MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.
Probabilistic models use the language of mathematics. But instead of relying on the traditional "theorem - proof" format, we develop the material in an intuitive -- but still rigorous and mathematically precise -- manner. Furthermore, while the applications are multiple and evident, we emphasize the basic concepts and methodologies that are universally applicable.
The course covers all of the basic probability concepts, including:
- multiple discrete or continuous random variables, expectations, and conditional distributions
- laws of large numbers
- the main tools of Bayesian inference methods
- an introduction to random processes (Poisson processes and Markov chains)
The contents of this course are heavily based upon the corresponding MIT class -- Introduction to Probability -- a course that has been offered and continuously refined over more than 50 years. It is a challenging class but will enable you to apply the tools of probability theory to real-world applications or to your research.
This course is part of the MicroMasters Program in Statistics and Data Science.
What you'll learn:
- The basic structure and elements of probabilistic models
- Random variables, their distributions, means, and variances
- Probabilistic calculations
- Inference methods
- Laws of large numbers and their applications
- Random processes
Syllabus
Unit 1: Probability models and axioms
- Probability models and axioms
- Mathematical background: Sets; sequences, limits, and series; (un)countable sets.
Unit 2: Conditioning and independence
Conditioning and Bayes' rule
- Independence
Unit 3: Counting
- Counting
Unit 4: Discrete random variables
- Probability mass functions and expectations
- Variance; Conditioning on an event; Multiple random variables
- Conditioning on a random variable; Independence of random variables
Unit 5: Continuous random variables
- Probability density functions
- Conditioning on an event; Multiple random variables
- Conditioning on a random variable; Independence; Bayes' rule
Unit 6: Further topics on random variables
- Derived distributions
- Sums of independent random variables; Covariance and correlation
- Conditional expectation and variance revisited; Sum of a random number of independent random variables
Unit 7: Bayesian inference
- Introduction to Bayesian inference
- Linear models with normal noise
- Least mean squares (LMS) estimation
- Linear least mean squares (LLMS) estimation
Unit 8: Limit theorems and classical statistics
- Inequalities, convergence, and the Weak Law of Large Numbers
- The Central Limit Theorem (CLT)
- An introduction to classical statistics
Unit 9: Bernoulli and Poisson processes
- The Bernoulli process
- The Poisson process
- More on the Poisson process
Unit 10 (Optional): Markov chains
- Finite-state Markov chains
- Steady-state behavior of Markov chains
-Absorption probabilities and expected time to absorption
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.