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Probability: The Science of Uncertainty and Data
Master probability and statistical inference with MIT's course on probabilistic modeling, random variables, and data science inference methods.
Master probability and statistical inference with MIT's course on probabilistic modeling, random variables, and data science inference methods.
This advanced course from MIT provides a rigorous introduction to probabilistic modeling and statistical inference. The curriculum develops material intuitively while maintaining mathematical precision, focusing on universally applicable concepts and methodologies. Students explore multiple random variables, expectations, conditional distributions, and laws of large numbers. The course covers Bayesian inference methods and introduces random processes including Poisson processes and Markov chains. Based on MIT's renowned Introduction to Probability class, this challenging course enables students to apply probability theory to real-world applications and research. As part of the MITx MicroMasters in Statistics and Data Science, it offers the same rigor as MIT's on-campus experience.
Instructors:
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What you'll learn
Master the fundamental concepts of probabilistic models and their structures
Understand random variables including their distributions means and variances
Develop proficiency in probabilistic calculations and inference methods
Apply laws of large numbers to real-world scenarios
Analyze and work with random processes
Implement Bayesian inference methods for practical applications
Skills you'll gain
This course includes:
PreRecorded video
Graded assignments, Exams
Access on Mobile, Tablet, Desktop
Limited Access access
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There are 10 modules in this course
The course provides comprehensive coverage of probability fundamentals and their applications in data science. Starting with basic probability concepts and axioms, it progresses through conditioning, independence, and counting. Students learn about discrete and continuous random variables, their distributions, and multiple variable relationships. Advanced topics include Bayesian inference, limit theorems, classical statistics, and stochastic processes. The course emphasizes both theoretical understanding and practical applications, incorporating real-world examples and rigorous mathematical frameworks.
Probability models and axioms
Module 1
Conditioning and independence
Module 2
Counting
Module 3
Discrete random variables
Module 4
Continuous random variables
Module 5
Further topics on random variables
Module 6
Bayesian inference
Module 7
Limit theorems and classical statistics
Module 8
Bernoulli and Poisson processes
Module 9
Markov chains
Module 10
Fee Structure
Instructors
21 Courses
Distinguished Pioneer in Systems Optimization and Control Theory
John N. Tsitsiklis, born in Thessaloniki, Greece in 1958, has established himself as a preeminent figure in electrical engineering and computer science at MIT, where he serves as the Clarence J. Lebel Professor. His remarkable academic journey began and flourished at MIT, where he earned his B.S. in Mathematics, B.S., M.S., and Ph.D. in Electrical Engineering. After a brief stint as an acting assistant professor at Stanford University, he joined MIT's faculty in 1984, where he has made transformative contributions to systems, optimization, control, and operations research. His influential work spans decentralized control, consensus algorithms, approximate dynamic programming, and statistical learning. Tsitsiklis has co-authored several seminal books, including "Parallel and Distributed Computation," "Neuro-Dynamic Programming," and "Introduction to Probability." His exceptional contributions have earned him numerous prestigious accolades, including the 2016 ACM SIGMETRICS Achievement Award, the 2018 IEEE Control Systems Award, and the John von Neumann Theory Prize. As a member of the National Academy of Engineering and director of the Laboratory for Information and Decision Systems, he continues to shape the field through his research and teaching. His impact extends beyond academia through seven awarded U.S. patents and honorary doctorates from multiple institutions, including the Université catholique de Louvain and the Athens University of Economics and Business.
21 Courses
Distinguished Leader in Operations Research and Optimization
Patrick Jaillet serves as the Dugald C. Jackson Professor in MIT's Department of Electrical Engineering and Computer Science, where he has made significant contributions to online optimization and decision-making under uncertainty. His academic journey began in France, where he earned his Diplôme d'Ingénieur, followed by an SM in Transportation and a PhD in Operations Research from MIT in 1985. Beyond his primary role, Jaillet holds multiple leadership positions at MIT, including Co-Director of the Operations Research Center, member of the Laboratory for Information and Decision Systems, and Faculty Director of the MIT-France program. His distinguished career includes serving as Head of Civil and Environmental Engineering at MIT from 2002 to 2009 and previously as Chair of the Management Science and Information Systems Department at the University of Texas Austin. Jaillet's research focuses on online and data-driven optimization, machine learning, and network science, with applications in transportation, logistics, energy, and finance. His contributions have earned him numerous accolades, including selection as an INFORMS Fellow and recognition through prestigious lectureships. He maintains active involvement in the academic community as an associate editor for several prominent journals, including the INFORMS Journal on Optimization and Networks, while his research continues to receive funding from major organizations including NSF, ONR, and AFOSR
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