, ic=None, method='stacking', b_samples=1000, alpha=1, seed=None, scale=None, var_name=None)[source]#

Compare models based on their expected log pointwise predictive density (ELPD).

The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out cross-validation (LOO) or using the widely applicable information criterion (WAIC). We recommend loo. Read more theory here - in a paper by some of the leading authorities on model comparison

compare_dict: dict of {str: InferenceData or ELPDData}

A dictionary of model names and arviz.InferenceData or ELPDData.

ic: str, optional

Method to estimate the ELPD, available options are “loo” or “waic”. Defaults to rcParams["stats.information_criterion"].

method: str, optional

Method used to estimate the weights for each model. Available options are:

  • ‘stacking’ : stacking of predictive distributions.

  • ‘BB-pseudo-BMA’ : pseudo-Bayesian Model averaging using Akaike-type weighting. The weights are stabilized using the Bayesian bootstrap.

  • ‘pseudo-BMA’: pseudo-Bayesian Model averaging using Akaike-type weighting, without Bootstrap stabilization (not recommended).

For more information read

b_samples: int, optional default = 1000

Number of samples taken by the Bayesian bootstrap estimation. Only useful when method = ‘BB-pseudo-BMA’. Defaults to rcParams["stats.ic_compare_method"].

alpha: float, optional

The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. Only useful when method = ‘BB-pseudo-BMA’. When alpha=1 (default), the distribution is uniform on the simplex. A smaller alpha will keeps the final weights more away from 0 and 1.

seed: int or np.random.RandomState instance, optional

If int or RandomState, use it for seeding Bayesian bootstrap. Only useful when method = ‘BB-pseudo-BMA’. Default None the global numpy.random state is used.

scale: str, optional

Output scale for IC. Available options are:

  • log : (default) log-score (after Vehtari et al. (2017))

  • negative_log : -1 * (log-score)

  • deviance : -2 * (log-score)

A higher log-score (or a lower deviance) indicates a model with better predictive accuracy.

var_name: str, optional

If there is more than a single observed variable in the InferenceData, which should be used as the basis for comparison.

A DataFrame, ordered from best to worst model (measured by the ELPD).
The index reflects the key with which the models are passed to this function. The columns are:
rank: The rank-order of the models. 0 is the best.
elpd: ELPD estimated either using (PSIS-LOO-CV elpd_loo or WAIC elpd_waic).

Higher ELPD indicates higher out-of-sample predictive fit (“better” model). If scale is deviance or negative_log smaller values indicates higher out-of-sample predictive fit (“better” model).

pIC: Estimated effective number of parameters.
elpd_diff: The difference in ELPD between two models.

If more than two models are compared, the difference is computed relative to the top-ranked model, that always has a elpd_diff of 0.

weight: Relative weight for each model.

This can be loosely interpreted as the probability of each model (among the compared model) given the data. By default the uncertainty in the weights estimation is considered using Bayesian bootstrap.

SE: Standard error of the ELPD estimate.

If method = BB-pseudo-BMA these values are estimated using Bayesian bootstrap.

dSE: Standard error of the difference in ELPD between each model and the top-ranked model.

It’s always 0 for the top-ranked model.

warning: A value of 1 indicates that the computation of the ELPD may not be reliable.

This could be indication of WAIC/LOO starting to fail see for details.

scale: Scale used for the ELPD.

See also


Compute the ELPD using the Pareto smoothed importance sampling Leave-one-out cross-validation method.


Compute the ELPD using the widely applicable information criterion.


Summary plot for model comparison.



Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017) see


Compare the centered and non centered models of the eight school problem:

Compare the models using PSIS-LOO-CV, returning the ELPD in log scale and calculating the weights using the stacking method.