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Bayesian Statistics: From Concept to Data Analysis
  • Level Professional
  • Duration 12 hours
  • Course by University of California, Santa Cruz
  • Offered by

About

This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses.

Modules

Module overview

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Course introduction

1 Readings

  • Module 1 objectives, assignments, and supplementary materials

Probability

    • 2 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 1: Demonstrate your knowledge

1 Discussions

  • Objectivity

2 Videos

  • Lesson 1.1 Classical and frequentist probability
  • Lesson 1.2 Bayesian probability and coherence

1 Readings

  • Background for Lesson 1

Bayes' theorem

    • 2 Videos
    • 1 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 2: Demonstrate your knowledge

2 Videos

  • Lesson 2.1 Conditional probability
  • Lesson 2.2 Bayes' theorem

1 Readings

  • Supplementary material for Lesson 2

Review of distributions

    • 3 Videos
    • 1 Readings
    • 2 Assignment
Show info about module content

2 Assignment

  • Lesson 3.1: Demonstrate your knowledge
  • Lesson 3.2-3.3: Demonstrate your knowledge

3 Videos

  • Lesson 3.1 Bernoulli and binomial distributions
  • Lesson 3.2 Uniform distribution
  • Lesson 3.3 Exponential and normal distributions

1 Readings

  • Supplementary material for Lesson 3

Probability and Bayes' theorem

    • 1 Assignment
Show info about module content

1 Assignment

  • Module 1 Honors

Module overview

    • 1 Readings
Show info about module content

1 Readings

  • Module 2 objectives, assignments, and supplementary materials

Frequentist inference

    • 7 Videos
    • 2 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 4: Demonstrate your knowledge

7 Videos

  • Lesson 4.1 Confidence intervals
  • Lesson 4.2 Likelihood function and maximum likelihood
  • Lesson 4.3 Computing the MLE
  • Lesson 4.4 Computing the MLE: examples
  • Introduction to R
  • Plotting the likelihood in R
  • Plotting the likelihood in Excel

2 Readings

  • Background for Lesson 4
  • Supplementary material for Lesson 4

Bayesian inference

    • 4 Videos
    • 2 Readings
    • 1 Discussion
    • 2 Assignment
Show info about module content

2 Assignment

  • Lesson 5.1-5.2: Demonstrate your knowledge
  • Lesson 5.3-5.4: Demonstrate your knowledge

1 Discussions

  • Confidence intervals and credible intervals

4 Videos

  • Lesson 5.1 Inference example: frequentist
  • Lesson 5.2 Inference example: Bayesian
  • Lesson 5.3 Continuous version of Bayes' theorem
  • Lesson 5.4 Posterior intervals

2 Readings

  • Background for Lesson 5
  • Supplementary material for Lesson 5

Statistical inference

    • 1 Assignment
Show info about module content

1 Assignment

  • Module 2 Honors

Module overview

    • 1 Readings
Show info about module content

1 Readings

  • Module 3 objectives, assignments, and supplementary materials

Priors

    • 3 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 6: Demonstrate your knowledge

3 Videos

  • Lesson 6.1 Priors and prior predictive distributions
  • Lesson 6.2 Prior predictive: binomial example
  • Lesson 6.3 Posterior predictive distribution

Bernoulli/binomial data

    • 5 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 7: Demonstrate your knowledge

1 Discussions

  • Prior elicitation

5 Videos

  • Lesson 7.1 Bernoulli/binomial likelihood with uniform prior
  • Lesson 7.2 Conjugate priors
  • Lesson 7.3 Posterior mean and effective sample size
  • Data analysis example in R
  • Data analysis example in Excel

1 Readings

  • R and Excel code from example analysis

Poisson data

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 8: Demonstrate your knowledge

1 Videos

  • Lesson 8.1 Poisson data

Priors and models for discrete data

    • 1 Assignment
Show info about module content

1 Assignment

  • Module 3 Honors

Module overview

    • 1 Readings
Show info about module content

1 Readings

  • Module 4 objectives, assignments, and supplementary materials

Exponential data

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 9: Demonstrate your knowledge

1 Videos

  • Lesson 9.1 Exponential data

Normal data

    • 2 Videos
    • 1 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 10: Demonstrate your knowledge

2 Videos

  • Lesson 10.1 Normal likelihood with variance known
  • Lesson 10.2 Normal likelihood with variance unknown

1 Readings

  • Supplementary material for Lesson 10

Alternative priors

    • 2 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
Show info about module content

1 Assignment

  • Lesson 11: Demonstrate your knowledge

1 Discussions

  • A non-informative prior

2 Videos

  • Lesson 11.1 Non-informative priors
  • Lesson 11.2 Jeffreys prior

1 Readings

  • Supplementary material for Lesson 11

Linear regression

    • 3 Videos
    • 2 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Regression: Demonstrate your knowledge

3 Videos

  • Linear regression in R
  • Linear regression in Excel (Analysis ToolPak)
  • Linear regression in Excel (StatPlus by AnalystSoft)

2 Readings

  • Background for Lesson 12
  • R and Excel code for regression

Course conclusion

    • 1 Videos
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1 Videos

  • Conclusion

Models for continuous data

    • 1 Assignment
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1 Assignment

  • Module 4 Honors

Auto Summary

Discover the Bayesian approach to statistics with this comprehensive course in Data Science & AI, led by Coursera. Dive into probability concepts, data analysis, and compare Bayesian with Frequentist methods. Enjoy a blend of lectures, computer demos, and interactive content, using either Microsoft Excel or R. Perfect for professionals, the course spans 720 minutes and offers Starter, Professional, and Paid subscription options.

Herbert Lee
Instructor

Herbert Lee