The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical inference are the keys to analyzing data and making scientifically sound predictions.
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 courseare 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 theMITx MicroMasters Program in Statistics and Data Science. Master the skills needed to be an informed and effective practitioner of data science. You will complete this course and three others from MITx, at a similar pace and level of rigor as an on-campus course at MIT, and then take a virtually-proctored exam to earn your MicroMasters, an academic credential that will demonstrate your proficiency in data science or accelerate your path towards an MIT PhD or a Master's at other universities. To learn more about this program, please visit https://micromasters.mit.edu/ds/.
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
Unit 3: 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
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
John Tsitsiklis, Patrick Jaillet, Qing He, Jimmy Li, Jagdish Ramakrishnan, Katie Szeto, Kuang Xu, Dimitri Bertsekas and Eren Can Kizildag
is taking this course right now, spending 4 hours a week on it and found the course difficulty to be medium.
This is a great introducing course on probability. A certain level in math is a prerequisite, but nothing complicated. The teacher is clear and the his explanations really help to understand notion that can appear complicated at first glance. The exercices are designed to help the understanding. They're not "challenging", but are helpful.
is taking this course right now, spending 12 hours a week on it and found the course difficulty to be hard.
It is an introductory course but, I would not recommend it to somebody that doesn't have any idea of probability or statistics. The problems and exams have some difficult exercises. After taking many probability courses, this is the first time I feel I really understand it. It is fun and rigorous at the same. It is one of the best MOOC I've taken if not the best.