NO. 39 · Computational & Data

Uncertainty by Simulation

Sampling as a way of knowing. MCMC, the bootstrap, and posterior checks, then straight to the subsurface: realisations, probabilistic facies, and Bayesian inversion, because every uncertainty you ship was generated by a simulator.

You can build a posterior and sample it with Metropolis, Gibbs, or HMC, bootstrap an answer when formulas run out, check a model against its own predictions, and carry all of it into reservoir realisations and uncertainty-aware inversion without hand-waving.

11 competencies · 6 interactive widget challenges · 7 to 11 hours of guided study

For geoscientists who must put error bars on maps and models

Draws on: 3D Seismic Interpretation Geostatistics Physics-Informed Neural Networks for Exploration Seismology Statistics and Data Science for Researchers

The posterior

Prior, likelihood, posterior

Bayes is bookkeeping for belief; do the mechanics by hand once and conjugate families stop looking like magic.

Reads: Prior, likelihood, posterior, the mechanics Conjugate priors and analytic posteriors

Samplers

Metropolis-Hastings by handwidget challenge

The accept-reject step is the whole trick of modern Bayesian computation; walk it by hand and MCMC is yours for life.

Reads: Metropolis-Hastings by hand

Gibbs and Hamiltonian Monte Carlowidget challenge

Gibbs samples the axes and HMC glides the geometry; between them they run most of the posteriors in modern science.

Reads: Gibbs sampling on a 2D example Hamiltonian Monte Carlo intuition

Checking the model

Posterior-predictive checks and comparisonwidget challenge

A model that cannot reproduce the data it was fit to has nothing to say about data it has not seen; PPCs are the simulation-native honesty test.

Reads: Posterior-predictive checks Model comparison: Bayes factors and WAIC

Resampling

Bootstrap and permutation, properlywidget challenge

Resampling generates the data you wish you had; parametric versus nonparametric and exchangeability are the fine print that keeps it honest.

Reads: Bootstrap, deeper: parametric vs nonparametric Permutation tests and exchangeability

Cross-validation and density estimationwidget challenge

CV is simulation of future data from present data, and KDE is how a histogram grows up; both are workhorses of computational practice.

Reads: Cross-validation done right Kernel density estimation

Quantile methods

When the distribution refuses to behave, quantile regression and distribution-free intervals still deliver defensible statements.

Reads: Quantile regression and distribution-free CIs

Hierarchies

Hierarchical models and shrinkage

Wells within fields within basins: geoscience data is nested by nature, and partial pooling is the honest way to borrow strength across levels.

Reads: Mixed-effects and hierarchical models intro

The subsurface payoff

Realisations into decisions

A stack of simulated reservoirs is uncertainty made tangible; percentile maps and decision metrics are how it earns a seat in the development plan.

Reads: Multiple realisations and uncertainty maps Post-processing realisations into decision metrics

Probabilistic facies

A facies probability at every voxel is a posterior wearing a hard hat; you now know exactly how it was made and how to check it.

Reads: Probabilistic facies classification: uncertainty at every voxel

Bayesian inversion and ensembleswidget challenge

Ensemble and Bayesian PINNs put a distribution where a single velocity model used to stand; this is uncertainty-aware inversion, the destination of the whole path.

Reads: Bayesian PINNs and ensemble PINNs Uncertainty-aware velocity inversion