Pareto smoothed importance sampling (PSIS) and PSIS leave-one-out cross-validation for Python and Matlab/Octave
Matlab Python Stan
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README.md

Pareto smoothed importance sampling (PSIS) and PSIS leave-one-out cross-validation reference code

Introduction

These files implement Pareto smoothed importance sampling (PSIS) and PSIS leave-one-out cross-validation for Matlab/Octave and Python (Python port made by Tuomas Sivula).

Corresponding R code

The corresponding R code can be found in R package called `loo' which is also available in CRAN.

Contents

Matlab/Octave code in 'm' folder

  • 'psislw.m' - Pareto smoothing of the log importance weights
  • 'psisloo.m' - Pareto smoothed importance sampling leave-one-out log predictive densities
  • 'gpdfitnew.m' - Estimate the paramaters for the Generalized Pareto Distribution
  • 'sumlogs.m' - Sum of vector where numbers are represented by their logarithms

Python module in 'py' folder

  • 'psis.py' - Includes the following functions in a Python (Numpy) module
    • psislw - Pareto smoothing of the log importance weights
    • psisloo - Pareto smoothed importance sampling leave-one-out log predictive densities
    • gpdfitnew - Estimate the paramaters for the Generalized Pareto Distribution
    • gpinv - Inverse Generalised Pareto distribution function.
    • sumlogs - Sum of vector where numbers are represented by their logarithms

References

  • Aki Vehtari, Andrew Gelman and Jonah Gabry (2016). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, doi:10.1007/s11222-016-9696-4. arXiv preprint arXiv:1507.04544
  • Aki Vehtari, Andrew Gelman and Jonah Gabry (2016). Pareto smoothed importance sampling. arXiv preprint arXiv:1507.02646
  • Jin Zhang & Michael A. Stephens (2009) A New and Efficient Estimation Method for the Generalized Pareto Distribution, Technometrics, 51:3, 316-325, DOI: 10.1198/tech.2009.08017