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January 28, 2025
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This course is part of Data Science Foundations: Statistical Inference Specialization
Instructor: Jem Corcoran
7,572 already enrolled
Included with
(86 reviews)
Recommended experience
Intermediate level
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.
(86 reviews)
Recommended experience
Intermediate level
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.
Identify characteristics of “good” estimators and be able to compare competing estimators.
Construct sound estimators using the techniques of maximum likelihood and method of moments estimation.
Construct and interpret confidence intervals for one and two population means, one and two population proportions, and a population variance.
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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) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings 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 MS-DS is 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. Logo adapted from photo by Christopher Burns on Unsplash.
Welcome to the course! This module contains logistical information to get you started!
1 video4 readings1 ungraded lab
In this module you will learn how to estimate parameters from a large population based only on information from a small sample. You will learn about desirable properties that can be used to help you to differentiate between good and bad estimators. We will review the concepts of expectation, variance, and covariance, and you will be introduced to a formal, yet intuitive, method of estimation known as the "method of moments".
10 videos11 readings1 quiz3 assignments1 programming assignment1 ungraded lab
In this module we will learn what a likelihood function is and the concept of maximum likelihood estimation. We will construct maximum likelihood estimators (MLEs) for one and two parameter examples and functions of parameters using the invariance property of MLEs.
5 videos5 readings2 assignments1 programming assignment1 ungraded lab
In this module we will explore large sample properties of maximum likelihood estimators including asymptotic unbiasedness and asymptotic normality. We will learn how to compute the “Cramér–Rao lower bound” which gives us a benchmark for the smallest possible variance for an unbiased estimator.
5 videos5 readings2 assignments1 programming assignment1 ungraded lab
In this module we learn about the theory of “interval estimation”. We will learn the definition and correct interpretation of a confidence interval and how to construct one for the mean of an unseen population based on both large and small samples. We will look at the cases where the variance is known and unknown.
5 videos5 readings1 quiz1 assignment1 programming assignment2 ungraded labs
In this module, we will generalize the lessons of Module 4 so that we can develop confidence intervals for other quantities of interest beyond the distribution mean and for other distributions entirely. This module covers two sample confidence intervals in more depth, and confidence intervals for population variances and proportions. We will also learn how to develop confidence intervals for parameters of interest in non-normal distributions.
5 videos5 readings2 assignments1 ungraded lab
We asked all learners to give feedback on our instructors based on the quality of their teaching style.
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This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹
This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹
University of Colorado Boulder
Degree · 2 years
¹Successful application and enrollment are required. Eligibility requirements apply. Each institution determines the number of credits recognized by completing this content that may count towards degree requirements, considering any existing credits you may have. Click on a specific course for more information.
86 reviews
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Reviewed on Sep 3, 2022
The instrustor, Dr. Jem, is really interesting. She made the hard part of the Statistics easy to understand!
Reviewed on Jan 27, 2024
Excellent. Challenging quizzes that really make you apply the points from the lectures. Very detailed course that has taken me to the next level of my understanding of statistical inference.
Reviewed on Jul 18, 2024
This course provided me with truly deep insights into the inner workings of statistics. Thank you very much.
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