One-Dimensional Random Field Theory

rft1d is a Python package for exploring and validating Random Field Theory (RFT) expectations regarding upcrossings in univariate and multivariate 1D continua. These expectations can be used to make statistical inferences regarding signals observed in experimentally measured 1D continua including scalar and vector time series.

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Please cite:

Pataky TC (2016) rft1d: Smooth One-Dimensional Random Field Upcrossing Probabilities in Python. Journal of Statistical Software 71 : i07. http://dx.doi.org/10.18637/jss.v071.i07

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Support

Please submit bug reports and questions to rft1d’s GitHub site.

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Contents

• Download
  • Automated installation
  • Source code download
  • Release Notes
  • License information
  • License agreement for rft1d
• RFT Overview
  • Gaussian random fields
  • Expected field maximum
  • Upcrossings
  • Expected upcrossing geometry

• Examples
  • Basic
    • Generating 1D Gaussian fields
    • Reproducing 1D Gaussian fields
    • Node-based vs. element-based sampling
    • Extracting maxima
    • Computing upcrossing metrics
    • Checking RFT expectations
    • Validating RFT expectations
  • Broken fields
    • Broken field generation
    • Validations for broken fields
  • Validation
    • Field maxima (Gaussian)
    • Set-level inference (Gaussian)
    • Cluster-level inference (Gaussian)
    • Test statistic field maxima
    • Conjugation analysis
  • Application
    • Example dataset
    • Parametric inference using RFT
    • Non-parametric inference
    • Field wrapping
  • Results from the paper
  • Scripts (overview)
    • Random field generation
    • Broken random field generation
    • Field smoothness estimation
    • Validation (conjunction analysis)
    • Validation (field maxima)
    • Validation (upcrossing extents)
    • Example application

• API
  • rft1d.data
  • rft1d.distributions
  • rft1d.geom
  • rft1d.prob
  • rft1d.random
• References
  • On the web
  • Software
  • Literature