This course is part of the Data Science Foundations: Statistical Inference Specialization

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Jem Corcoran

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Data Science Foundations: Statistical Inference SpecializationUniversity of Colorado Boulder

About this Course

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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.

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Earn a Certificate upon completion

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Coursera Labs

Includes hands on learning projects.

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Course 2 of 3 in the

Data Science Foundations: Statistical Inference Specialization

Intermediate Level

Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.

Approx. 27 hours to complete

English

What you will learn

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.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Coursera Labs

Includes hands on learning projects.

Learn more about Coursera Labs

Course 2 of 3 in the

Data Science Foundations: Statistical Inference Specialization

Intermediate Level

Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.

Approx. 27 hours to complete

English

Instructor

Instructor rating

4.46/5 (15 Ratings)

Jem Corcoran

Offered by

University of Colorado Boulder

Start working towards your Master's degree

This course is part of the 100% online Master of Science in Data Science from University of Colorado Boulder. If you are admitted to the full program, your courses count towards your degree learning.

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Syllabus - What you will learn from this course

Week1

Week 1

1 hour to complete

Start Here!

1 hour to complete

1 video (Total 7 min), 3 readings

7 hours to complete

Point Estimation

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".

7 hours to complete

10 videos (Total 153 min), 11 readings, 5 quizzes

10 videos

Discrete Random Variables and Probability Mass Functions11mContinuous Random Variables and Probability Density Functions7mJoint Distributions and Independence10mThe Gamma Distribution17mTransformations of Distributions20mExpectation and Properties of Expectation16mVariance and Covariance17mEstimators and Sampling Distributions15mDistributions of Sums22mMethod of Moments Estimators13m

11 readings

Important Discrete Distributions10mImportant Continuous Distributions20mTable Summarizing Important Distributions 10mJoint Distributions10mVideo Slides: The Gamma Distribution15mVideo Slides for Transformations of DistributionsVideo Slides for Expectation and Properties of ExpectationVideo Slides for Variance and CovarianceVideo Slides for Estimators and Sampling DistributionsVideo Slides for Distributions of SumsVideo Slides for Method of Moments Estimators

4 practice exercises

Recognizing Discrete Distributions15mCalculations with Continuous Distributions25mProbability, Expectation, and Variance30mMethod of Moments Estimation30m

Week2

Week 2

4 hours to complete

Maximum Likelihood Estimation

4 hours to complete

5 videos (Total 67 min), 5 readings, 3 quizzes

5 videos

A Motivating Example8mNotation, Terminology, and First Complete Examples13mMLEs for Multiple and Support Parameters17mThe Invariance Property20mMean Squared Error, Bias, and Relative Efficiency7m

5 readings

Video Slides for A Motivating ExampleVideo Slides for Notation, Terminology, and First Complete ExamplesVideo Slides for MLEs for Multiple and Support ParametersVideo Slides for The Invariance PropertyVideo Slides for Mean Squared Error, Bias and Relative Efficiency

2 practice exercises

Finding MLEs30mInvariance, Mean-Squared Error, and Efficiency30m

Week3

Week 3

6 hours to complete

Large Sample Properties of Maximum Likelihood Estimators

6 hours to complete

5 videos (Total 100 min), 5 readings, 3 quizzes

5 videos

Fisher Information and the Cramer-Rao Lower Bound19mComputational Simplifications for the CRLB14mThe Weak Law of Large Numbers22mThe Central Limit Theorem22mLarge Sample Properties of MLEs21m

5 readings

Video Slides for Fisher Information and the Cramér-Rao Lower Bound10mVideo Slides for Computational Simplifications for the CRLB10mVideo Slides for The Weak Law of Large Numbers10mVideo Slides for The Central Limit Theorem10mVideo Slides for Large Sample Properties of MLEs10m

2 practice exercises

The Cramer-Rao Lower Bound30mFurther Computations with MLEs30m

Week4

Week 4

6 hours to complete

Confidence Intervals Involving the Normal Distribution

6 hours to complete

5 videos (Total 99 min), 5 readings, 3 quizzes

5 videos

Let's Build a Confidence Interval!19mThe Chi-Squared and t- Distributions27mt-Distribution Confidence Intervals20mConfidence Intervals for the Difference Between Population Means11mSmall Sample Confidence Intervals for the Difference Between Population Means20m

5 readings

Video Slides for Let's Build a Confidence Interval!10mVideo Slides for the Chi-Squared and t-Distributions10mVideo Slides for t-Distribution Confidence Intervals10mVideo Slides for Confidence Intervals for the Difference Between Population Means10mVideo Slides for Small Sample Confidence Intervals for the Difference Between Population Means10m

2 practice exercises

Confidence Intervals Involving the Normal Distribution30mConfidence Intervals for Differences Between Means30m

About the Data Science Foundations: Statistical Inference Specialization

This program is designed to provide the learner with a solid foundation in probability theory to prepare for the broader study of statistics. It will also introduce the learner to the fundamentals of statistics and statistical theory and will equip the learner with the skills required to perform fundamental statistical analysis of a data set in the R programming language.

This specialization 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.

Data Science Foundations: Statistical Inference

Frequently Asked Questions

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Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
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What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

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Statistical Inference for Estimation in Data Science

About this Course

What you will learn