Offered By

University of California, Santa Cruz

About this Course

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This is the second of a two-course sequence introducing the fundamentals of Bayesian statistics. It builds on the course Bayesian Statistics: From Concept to Data Analysis, which introduces Bayesian methods through use of simple conjugate models. Real-world data often require more sophisticated models to reach realistic conclusions. This course aims to expand our “Bayesian toolbox” with more general models, and computational techniques to fit them. In particular, we will introduce Markov chain Monte Carlo (MCMC) methods, which allow sampling from posterior distributions that have no analytical solution. We will use the open-source, freely available software R (some experience is assumed, e.g., completing the previous course in R) and JAGS (no experience required). We will learn how to construct, fit, assess, and compare Bayesian statistical models to answer scientific questions involving continuous, binary, and count data. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. The lectures provide some of the basic mathematical development, explanations of the statistical modeling process, and a few basic modeling techniques commonly used by statisticians. Computer demonstrations provide concrete, practical walkthroughs. Completion of this course will give you access to a wide range of Bayesian analytical tools, customizable to your data.

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Suggested: 5 weeks of study, 4-6 hours/week....

Subtitles: English

Gibbs SamplingBayesian StatisticsBayesian InferenceR Programming

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

Suggested: 5 weeks of study, 4-6 hours/week....

Subtitles: English

Week

1Statistical modeling, Bayesian modeling, Monte Carlo estimation...

11 videos (Total 99 min), 4 readings, 4 quizzes

Objectives7m

Modeling process8m

Components of Bayesian models8m

Model specification7m

Posterior derivation9m

Non-conjugate models7m

Monte Carlo integration9m

Monte Carlo error and marginalization6m

Computing examples15m

Computing Monte Carlo error13m

Module 1 assignments and materials3m

Reference: Common probability distributions

Code for Lesson 3

Markov chains20m

Lesson 120m

Lesson 225m

Lesson 330m

Markov chains20m

Week

2Metropolis-Hastings, Gibbs sampling, assessing convergence...

11 videos (Total 129 min), 7 readings, 4 quizzes

Demonstration10m

Random walk example, Part 112m

Random walk example, Part 216m

Download, install, setup3m

Model writing, running, and post-processing12m

Multiple parameter sampling and full conditional distributions8m

Conditionally conjugate prior example with Normal likelihood10m

Computing example with Normal likelihood16m

Trace plots, autocorrelation17m

Multiple chains, burn-in, Gelman-Rubin diagnostic8m

Module 2 assignments and materials3m

Code for Lesson 4

Alternative MCMC software10m

Code from JAGS introduction

Code for Lesson 510m

Autocorrelation10m

Code for Lesson 6

Lesson 420m

Lesson 530m

Lesson 620m

MCMC45m

Week

3Linear regression, ANOVA, logistic regression, multiple factor ANOVA...

11 videos (Total 131 min), 5 readings, 5 quizzes

Setup in R9m

JAGS model (linear regression)12m

Model checking17m

Alternative models10m

Deviance information criterion (DIC)4m

Introduction to ANOVA10m

One way model using JAGS18m

Introduction to logistic regression6m

JAGS model (logistic regression)18m

Prediction15m

Module 3 assignments and materials3m

Code for Lesson 7

Code for Lesson 8

Code for Lesson 9

Multiple factor ANOVA20m

Lesson 7 Part A30m

Lesson 7 Part B30m

Lesson 830m

Lesson 945m

Common models and multiple factor ANOVA30m

Week

4Poisson regression, hierarchical modeling...

10 videos (Total 106 min), 7 readings, 4 quizzes

JAGS model (Poisson regression)17m

Predictive distributions11m

Correlated data8m

Prior predictive simulation10m

JAGS model and model checking (hierarchical modeling)13m

Posterior predictive simulation8m

Linear regression example7m

Linear regression example in JAGS10m

Mixture model in JAGS13m

Module 4 assignments and materials3m

Prior sensitivity analysis20m

Code for Lesson 10

Normal hierarchical model20m

Applications of hierarchical modeling10m

Code and data for Lesson 11

Mixture model introduction, data, and code20m

Lesson 1040m

Lesson 11 Part A40m

Lesson 11 Part B30m

Predictive distributions and mixture models30m

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.

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Is financial aid available?

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