This course is part of the Bayesian Statistics Specialization

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Herbert Lee

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Bayesian Statistics SpecializationUniversity of California, Santa Cruz

About this Course

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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.

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Course 1 of 5 in the

Bayesian Statistics Specialization

Intermediate Level

Approx. 12 hours to complete

English

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Skills you will gain

Statistics
Bayesian Statistics
Bayesian Inference
R Programming

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.

Course 1 of 5 in the

Bayesian Statistics Specialization

Intermediate Level

Approx. 12 hours to complete

English

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Instructor

Instructor rating

4.58/5 (455 Ratings)

Herbert Lee

Offered by

University of California, Santa Cruz

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Syllabus - What you will learn from this course

Content Rating91%(10,755 ratings)

Week

Week 1

3 hours to complete

Probability and Bayes' Theorem

In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.

3 hours to complete

8 videos (Total 38 min), 4 readings, 5 quizzes

8 videos

Course introduction4m

Lesson 1.1 Classical and frequentist probability6m

Lesson 1.2 Bayesian probability and coherence3m

Lesson 2.1 Conditional probability4m

Lesson 2.2 Bayes' theorem6m

Lesson 3.1 Bernoulli and binomial distributions5m

Lesson 3.2 Uniform distribution5m

Lesson 3.3 Exponential and normal distributions2m

4 readings

Module 1 objectives, assignments, and supplementary materials3m

Background for Lesson 110m

Supplementary material for Lesson 23m

Supplementary material for Lesson 320m

5 practice exercises

Lesson 1: Demonstrate your knowledge30m

Lesson 2: Demonstrate your knowledge12m

Lesson 3.1: Demonstrate your knowledge30m

Lesson 3.2-3.3: Demonstrate your knowledge10m

Module 1 Honors15m

Week

Week 2

3 hours to complete

Statistical Inference

This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives. Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data. Lesson 5 introduces the fundamentals of Bayesian inference. Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayes’ theorem to update the prior with data to obtain posterior probabilities. This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals.

3 hours to complete

11 videos (Total 59 min), 5 readings, 4 quizzes

11 videos

Lesson 4.1 Confidence intervals4m

Lesson 4.2 Likelihood function and maximum likelihood7m

Lesson 4.3 Computing the MLE3m

Lesson 4.4 Computing the MLE: examples4m

Introduction to R6m

Plotting the likelihood in R4m

Plotting the likelihood in Excel4m

Lesson 5.1 Inference example: frequentist4m

Lesson 5.2 Inference example: Bayesian6m

Lesson 5.3 Continuous version of Bayes' theorem4m

Lesson 5.4 Posterior intervals7m

5 readings

Module 2 objectives, assignments, and supplementary materials3m

Background for Lesson 410m

Supplementary material for Lesson 45m

Background for Lesson 510m

Supplementary material for Lesson 510m

4 practice exercises

Lesson 4: Demonstrate your knowledge8m

Lesson 5.1-5.2: Demonstrate your knowledge30m

Lesson 5.3-5.4: Demonstrate your knowledge30m

Module 2 Honors6m

Week

Week 3

3 hours to complete

Priors and Models for Discrete Data

In this module, you will learn methods for selecting prior distributions and building models for discrete data. Lesson 6 introduces prior selection and predictive distributions as a means of evaluating priors. Lesson 7 demonstrates Bayesian analysis of Bernoulli data and introduces the computationally convenient concept of conjugate priors. Lesson 8 builds a conjugate model for Poisson data and discusses strategies for selection of prior hyperparameters.

3 hours to complete

9 videos (Total 66 min), 2 readings, 4 quizzes

9 videos

Lesson 6.1 Priors and prior predictive distributions3m

Lesson 6.2 Prior predictive: binomial example5m

Lesson 6.3 Posterior predictive distribution4m

Lesson 7.1 Bernoulli/binomial likelihood with uniform prior3m

Lesson 7.2 Conjugate priors4m

Lesson 7.3 Posterior mean and effective sample size7m

Data analysis example in R12m

Data analysis example in Excel16m

Lesson 8.1 Poisson data8m

2 readings

Module 3 objectives, assignments, and supplementary materials3m

R and Excel code from example analysis10m

4 practice exercises

Lesson 6: Demonstrate your knowledge30m

Lesson 7: Demonstrate your knowledge15m

Lesson 8: Demonstrate your knowledge15m

Module 3 Honors8m

Week

Week 4

3 hours to complete

Models for Continuous Data

This module covers conjugate and objective Bayesian analysis for continuous data. Lesson 9 presents the conjugate model for exponentially distributed data. Lesson 10 discusses models for normally distributed data, which play a central role in statistics. In Lesson 11, we return to prior selection and discuss ‘objective’ or ‘non-informative’ priors. Lesson 12 presents Bayesian linear regression with non-informative priors, which yield results comparable to those of classical regression.

3 hours to complete

9 videos (Total 69 min), 5 readings, 5 quizzes

9 videos

Lesson 9.1 Exponential data4m

Lesson 10.1 Normal likelihood with variance known3m

Lesson 10.2 Normal likelihood with variance unknown3m

Lesson 11.1 Non-informative priors8m

Lesson 11.2 Jeffreys prior3m

Linear regression in R17m

Linear regression in Excel (Analysis ToolPak)13m

Linear regression in Excel (StatPlus by AnalystSoft)14m

Conclusion1m

5 readings

Module 4 objectives, assignments, and supplementary materials3m

Supplementary material for Lesson 1010m

Supplementary material for Lesson 115m

Background for Lesson 1210m

R and Excel code for regression5m

5 practice exercises

Lesson 9: Demonstrate your knowledge12m

Lesson 10: Demonstrate your knowledge20m

Lesson 11: Demonstrate your knowledge10m

Regression: Demonstrate your knowledge15m

Module 4 Honors6m

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TOP REVIEWS FROM BAYESIAN STATISTICS: FROM CONCEPT TO DATA ANALYSIS

by MTJul 18, 2017

Exceptional course on probabilities and statistics from a Bayesian point of view. I would recommend this course to anyone wishing to learn more about probabilities and statistics.

by JHJun 26, 2018

Great course. The content moves at a nice pace and the videos are really good to follow. The Quizzes are also set at a good level. You can't pass this course unless you have understood the material.

by BUMay 24, 2020

This was an invaluable learning experience. I was delighted to go through this learning.

I strongly suggest this course to anyone who wants to learn or refresh their statistics knowledge.

by AOJul 20, 2020

Prof. Lee's approach is simple and intuitive. There are exercises throughout the videos, which help you make sure you and the professor are on the same track. I would certainly recommend it!

View all reviews

About the Bayesian Statistics Specialization

This Specialization is intended for all learners seeking to develop proficiency in statistics, Bayesian statistics, Bayesian inference, R programming, and much more. Through four complete courses (From Concept to Data Analysis; Techniques and Models; Mixture Models; Time Series Analysis) and a culminating project, you will cover Bayesian methods — such as conjugate models, MCMC, mixture models, and dynamic linear modeling — which will provide you with the skills necessary to perform analysis, engage in forecasting, and create statistical models using real-world data.

Frequently Asked Questions

When will I have access to the lectures and assignments?
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:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
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.
What are the pre-requisites for this course?
You should have exposure to the concepts from a basic statistics class (for example, probability, the Central Limit Theorem, confidence intervals, linear regression) and calculus (integration and differentiation), but it is not expected that you remember how to do all of these items. The course will provide some overview of the statistical concepts, which should be enough to remind you of the necessary details if you've at least seen the concepts previously. On the calculus side, the lectures will include some use of calculus, so it is important that you understand the concept of an integral as finding the area under a curve, or differentiating to find a maximum, but you will not be required to do any integration or differentiation yourself.
What computing resources are expected for this course?
Data analysis is done using computer software. This course provides the option of Excel or R. Equivalent content is provided for both options. A very brief introduction to R is provided for people who have never used it before, but this is not meant to be a course on R. Learners using Excel are expected to already have basic familiarity of Excel.

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Bayesian Statistics: From Concept to Data Analysis

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