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Offered By

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

Subtitles: English

StatisticsBayesian StatisticsBayesian InferenceR Programming

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

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

Subtitles: English

Week

1In 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....

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

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

Module 1 objectives, assignments, and supplementary materials3m

Background for Lesson 110m

Supplementary material for Lesson 23m

Supplementary material for Lesson 320m

Lesson 116m

Lesson 212m

Lesson 3.120m

Lesson 3.2-3.310m

Module 1 Honors15m

Week

2This 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....

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

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

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

Lesson 48m

Lesson 5.1-5.218m

Lesson 5.3-5.416m

Module 2 Honors6m

Week

3In 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....

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

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

Module 3 objectives, assignments, and supplementary materials3m

R and Excel code from example analysis10m

Lesson 612m

Lesson 715m

Lesson 815m

Module 3 Honors8m

Week

4This 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.
...

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

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

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

Lesson 912m

Lesson 1020m

Lesson 1110m

Regression15m

Module 4 Honors6m

4.6

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By GS•Sep 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 JH•Jun 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.

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....

When will I have access to the lectures and assignments?

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.

What will I get if I purchase the Certificate?

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.

What is the refund policy?

Is financial aid available?

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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