Introduction to Probability - The Science of Uncertainty

开始时间: 04/22/2022 持续时间: 16 weeks

所在平台: EdxArchive 课程类别: 其他类别 大学或机构: MITx 授课老师： John Tsitsiklis Patrick Jaillet Zied Ben Chaouch Dimitri Bertsekas Qing He Jimmy Li Jagdish Ramakrishnan Katie Szeto Kuang Xu

课程主页: https://www.edx.org/archive/introduction-probability-science-mitx-6-041x-2

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课程详情

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 course are essentially the same as those of the corresponding MIT class (Probabilistic Systems Analysis and Applied Probability) -- a course that has been offered and continuously refined over more than 50 years. It is a challenging class, but it will enable you to apply the tools of probability theory to real-world applications or your research.

课程大纲

• 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

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