Bayesian Statistics: Techniques and Models
Description
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About this course: 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 ex…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan .
- Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
- Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.
About this course: 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.
Created by: University of California, Santa Cruz-
Taught by: Matthew Heiner, Doctoral Student
Applied Mathematics and Statistics
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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.Syllabus
WEEK 1
Statistical modeling and Monte Carlo estimation
Statistical modeling, Bayesian modeling, Monte Carlo estimation
11 videos, 4 readings expand
- Video: Course introduction
- Материал для самостоятельного изучения: Module 1 assignments and materials
- Video: Objectives
- Video: Modeling process
- Вопрос для обсуждения: Statistical modeling process
- Video: Components of Bayesian models
- Video: Model specification
- Video: Posterior derivation
- Video: Non-conjugate models
- Материал для самостоятельного изучения: Reference: Common probability distributions
- Video: Monte Carlo integration
- Video: Monte Carlo error and marginalization
- Video: Computing examples
- Video: Computing Monte Carlo error
- Материал для самостоятельного изучения: Code for Lesson 3
- Материал для самостоятельного изучения: Markov chains
Graded: Lesson 1
Graded: Lesson 2
Graded: Lesson 3
Graded: Markov chains
WEEK 2
Markov chain Monte Carlo (MCMC)
Metropolis-Hastings, Gibbs sampling, assessing convergence
11 videos, 7 readings expand
- Материал для самостоятельного изучения: Module 2 assignments and materials
- Video: Algorithm
- Video: Demonstration
- Video: Random walk example, Part 1
- Video: Random walk example, Part 2
- Материал для самостоятельного изучения: Code for Lesson 4
- Video: Download, install, setup
- Video: Model writing, running, and post-processing
- Материал для самостоятельного изучения: Alternative MCMC software
- Материал для самостоятельного изучения: Code from JAGS introduction
- Video: Multiple parameter sampling and full conditional distributions
- Video: Conditionally conjugate prior example with Normal likelihood
- Video: Computing example with Normal likelihood
- Материал для самостоятельного изучения: Code for Lesson 5
- Video: Trace plots, autocorrelation
- Материал для самостоятельного изучения: Autocorrelation
- Video: Multiple chains, burn-in, Gelman-Rubin diagnostic
- Материал для самостоятельного изучения: Code for Lesson 6
Graded: Lesson 4
Graded: Lesson 5
Graded: Lesson 6
Graded: MCMC
WEEK 3
Common statistical models
Linear regression, ANOVA, logistic regression, multiple factor ANOVA
11 videos, 5 readings expand
- Материал для самостоятельного изучения: Module 3 assignments and materials
- Video: Introduction to linear regression
- Video: Setup in R
- Video: JAGS model (linear regression)
- Video: Model checking
- Video: Alternative models
- Video: Deviance information criterion (DIC)
- Материал для самостоятельного изучения: Code for Lesson 7
- Video: Introduction to ANOVA
- Video: One way model using JAGS
- Материал для самостоятельного изучения: Code for Lesson 8
- Video: Introduction to logistic regression
- Video: JAGS model (logistic regression)
- Video: Prediction
- Вопрос для обсуждения: Why linear models?
- Материал для самостоятельного изучения: Code for Lesson 9
- Материал для самостоятельного изучения: Multiple factor ANOVA
Graded: Lesson 7 Part A
Graded: Lesson 7 Part B
Graded: Lesson 8
Graded: Lesson 9
Graded: Common models and multiple factor ANOVA
WEEK 4
Count data and hierarchical modeling
Poisson regression, hierarchical modeling
10 videos, 7 readings expand
- Материал для самостоятельного изучения: Module 4 assignments and materials
- Video: Introduction to Poisson regression
- Video: JAGS model (Poisson regression)
- Video: Predictive distributions
- Материал для самостоятельного изучения: Prior sensitivity analysis
- Материал для самостоятельного изучения: Code for Lesson 10
- Video: Correlated data
- Материал для самостоятельного изучения: Normal hierarchical model
- Video: Prior predictive simulation
- Video: JAGS model and model checking (hierarchical modeling)
- Video: Posterior predictive simulation
- Video: Linear regression example
- Video: Linear regression example in JAGS
- Материал для самостоятельного изучения: Applications of hierarchical modeling
- Вопрос для обсуждения: Selecting prior distributions
- Материал для самостоятельного изучения: Code and data for Lesson 11
- Материал для самостоятельного изучения: Mixture model introduction, data, and code
- Video: Mixture model in JAGS
Graded: Lesson 10
Graded: Lesson 11 Part A
Graded: Lesson 11 Part B
Graded: Predictive distributions and mixture models
WEEK 5
Capstone project
Peer-reviewed data analysis project
1 video, 1 reading expand
- Video: Course conclusion
- Материал для самостоятельного изучения: Further reading and acknowledgements
Graded: Data Analysis Project
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