Bayesian and Probabilistic Methods

Probability as a working tool: Bayes' rule for classification, priors and posteriors in geoscience inference, and uncertainty quantification for physics-informed networks. Each section pairs the math with an interactive example you can perturb.

20 interactive sections across 6 books
Start here → Naive Bayes Practice, from Applied Machine Learning for Geoscientists

Applied Machine Learning for Geoscientists

  1. Naive Bayes Practice
  2. Naive Bayes

Physics-Informed Neural Networks for Exploration Seismology

  1. Bayesian PINNs and ensemble PINNs
  2. Generative priors for velocity models
  3. Uncertainty-aware velocity inversion

Geostatistics

  1. The kriging variance, what it means and what it doesn't
  2. From kriging to simulation: why one map is never enough

Statistics and Data Science for Researchers

  1. Equivalence testing and TOST
  2. Capstone: Bayesian dose-response with MCMC
  3. Exact vs asymptotic CIs
  4. Prior, likelihood, posterior, the mechanics
  5. Type-I, Type-II, power, and effect size
  6. Communicating uncertainty without lying
  7. Posterior-predictive checks
  8. The replication crisis and what to actually do
  9. Conjugate priors and analytic posteriors
  10. Model comparison: Bayes factors and WAIC
  11. Multiple testing: FWER and FDR

3D Seismic Interpretation

  1. Probabilistic facies classification: uncertainty at every voxel

A Mathematician's Survey

  1. Conditional Probability and Independence

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