Stan Development Team

This package implements the methods described in Vehtari, Gelman, and Gabry (2017), Vehtari, Simpson, Gelman, Yao, and Gabry (2019), and Yao et al. (2018). To get started see the loo package vignettes, the loo() function for efficient approximate leave-one-out cross-validation (LOO-CV), the psis() function for the Pareto smoothed importance sampling (PSIS) algorithm, or loo_model_weights() for an implementation of Bayesian stacking of predictive distributions from multiple models.


Leave-one-out cross-validation (LOO-CV) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameter values. LOO-CV and WAIC have various advantages over simpler estimates of predictive error such as AIC and DIC but are less used in practice because they involve additional computational steps. This package implements the fast and stable computations for approximate LOO-CV laid out in Vehtari, Gelman, and Gabry (2017a). From existing posterior simulation draws, we compute LOO-CV using Pareto smoothed importance sampling (PSIS; Vehtari, Simpson, Gelman, Yao, and Gabry, 2019), a new procedure for stabilizing and diagnosing importance weights. As a byproduct of our calculations, we also obtain approximate standard errors for estimated predictive errors and for comparing of predictive errors between two models.

We recommend PSIS-LOO-CV instead of WAIC, because PSIS provides useful diagnostics and effective sample size and Monte Carlo standard error estimates.


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Vehtari, A., Simpson, D., Gelman, A., Yao, Y., and Gabry, J. (2019). Pareto smoothed importance sampling. preprint arXiv:1507.02646

Yao, Y., Vehtari, A., Simpson, D., and Gelman, A. (2018) Using stacking to average Bayesian predictive distributions. Bayesian Analysis, advance publication, doi:10.1214/17-BA1091. (online).

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