
This course uses the R programming application. For those of you who are new to R, it is a statistical programming environment. R is a free, widely available software system. Students may choose to use the R console or the RStudio package.
- R can be downloaded at www.r-project.org
- Rstudio is available at https://www.rstudio.com/products/rstudio/download/
- Choose the free RStudio Desktop.
An R tutorial video is embedded in module 1.
Student Coursework Requirements
It is expected that each module will take approximately 4–7 hours per week to complete. This estimate includes reading the assigned materials, listening to the video lectures, and completing assignments.
This course consist of the following requirements:
1. Problems Sets (6 total/70% of final grade)
2. Quizzes (2 total/30% of final grade)
Grading Policy
Final Grades: The chart below gives you the minimum grade you will receive if your final average is within a specified range. If I feel that the distribution of the final averages need to be curved, one will be given.
Final Average | Grade |
96 − 100 | A |
90 − 95 | A- |
87 − 89 | B+ |
83 − 86 | B |
80 - 82 | B- |
77 - 79 | C+ |
73 - 76 | C |
70 - 72 | C- |
67 - 69 | D+ |
63 - 66 | D |
60 - 62 | D- |
0 - 60 | F |
Course Policies
EN.625. 665 81 : Bayesian Statistics
Course Information
Required Text and Other Materials
Evaluation and Grading
Policies
Academic Policies
Deadlines for Adding, Dropping and Withdrawing from Courses
Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.
Academic Misconduct Policy
All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.
This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.
Students with Disabilities - Accommodations and Accessibility
Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.
For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.
Student Conduct Code
The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.
For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/
Classroom Climate
JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).
Course Auditing
When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.