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Statistical Inference for Estimation in Data Science
  • Level Professional
  • Duration 28 hours
  • Course by University of Colorado Boulder
  • Offered by

About

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.

Modules

Welcome to the Course!

    • 1 Videos
    • 4 Readings
    • 1 Lab
Show info about module content

1 Labs

  • An Introduction to Jupyter Notebooks and R

1 Videos

  • Welcome to Statistical Inference

4 Readings

  • Welcome to Statistical Inference
  • Earn Academic Credit for your Work!
  • Course Support
  • Course Resources and Reading

Lesson 1: Review of Discrete and Continuous Random Variables

    • 2 Videos
    • 3 Readings
    • 2 Quiz
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2 Videos

  • Discrete Random Variables and Probability Mass Functions
  • Continuous Random Variables and Probability Density Functions

3 Readings

  • Important Discrete Distributions
  • Important Continuous Distributions
  • Table Summarizing Important Distributions

2 Quiz

  • Recognizing Discrete Distributions
  • Calculations with Continuous Distributions

Lesson 2: Joint Distributions

    • 1 Videos
    • 1 Readings
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1 Videos

  • Joint Distributions and Independence

1 Readings

  • Joint Distributions

Lesson 3: The Gamma Distribution

    • 1 Videos
    • 1 Readings
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1 Videos

  • The Gamma Distribution

1 Readings

  • Video Slides: The Gamma Distribution

Lesson 4: Transformations of Distributions

    • 1 Videos
    • 1 Readings
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1 Videos

  • Transformations of Distributions

1 Readings

  • Video Slides for Transformations of Distributions

Lesson 5: Expectation and Properties of Expectation

    • 1 Videos
    • 1 Readings
    • 1 Quiz
Show info about module content

1 Videos

  • Expectation and Properties of Expectation

1 Readings

  • Video Slides for Expectation and Properties of Expectation

1 Quiz

  • Probability, Expectation, and Variance

Lesson 6: Variance and Covariance

    • 1 Videos
    • 1 Readings
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1 Videos

  • Variance and Covariance

1 Readings

  • Video Slides for Variance and Covariance

Lesson 7: Estimators and Sampling Distributions

    • 1 Videos
    • 1 Readings
    • 1 Lab
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1 Labs

  • The Shape of Data

1 Videos

  • Estimators and Sampling Distributions

1 Readings

  • Video Slides for Estimators and Sampling Distributions

Lesson 8: Distributions of Sums

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Distributions of Sums

1 Readings

  • Video Slides for Distributions of Sums

Lesson 9: Method of Moments Estimators

    • 1 Videos
    • 1 Readings
    • 1 Quiz
Show info about module content

1 Videos

  • Method of Moments Estimators

1 Readings

  • Video Slides for Method of Moments Estimators

1 Quiz

  • Method of Moments Estimation

Module One Summary Assignment

    • 1 Programming
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1 Programming

  • Point Estimation

Lesson 1: A Motivating Example

    • 1 Videos
    • 1 Readings
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1 Videos

  • A Motivating Example

1 Readings

  • Video Slides for A Motivating Example

Lesson 2: Notation, Terminology, and First Complete Examples

    • 1 Videos
    • 1 Readings
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1 Videos

  • Notation, Terminology, and First Complete Examples

1 Readings

  • Video Slides for Notation, Terminology, and First Complete Examples

Lesson 3: Multiple Parameters and Parameters in the Support of a Distribution

    • 1 Videos
    • 1 Readings
    • 1 Quiz
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1 Videos

  • MLEs for Multiple and Support Parameters

1 Readings

  • Video Slides for MLEs for Multiple and Support Parameters

1 Quiz

  • Finding MLEs

Lesson 4: The Invariance Property of Maximum Likelihood Estimators

    • 1 Videos
    • 1 Readings
    • 1 Lab
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1 Labs

  • Sampling Distributions of MLEs

1 Videos

  • The Invariance Property

1 Readings

  • Video Slides for The Invariance Property

Lesson 5: Mean Squared Error, Bias and Relative Efficiency

    • 1 Videos
    • 1 Readings
    • 1 Quiz
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1 Videos

  • Mean Squared Error, Bias, and Relative Efficiency

1 Readings

  • Video Slides for Mean Squared Error, Bias and Relative Efficiency

1 Quiz

  • Invariance, Mean-Squared Error, and Efficiency

Module Two Summary Assignment

    • 1 Programming
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1 Programming

  • Maximum Likelihood Estimation

Lesson 1: Fisher Information and the Cramér-Rao Lower Bound

    • 1 Videos
    • 1 Readings
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1 Videos

  • Fisher Information and the Cramer-Rao Lower Bound

1 Readings

  • Video Slides for Fisher Information and the Cramér-Rao Lower Bound

Lesson 2: Computational Simplifications for the Cramér-Rao Lower Bound

    • 1 Videos
    • 1 Readings
    • 1 Quiz
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1 Videos

  • Computational Simplifications for the CRLB

1 Readings

  • Video Slides for Computational Simplifications for the CRLB

1 Quiz

  • The Cramer-Rao Lower Bound

Lesson 3: Convergence for Sequences of Random Variables

    • 1 Videos
    • 1 Readings
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1 Videos

  • The Weak Law of Large Numbers

1 Readings

  • Video Slides for The Weak Law of Large Numbers

Lesson 4: The Central Limit Theorem

    • 1 Videos
    • 1 Readings
    • 1 Lab
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1 Labs

  • Central Limit Theorem Lab Walkthrough

1 Videos

  • The Central Limit Theorem

1 Readings

  • Video Slides for The Central Limit Theorem

Lesson 5: Properties of Maximum Likelihood Estimators

    • 1 Videos
    • 1 Readings
    • 1 Quiz
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1 Videos

  • Large Sample Properties of MLEs

1 Readings

  • Video Slides for Large Sample Properties of MLEs

1 Quiz

  • Further Computations with MLEs

Module Three Summary Assignment

    • 1 Programming
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1 Programming

  • Large Sample Properties of MLEs

Lesson 1: A Normal Introduction to Confidence Intervals

    • 1 Videos
    • 1 Readings
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1 Videos

  • Let's Build a Confidence Interval!

1 Readings

  • Video Slides for Let's Build a Confidence Interval!

Lesson 2: The t and Chi-Squared Distributions and the Sample Variance

    • 1 Videos
    • 1 Readings
    • 1 Lab
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1 Labs

  • Exploring the Normal, t, and Chi-Squared Relationships

1 Videos

  • The Chi-Squared and t- Distributions

1 Readings

  • Video Slides for the Chi-Squared and t-Distributions

Lesson 3: One Sample Confidence Intervals Based on the t-Distribution

    • 1 Videos
    • 1 Readings
    • 1 Quiz
Show info about module content

1 Videos

  • t-Distribution Confidence Intervals

1 Readings

  • Video Slides for t-Distribution Confidence Intervals

1 Quiz

  • Confidence Intervals Involving the Normal Distribution

Lesson 4: Two Sample Confidence Intervals for Means

    • 1 Videos
    • 1 Readings
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1 Videos

  • Confidence Intervals for the Difference Between Population Means

1 Readings

  • Video Slides for Confidence Intervals for the Difference Between Population Means

Lesson 5: Small Population Confidence Intervals for Differences in Means

    • 1 Videos
    • 1 Readings
    • 1 Quiz
    • 1 Lab
Show info about module content

1 Labs

  • Confidence Intervals in R

1 Videos

  • Small Sample Confidence Intervals for the Difference Between Population Means

1 Readings

  • Video Slides for Small Sample Confidence Intervals for the Difference Between Population Means

1 Quiz

  • Confidence Intervals for Differences Between Means

Module Four Summary Assignment

    • 1 Programming
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1 Programming

  • Normal Distribution Confidence Intervals

Lesson 1: A Confidence Interval for Proportions

    • 1 Videos
    • 1 Readings
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1 Videos

  • A Confidence Interval for Proportions

1 Readings

  • Video Slides for A Confidence Interval for Proportions

Lesson 2: Confidence Intervals for Variances and a Difference of Propoertions

    • 1 Videos
    • 1 Readings
    • 1 Quiz
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1 Videos

  • Confidence Intervals for Variances

1 Readings

  • Video Slides for Confidence Intervals for Variances

1 Quiz

  • Confidence Intervals for Proportions and Variances

Lesson 3: A Confidence Interval for a Ratio of Variances

    • 1 Videos
    • 1 Readings
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1 Videos

  • A Confidence Interval for a Ratio of Variances

1 Readings

  • Video Slides for A Confidence Interval for a Ratio of Variances

Lesson 4: General Confidence Intervals

    • 1 Videos
    • 1 Readings
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1 Videos

  • Who Needs Normality?

1 Readings

  • Video Slides for Who Needs Normality?

Lesson 5: General Confidence Intervals 2

    • 1 Videos
    • 1 Readings
    • 1 Quiz
    • 1 Lab
Show info about module content

1 Labs

  • Non-Normal Confidence Intervals in R

1 Videos

  • General Confidence Intervals 2

1 Readings

  • Video Slides for General Confidence Intervals 2

1 Quiz

  • Build Your Own Confidence Intervals

Auto Summary

"Statistical Inference for Estimation in Data Science" is an advanced course focused on statistical inference, sampling distributions, and confidence intervals. Offered by Coursera, it is part of CU Boulder's MS in Data Science program. The course covers constructing good estimators, method of moments, and maximum likelihood estimation. Designed for professionals in maths, statistics, computer science, and information science, it spans 1680 minutes and offers both Starter and Professional subscription options.

Jem Corcoran
Instructor

Jem Corcoran