About this course: This class presents the fundamental probability and statistical concepts used in elementary data analysis. It will be taught at an introductory level for students with junior or senior college-level mathematical training including a working knowledge of calculus. A small amount of linear algebra and programming are useful for the class, but not required.
Created by: Johns Hopkins University
Taught by: Brian Caffo, PhD, Professor, Biostatistics
Bloomberg School of Public Health
| Commitment | 3-5 hours/week |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
Introduction, Probability, Expectations, and Random Vectors
You are about to undergo an intense and demanding immersion into the world of mathematical biostatistics. Over the next few weeks, you will learn about probability, expectations, conditional probabilities, distributions, confidence intervals, bootstrapping, binomial proportions, and much more. Module 1 covers experiments, probability, variables, mass functions, density functions, cumulative distribution functions, expectations, variations, and vectors.
13 videos, 2 readings, 1 practice quiz
- Video: Welcome to the Course
- Reading: Syllabus
- Reading: Faculty
- Video: Biostatistics and Experiments
- Video: Set Notation and Probability
- Video: Probability
- Video: Random Variables
- Video: PMFs and PDFs
- Video: CDFs, Survival Functions, and Quantiles
- Video: Expected Values
- Video: Rules About Expected Values
- Video: Variances and Chebyshev's Inequality
- Video: Random Vectors and Independence
- Video: Correlation
- Video: Variance Properties and Sample Variance
- Practice Quiz: Module 1 Homework
Graded: Module 1 Quiz: Introduction, Probability, Expectations, and Random Vectors
WEEK 2
Conditional Probability, Bayes' Rule, Likelihood, Distributions, and Asymptotics
This module covers Conditional Probability, Bayes' Rule, Likelihood, Distributions, and Asymptotics. These are the most fundamental core concepts in mathematical biostatistics and statistics. After this module you should be able to recognize and be functional in these key concepts.
7 videos, 1 practice quiz
- Video: Conditional Probabilities and Densities
- Video: Bayes' Rule and DLRs
- Video: Likelihood
- Video: Bernoulli Distribution and Binomial Trials
- Video: The Normal Distribution
- Video: Limits and LLN
- Video: CLT and Confidence Intervals
- Practice Quiz: Module 2 Homework
Graded: Module 2 Quiz: Conditional Probability, Bayes' Rule, Likelihood, Distributions, and Asymptotics
WEEK 3
Confidence Intervals, Bootstrapping, and Plotting
This module covers Confidence Intervals, Bootstrapping, and Plotting. These are core concepts in mathematical biostatistics and statistics. After this module you should be able to recognize and be functional in these key concepts.
7 videos, 1 practice quiz
- Video: Confidence Intervals and CI for Normal Variance
- Video: Student's t Distribution and CI for Normal Means
- Video: Profile Likelihoods
- Video: T Confidence Intervals
- Video: Plotting
- Video: The Jackknife
- Video: Bootstrapping
- Practice Quiz: Module 3 Homework
Graded: Module 3 Quiz: Confidence Intervals, Bootstrapping, and Plotting
WEEK 4
Binomial Proportions and Logs
This module covers Binomial Proportions and Logs. These are core concepts in mathematical biostatistics and statistics. After this module you should be able to recognize and be functional in these key concepts.
3 videos, 1 practice quiz
- Video: Binomial Proportions Part A
- Video: Binomial Proportions Part B
- Video: Logs
- Practice Quiz: Module 4 Homework
Graded: Module 4 Quiz: Binomial Proportions and Logs
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Ratings and Reviews
A solid course on some of the fundamental principles of statistics and probability.
I knew a lot about probability before starting this course, but I didn't know much of anything about frequentist statistics. This course helped me understand some tricky concepts.
Overall good lectures and good practice material. Certainly not an introductory stat course - requires working knowledge of calculus and basic biostats.
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JB
Great course, though a little difficult in parts, particularly the first week. Worth working through though for a better understanding of probability and statistics.