This course is all about variation, uncertainty, and randomness. Students will learn the vocabulary of uncertainty and the mathematical and computational tools to understand and describe it.
Thomas Stewart
Elson Building, 400 Brandon Ave, Room 156
thomas.stewart@virginia.edu
Github: thomasgstewart
Ethan Nelson
Graduate student in Data Science
ean8fr@virginia.edu
Github: eanelson01
Format of the class: Inclass time will be a combination of lectures, group assignments, live coding, and student presentations. Please note: Circumstances may require the facetoface portion of the class to be online.
Time: MWF, 9  9:50am, Dell 1 Room 105
Office Hours: MWF, 10am, Dell 1 Commons
TA Office Hours: Thursdays, 2pm, Dell 1 Commons
The following textbooks are freely available online via the UVA library.
Understanding uncertainty by Dennis V. Lindley
Understanding Probability, 3rd edition
by Henk Tijms
Introduction to Probability: Models and Applications
by N. Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
The following textbooks may also be helpful.
Probability and Statistics for Data Science
by Norman Matloff
Introduction to Probability Models
by Sheldon M. Ross
The course will be taught using R.
This course covers the fundamentals of probability theory and stochastic processes. The goal of the course is that students will become conversant in the tools of probability. At the end of the course, students should be able to clearly describe and implement concepts related to random variables, properties of probability, distributions, expectations, moments, transformations, model fit, basic inference, sampling distributions, discrete and continuous time Markov chains, and Brownian motion. The course will illustrate most topics with both analytic and computational solutions.
The final exam will be a 2030 minute oneonone oral exam with the instructor recorded in Zoom. Prior to the exam, a set of practice questions will be provided, with the expectation that students will prepare for the oral exam by codingup solutions and writing explanations. During the oral exam, the instructor will ask a series of questions covering topics from the course and the practice questions. For example, the instructor may ask:
Students will be graded on both the accuracy of their responses and the clarity with which they explain course concepts and solutions to questions. The final exam will occur on 14 December 2023. Students will sign up for oral exam slots in early December.
Each class will have an assigned reading. Each reading is paired with a deliverable. Please read the assigned material and make a goodfaith effort on the deliverable before class.
Symbol  Text 

UU  Understanding Uncertainty 
Class period  Material  Deliverable 

Fri, 20230901  UU 4.1, 4.2  4 
Mon, 20230904  UU 4.3 to 4.7  5 
Wed, 20230906  UU 5.1 to 5.5  6 
Fri, 20230908  UU 5.6 to 5.13  7 
Mon, 20230911  UU 6.1 to 6.4  8 
Wed, 20230913  UU 6.5 to 6.9  Catch up 
Fri, 20230915  UU 6.10 to 6.12  Catch up 
Mon, 20230918  9  
Wed, 20230920  10  
Fri, 20230922  UU 7.1 to 7.3  11 
Mon, 20230925  UU 7.4 to 7.8  12 
Wed, 20230927  UU 8.1 to 8.3  13 
Fri, 20230929  UU 8.4 to 8.9  14 
Mon, 20231002  Fall Break  
Wed, 20231004  Binomial probabilities  
Fri, 20231006  ”  15 
Mon, 20231009  slides slides 
16 
Wed, 20231011  video  16 
Fri, 20231013  ”  16 
Mon, 20231016  ”  16 
Wed, 20231018  slides  17 
Fri, 20231020  17  
Mon, 20231023  Rock, paper, scissors  
Wed, 20231025  World Series  18 
Fri, 20231027  World Series hints 
18 
Mon, 20231003  
Wed, 20231101  slides slides lotsopdfs 

Fri, 20231103  
Mon, 20231106  19 module 

Wed, 20231108  20 module 

Fri, 20231110  21 module 

Mon, 20231113  22 slides 

Wed, 20231115  22 slides 

Fri, 20231117  23 module 

Mon, 20231120  23 module 

Mon, 20231127  24 slides, slides 9 to 21 
Some of the assignments will be traditional problem sets. Others will be more substantial projects requiring you to perform a simulation and summarize findings in a blog format. Each assignment will be graded on a pass/fail basis. Students will have opportunities to resubmit each assignment multiple times within a 2 week window after of initial feedback.
Deliverable  First Submission Due Date  Resubmission Due Date 

0. Getting started with Github (not graded)  None  
1. Uncertainty  20230901  20231002 
2. Calculus of belief  20230901  20231002 
3. Birthday problem  20230904  20231002 
4. Two events  20230906  20231002 
5. Independence  20230908  20231002 
6. Basic rules  20230911  20231002 
7. More rules  20230913  20231002 
8. Bayes rule  20230915  20231003 
9. Bayes rule, more practice  20230918  20231004 
10. Diagnostic odds  20230920  20231009 
11. Exchangeability  20230925  20231018 
12. Probability, Likelihood, Chance  20230927  20231018 
13. Simpson’s paradox  20230929  20231018 
14. Randomization  20231002  20231023 
15. Binomial practice  20231006  20231023 
16. Roulette  20231016  20231108 
17. Simulation error  20231023  20231115 
18. World Series  20231030  20231120 
19. Birth weight  20231108  20231127 
20. Birth weight with kernels  20231110  20231201 
21. Birth weight with kernels (part 2)  20231113  20231201 
22. Estimating the maternal age distribution with Maximum Likelihood  20231127  20231205 
23. Bayesian updating  20231127  20231205 
24. Estimating the weight distribution with method of moments  20231129  20231205 
Topic  Slides  Textbook sections  Whiteboards  Videos 

Class logistics  
Overview  
Definitions of Probability  
Intro to R  Getting R  
→ Markdown  Cheatsheet  
→ Rmarkdown  Example input Example output 

Simulation & Operating Characteristics  slides slides 

Basic Probability Ideas  
→ Belief vs Frequency vs Information  
→ Notebook / data.frame definition  
→ And, Or  Slides  
→ Conditional Probability  Slides  
→ Law of Total Probability  Slides  
→ Bayes Rule  Slides  
→ Diagnostics  Diagnostics PPV plot R code 

→ Exchangeability  
→ Posterior, Prior, Likelihood, Chance  
→ Random variable  
Discrete Probability Models  
→ Probability Mass Function  
→ Bernoulli Random Variables  Slides Hands and Sequences 

→ Binomial Random Variables  ”  
→ Negative Binomial Random Variables  ”  
→ Poisson Random Variables  Slides  
→ World Series Distribution  Hints  
Continuous Probability Models  slides slides lotsopdfs 

→ Cumulative Distribution Function  
→ Probability Density Function  
→ Uniform Random Variables  
→ Normal Random Variables  
→ Exponential Random Variables  
→ Gamma Random Variables  
→ Beta Random Variables  
→ Mixture Distributions  
Expectation and Variance  
→ Data Types  
→ Categorical, Ordinal, Interval, and Ratio Variables  
→ Covariance  
Transformations of individual observations  
Transformations of samples  
→ Min and Max  
→ Quantiles  
→ Order Statistics  
→ Sampling distributions  
Methods of Fitting Models  slides slides 

→ QQplot  
→ Method of moments  deliverable 24  
→ Maximum likelihood  deliverable 22  
→ Bayesian  deliverable 23  
→ Kernel Density Estimation  deleverables 19, 20, 21  
Sampling Distributions from Fitted Models  
→ Bootstrap  
→ Simulation  
→ Central Limit Theorem  
Simulation  
→ Parallel Computing  
→ Batch processing on the cloud  
Brief introduction to inference  
→ Sampling and Inference  
→ Inference with CI  
→ Inference with Hypothsis testing  
Multivariate Normal Distribution  
→ Properties  
→ Correlation  
→ Conditional Distribution  
→ Marginal Distribution 
Grading Policies: Courses carrying a Data Science subject area use the following grading system: A, A; B+, B, B; C+, C, C; D+, D, D; F. The symbol W is used when a student officially drops a course before its completion or if the student withdraws from an academic program of the University.
Grading Scale:
Grades will be a weighted average of the final exam score (50%) and the deliverables score (50%). As deliverables are graded on a pass/fail basis, the deliverable score will be the percentage of deliverables which earn a pass. For example, a student that earns an 90 on the final and passes 8 of 10 deliverables will earn 90.5 + 80.5 = 85 which is a B.
The instructor may alter the course content and grading policies during the semester.
Students are encouraged to study together. The instructions for each assignment will indicate if and how students may work together on the deliverable. Students should not collaborate on the final exam. Students that violate the collaborativework policy on an assignment will fail the assignment in question and forfeit the opportunity to retake or resubmit. Students that violate the collaborativework policy on the final exam will fail all sections of the final exam and forfeit the opportunity to retake or resubmit. Students may be referred to UVA Honor Committee.
University of Virginia Honor System: All work should be pledged in the spirit of the Honor System at the University of Virginia. The following pledge should be written out at the end of all quizzes, examinations, individual assignments, and papers: “I pledge that I have neither given nor received help on this examination (quiz, assignment, etc.)”. The pledge must be signed by the student. For more information, visit www.virginia.edu/honor.
UVA is committed to creating a learning environment that meets the needs of its diverse student body. If you anticipate or experience any barriers to learning in this course, please feel welcome to discuss your concerns with me. If you have a disability, or think you may have a disability, you may also want to meet with the Student Disability Access Center (SDAC), to request an official accommodation. You can find more information about SDAC, including how to apply online, through their website at www.studenthealth.virginia.edu/SDAC. If you have already been approved for accommodations through SDAC, please make sure to send me your accommodation letter and meet with me so we can develop an implementation plan together.