arviz.psens#

arviz.psens(data, *, component='prior', component_var_names=None, component_coords=None, var_names=None, coords=None, filter_vars=None, delta=0.01, dask_kwargs=None)[source]#

Compute power-scaling sensitivity diagnostic.

Power-scales the prior or likelihood and calculates how much the posterior is affected.

Parameters:

dataobj: Any object that can be converted to an arviz.InferenceData object. Refer to documentation of arviz.convert_to_dataset() for details. For ndarray: shape = (chain, draw). For n-dimensional ndarray transform first to dataset with az.convert_to_dataset.
component{“prior”, “likelihood”}, default “prior”: When component is “likelihood”, the log likelihood values are retrieved from the log_likelihood group as pointwise log likelihood and added together. With “prior”, the log prior values are retrieved from the log_prior group.
component_var_namesstr, optional: Name of the prior or log likelihood variables to use
component_coordsdict, optional: Coordinates defining a subset over the component element for which to compute the prior sensitivity diagnostic.
var_nameslist of str, optional: Names of posterior variables to include in the power scaling sensitivity diagnostic
coordsdict, optional: Coordinates defining a subset over the posterior. Only these variables will be used when computing the prior sensitivity.
filter_vars: {None, “like”, “regex”}, default None: If None (default), interpret var_names as the real variables names. If “like”, interpret var_names as substrings of the real variables names. If “regex”, interpret var_names as regular expressions on the real variables names.
deltafloat: Value for finite difference derivative calculation.
dask_kwargsdict, optional: Dask related kwargs passed to wrap_xarray_ufunc().

Returns:

xarray.Dataset: Returns dataset of power-scaling sensitivity diagnostic values. Higher sensitivity values indicate greater sensitivity. Prior sensitivity above 0.05 indicates informative prior. Likelihood sensitivity below 0.05 indicates weak or nonin-formative likelihood.

Notes

The diagnostic is computed by power-scaling the specified component (prior or likelihood) and determining the degree to which the posterior changes as described in [1]. It uses Pareto-smoothed importance sampling to avoid refitting the model.

References

[1]

Kallioinen et al, Detecting and diagnosing prior and likelihood sensitivity with power-scaling, 2022, https://arxiv.org/abs/2107.14054

Examples

Compute the likelihood sensitivity for the non centered eight model:

In [1]: import arviz as az
   ...: data = az.load_arviz_data("non_centered_eight")
   ...: az.psens(data, component="likelihood")
   ...: 
Out[1]: 
<xarray.Dataset> Size: 656B
Dimensions:  (school: 8)
Coordinates:
  * school   (school) <U16 512B 'Choate' 'Deerfield' ... 'Mt. Hermon'
Data variables:
    mu       float64 8B 0.09673
    theta_t  (school) float64 64B 0.03804 0.01805 0.01727 ... 0.04732 0.007672
    tau      float64 8B 0.03095
    theta    (school) float64 64B 0.07747 0.08618 0.03315 ... 0.08787 0.03992

To compute the prior sensitivity, we need to first compute the log prior at each posterior sample. In our case, we know mu has a normal prior \(N(0, 5)\), tau is a half cauchy prior with scale/beta parameter 5, and theta has a standard normal as prior. We add this information to the log_prior group before computing powerscaling check with psens

In [2]: from xarray_einstats.stats import XrContinuousRV
   ...: from scipy.stats import norm, halfcauchy
   ...: post = data.posterior
   ...: log_prior = {
   ...:     "mu": XrContinuousRV(norm, 0, 5).logpdf(post["mu"]),
   ...:     "tau": XrContinuousRV(halfcauchy, scale=5).logpdf(post["tau"]),
   ...:     "theta_t": XrContinuousRV(norm, 0, 1).logpdf(post["theta_t"]),
   ...: }
   ...: data.add_groups({"log_prior": log_prior})
   ...: az.psens(data, component="prior")
   ...: 
Out[2]: 
<xarray.Dataset> Size: 656B
Dimensions:  (school: 8)
Coordinates:
  * school   (school) <U16 512B 'Choate' 'Deerfield' ... 'Mt. Hermon'
Data variables:
    mu       float64 8B 0.1106
    theta_t  (school) float64 64B 0.1282 0.08115 0.06867 ... 0.1025 0.08952
    tau      float64 8B 0.06421
    theta    (school) float64 64B 0.1684 0.07522 0.06509 ... 0.1197 0.09038