Welcome to statFEM_analysis’s documentation

This is the documentation for code accompanying our error analysis of the Statistical Finite Element Method (StatFEM) 1. This code is hosted on GitHub here.

Instructions for installing and running the code can be found in the “Getting started” section.

In the “Reference Documentation” section there are several notebooks which aim to explain in detail how the code was developed.

In the “Experiments from paper” section the scripts for the numerical experiments can be found. These scripts can be downloaded from here.

Contents:

• Getting started
  • Overview
  • Installation
  • Running the code
• Reference Documentation
  • Building up tools to analyse a 1-D problem
  • Building up tools to analyse a 2-D problem
  • Building up tools to compute an approximation of the 2-Wasserstein distance
  • 1-D prior toy example (RBF covariance)
  • 1-D posterior toy example (RBF covariance)
  • 2-D prior toy example (RBF covariance)
  • 2-D posterior toy example (RBF covariance)
  • Distribution of maximum for 1-D prior example (RBF covariance)
  • Distribution of maximum for 1-D posterior example (RBF covariance)
• Experiments from paper
  • 1-D prior example (Matern-1/2 covariance)
  • 1-D posterior example (Matern-1/2 covariance)
  • 2-D prior example (Matern-1/2 covariance)
  • 2-D posterior example (Matern-1/2 covariance)
  • 1-D max prior example (Matern-1/2 covariance)
  • 1-D max posterior example (Matern-1/2 covariance)
• API Documentation
  • statFEM_analysis package

Indices and tables

• Index

• Module Index

• Search Page

1

Yanni Papandreou, Jon Cockayne, Mark Girolami, and Andrew B Duncan. Theoretical guarantees for the statistical finite element method. arXiv preprint arXiv:2111.07691, 2021. URL: https://arxiv.org/abs/2111.07691.