arviz.loo_pit#

arviz.loo_pit(idata=None, *, y=None, y_hat=None, log_weights=None)[source]#

Compute leave one out (PSIS-LOO) probability integral transform (PIT) values.

Parameters:

idata: InferenceData: arviz.InferenceData object.
y: array, DataArray or str: Observed data. If str, idata must be present and contain the observed data group
y_hat: array, DataArray or str: Posterior predictive samples for y. It must have the same shape as y plus an extra dimension at the end of size n_samples (chains and draws stacked). If str or None, idata must contain the posterior predictive group. If None, y_hat is taken equal to y, thus, y must be str too.
log_weights: array or DataArray: Smoothed log_weights. It must have the same shape as y_hat
dask_kwargsdict, optional: Dask related kwargs passed to wrap_xarray_ufunc().

Returns:

loo_pit: array or DataArray: Value of the LOO-PIT at each observed data point.

See also

plot_loo_pit: Plot Leave-One-Out probability integral transformation (PIT) predictive checks.
loo: Compute Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO-CV).
plot_elpd: Plot pointwise elpd differences between two or more models.
plot_khat: Plot Pareto tail indices for diagnosing convergence.

Examples

Calculate LOO-PIT values using as test quantity the observed values themselves.

In [1]: import arviz as az
   ...: data = az.load_arviz_data("centered_eight")
   ...: az.loo_pit(idata=data, y="obs")
   ...: 
Out[1]: 
array([0.94351854, 0.63801199, 0.31667553, 0.58227349, 0.29535953,
       0.40245763, 0.90248636, 0.65535611])

Calculate LOO-PIT values using as test quantity the square of the difference between each observation and mu. Both y and y_hat inputs will be array-like, but idata will still be passed in order to calculate the log_weights from there.

In [2]: T = data.observed_data.obs - data.posterior.mu.median(dim=("chain", "draw"))
   ...: T_hat = data.posterior_predictive.obs - data.posterior.mu
   ...: T_hat = T_hat.stack(__sample__=("chain", "draw"))
   ...: az.loo_pit(idata=data, y=T**2, y_hat=T_hat**2)
   ...: 
Out[2]: 
<xarray.DataArray (school: 8)> Size: 64B
array([0.87362668, 0.24372043, 0.35747353, 0.14990468, 0.4351767 ,
       0.2213341 , 0.77505937, 0.29666314])
Coordinates:
  * school   (school) <U16 512B 'Choate' 'Deerfield' ... 'Mt. Hermon'