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Lessons

  • 0. Setting up computing resources
  • 1. Probability and the logic of scientific reasoning
  • 2. Introduction to Bayesian modeling
  • 3. Plotting posteriors
  • 4. Marginalization by numerical quadrature
  • 5. Conjugacy
  • E1. To be completed after lesson 5
  • 6. Parameter estimation by optimization
  • E2. To be completed after lesson 6
  • 7. Introduction to Markov chain Monte Carlo
  • 8. Introduction to MCMC with Stan
  • 9. Mixture models and label switching with MCMC
  • 10. Variate-covariate models with MCMC
  • E3. To be completed after lesson 10
  • 11. Display of MCMC results
  • 12. Model building with prior predictive checks
  • 13. Posterior predictive checks
  • E4. To be completed after lesson 13
  • 14. Collector’s box of distributions
  • 15. MCMC diagnostics
  • 16. A diagnostics case study: Artificial funnel of hell
  • E5. To be completed after lesson 16
  • 17. Model comparison
  • 18. Model comparison in practice
  • E6. To be completed after lesson 18
  • 19. Hierarchical models
  • 20. Implementation of hierarchical models
  • E7. To be completed after lesson 20
  • 21. Principled analysis pipelines
  • 22: Simulation based calibration and related checks in practice
  • E8. To be completed after lesson 22
  • 23. Introduction to Gaussian processes
  • 24. Implementation of Gaussian processes
    • Gaussian process hyperparameters by optimization
    • MCMC with GPs with Normal likelihoods
    • Calculating derivatives from data with GPs
    • Gaussian processes with non-Normal likelihoods
  • 25. Variational Bayesian inference
  • E9. To be completed after lesson 25
  • 26: Wrap-up

Homework

  • 1. Intuitive generative modeling
  • 2. Analytical and graphical methods for analysis of the posterior
  • 3. Maximum a posteriori parameter estimation
  • 4. Sampling with MCMC
  • 5. Inference with Stan
  • 6. MCMC with ion channels
  • 7. Model comparison
  • 8. Hierarchical models
  • 9. Principled pipelines and/or VI and/or hierarchical modeling
  • 10. The grand finale

Schedule

  • Schedule overview
  • Homework due dates
  • Lesson exercise due dates
  • Weekly schedule

Policies

  • Meetings
  • Lab sessions
  • Submission of assignments
  • Lessons and lesson exercises
  • Homework
  • Grading
  • Collaboration policy and Honor Code
  • Course communications
  • “Ediquette”

Resources

  • Software
  • Reading/tutorials
BE/Bi 103 b
  • 24. Implementation of Gaussian processes
  • View page source

24. Implementation of Gaussian processes

  • Gaussian process hyperparameters by optimization
  • MCMC with GPs with Normal likelihoods
  • Calculating derivatives from data with GPs
  • Gaussian processes with non-Normal likelihoods
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Last updated on Feb 20, 2025.

© 2014–2024 Justin Bois and BE/Bi 103 b course staff. With the exception of pasted graphics, where the source is noted, this work is licensed under a Creative Commons Attribution License CC-BY 4.0 license. All code contained herein is licensed under an MIT license.

This document was prepared at Caltech with financial support from the Donna and Benjamin M. Rosen Bioengineering Center.



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