arviz.psislw#

arviz.psislw(log_weights, reff=1.0)[source]#

Pareto smoothed importance sampling (PSIS).

Parameters

log_weights: array: Array of size (n_observations, n_samples)
reff: float: relative MCMC efficiency, ess / n

Returns

lw_out: array: Smoothed log weights
kss: array: Pareto tail indices

See also

loo: Compute Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO-CV).

Notes

If the log_weights input is an DataArray with a dimension named __sample__ (recommended) psislw will interpret this dimension as samples, and all other dimensions as dimensions of the observed data, looping over them to calculate the psislw of each observation. If no __sample__ dimension is present or the input is a numpy array, the last dimension will be interpreted as __sample__.

References

Vehtari et al. (2015) see https://arxiv.org/abs/1507.02646

Examples

Get Pareto smoothed importance sampling (PSIS) log weights:

In [1]: import arviz as az
   ...: data = az.load_arviz_data("centered_eight")
   ...: log_likelihood = data.sample_stats.log_likelihood.stack(
   ...:     __sample__=("chain", "draw")
   ...: )
   ...: az.psislw(-log_likelihood, reff=0.8)
   ...: 
Out[1]: 
(<xarray.DataArray 'log_weights' (school: 8, __sample__: 2000)>
 array([[-7.34995066, -6.32418143, -7.41094349, ..., -8.46666497,
         -6.96363409, -7.14223582],
        [-6.44840009, -7.55679071, -7.18955445, ..., -7.72602726,
         -7.07920345, -7.48188027],
        [-7.76466076, -7.76043872, -7.7644619 , ..., -7.64961779,
         -6.9420515 , -7.5451356 ],
        ...,
        [-7.32584608, -7.76025117, -7.70454826, ..., -7.73877505,
         -7.61780418, -7.74341114],
        [-7.10727871, -6.20091776, -6.42891471, ..., -6.96829636,
         -8.6763585 , -8.42513384],
        [-7.19682912, -7.48004722, -7.48344873, ..., -7.48068176,
         -7.64687783, -7.65904775]])
 Coordinates:
   * school      (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon'
   * __sample__  (__sample__) MultiIndex
   - chain       (__sample__) int64 0 0 0 0 0 0 0 0 0 0 0 ... 3 3 3 3 3 3 3 3 3 3
   - draw        (__sample__) int64 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499,
 <xarray.DataArray 'pareto_shape' (school: 8)>
 array([0.35683758, 0.32524967, 0.53342172, 0.33519276, 0.25373991,
        0.64466503, 0.71238247, 0.28943932])
 Coordinates:
   * school   (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon')

arviz.loo_pit

arviz.r2_score