About this Course
4.6
1,307 ratings
348 reviews
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100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Intermediate Level

Intermediate Level

Hours to complete

Approx. 21 hours to complete

Suggested: Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics....
Available languages

English

Subtitles: English

Skills you will gain

StatisticsBayesian StatisticsBayesian InferenceR Programming
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Intermediate Level

Intermediate Level

Hours to complete

Approx. 21 hours to complete

Suggested: Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics....
Available languages

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
Hours to complete
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....
Reading
8 videos (Total 38 min), 4 readings, 5 quizzes
Video8 videos
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
Reading4 readings
Module 1 objectives, assignments, and supplementary materials3m
Background for Lesson 110m
Supplementary material for Lesson 23m
Supplementary material for Lesson 320m
Quiz5 practice exercises
Lesson 116m
Lesson 212m
Lesson 3.120m
Lesson 3.2-3.310m
Module 1 Honors15m
Week
2
Hours to complete
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....
Reading
11 videos (Total 59 min), 5 readings, 4 quizzes
Video11 videos
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
Reading5 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
Quiz4 practice exercises
Lesson 48m
Lesson 5.1-5.218m
Lesson 5.3-5.416m
Module 2 Honors6m
Week
3
Hours to complete
2 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....
Reading
9 videos (Total 66 min), 2 readings, 4 quizzes
Video9 videos
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
Reading2 readings
Module 3 objectives, assignments, and supplementary materials3m
R and Excel code from example analysis10m
Quiz4 practice exercises
Lesson 612m
Lesson 715m
Lesson 815m
Module 3 Honors8m
Week
4
Hours to complete
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. ...
Reading
9 videos (Total 69 min), 5 readings, 5 quizzes
Video9 videos
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
Reading5 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
Quiz5 practice exercises
Lesson 912m
Lesson 1020m
Lesson 1110m
Regression15m
Module 4 Honors6m
4.6
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Top Reviews

By GSSep 1st 2017

Good intro to Bayesian Statistics. Covers the basic concepts. Workload is reasonable and quizzes/exercises are helpful. Could include more exercises and additional backgroung/future reading materials.

By JHJun 27th 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.

Instructor

Avatar

Herbert Lee

Professor
Applied Mathematics and Statistics

About University of California, Santa Cruz

UC Santa Cruz is an outstanding public research university with a deep commitment to undergraduate education. It’s a place that connects people and programs in unexpected ways while providing unparalleled opportunities for students to learn through hands-on experience....

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, 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.

  • 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.

  • 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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