Foundations of Probability and Statistics

University of Colorado Boulder via Coursera Specialization

Go to class Write review

Overview

Coursera Flash Sale

40% Off Coursera Plus for 3 Months!

Grab it

In this three-course Specialization, you’ll build a strong mathematical foundation in probability, statistics, and basic stochastic processes, with direct applications to data science and artificial intelligence. You’ll begin by mastering the fundamentals of probability, learning to quantify uncertainty, work with random variables, and apply the Central Limit Theorem. Next, you’ll explore discrete-time Markov chains, discovering how to model dynamic systems, analyze long-term behavior, and apply Monte Carlo methods to sample from complex distributions. Finally, you’ll develop expertise in statistical estimation, learning to construct and evaluate estimators, apply maximum likelihood and method of moments estimation, and interpret confidence intervals. By the end of the specialization, you’ll have the analytical skills to make data-driven decisions, model real-world phenomena, and support advanced AI applications.

Syllabus

Course 1: Probability Foundations for Data Science and AI
Course 2: Discrete-Time Markov Chains and Monte Carlo Methods
Course 3: Statistical Estimation for Data Science and AI

Courses

0 reviews
1 day 18 hours 21 minutes
View details

Understand the foundations of probability and its relationship to statistics and data science. We’ll learn what it means to calculate a probability, independent and dependent outcomes, and conditional events. We’ll study discrete and continuous random variables and see how this fits with data collection. We’ll end the course with Gaussian (normal) random variables and the Central Limit Theorem and understand its fundamental importance for all of statistics and data science. This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) and the Master of Science in Artificial Intelligence (MS-AI) degrees offered on the Coursera platform. These interdisciplinary degrees bring together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the CU degrees on Coursera are ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Learn more about the MS-AI program at https://www.coursera.org/degrees/ms-artificial-intelligence-boulder Logo adapted from photo by Christopher Burns on Unsplash.
0 reviews
1 day 5 hours 23 minutes
View details

This course introduces statistical inference, sampling distributions, and confidence intervals. Students will learn how to define and construct good estimators, method of moments estimation, maximum likelihood estimation, and methods of constructing confidence intervals that will extend to more general settings. This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) and the Master of Science in Artificial Intelligence (MS-AI) degrees offered on the Coursera platform. These interdisciplinary degrees bring together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the CU degrees on Coursera are ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Learn more about the MS-AI program at https://www.coursera.org/degrees/ms-artificial-intelligence-boulder Logo adapted from photo by Christopher Burns on Unsplash.
0 reviews
1 day 8 hours 32 minutes
View details

A Markov chain can be used to model the evolution of a sequence of random events where probabilities for each depend solely on the previous event. Once a state in the sequence is observed, previous values are no longer relevant for the prediction of future values. Markov chains have many applications for modeling real-world phenomena in a myriad of disciplines including physics, biology, chemistry, queueing, and information theory. More recently, they are being recognized as important tools in the world of artificial intelligence (AI) where algorithms are designed to make intelligent decisions based on context and without human input. Markov chains can be particularly useful for natural language processing and generative AI algorithms where the respective goals are to make predictions and to create new data in the form or, for example, new text or images. In this course, we will explore examples of both. While generative AI models are generally far more complex than Markov chains, the study of the latter provides an important foundation for the former. Additionally, Markov chains provide the basis for a powerful class of so-called Markov chain Monte Carlo (MCMC) algorithms that can be used to sample values from complex probability distributions used in AI and beyond. Outside of certain AI-focused examples, this course is first and foremost a mathematical introduction to Markov chains. It is assumed that the learner has already had at least one course in basic probability. This course will include a review of conditional probability and will cover basic definitions for stochastic processes and Markov chains, classification and communication of states, absorbing states, ergodicity, stationary and limiting distributions, rates of convergence, first hitting times, periodicity, first-step analyses, mean pattern times, and decision processes. This course will also include basic stochastic simulation concepts and an introduction to MCMC algorithms including the Metropolis-Hastings algorithm and the Gibbs Sampler.