posterior_contraction

bayesflow.diagnostics.posterior_contraction(estimates: ~collections.abc.Mapping[str, ~numpy.ndarray] | ~numpy.ndarray, targets: ~collections.abc.Mapping[str, ~numpy.ndarray] | ~numpy.ndarray, variable_keys: ~collections.abc.Sequence[str] = None, variable_names: ~collections.abc.Sequence[str] = None, aggregation: ~collections.abc.Callable = <function median>) → dict[str, any]

Computes the posterior contraction (PC) from prior to posterior for the given samples.

Parameters:

estimatesnp.ndarray of shape (num_datasets, num_draws_post, num_variables)

Posterior samples, comprising num_draws_post random draws from the posterior distribution for each data set from num_datasets.

targetsnp.ndarray of shape (num_datasets, num_variables)

Prior samples, comprising num_datasets ground truths.

variable_keysSequence[str], optional (default = None)

Select keys from the dictionaries provided in estimates and targets. By default, select all keys.

variable_namesSequence[str], optional (default = None)

Optional variable names to show in the output.

aggregationcallable, optional (default = np.median)

Function to aggregate the PC across draws. Typically np.mean or np.median.

Returns:

resultdict

Dictionary containing:

• “values”float or np.ndarray

  The aggregated posterior contraction per variable

• “metric_name”str

  The name of the metric (“Posterior Contraction”).

• “variable_names”str

  The (inferred) variable names.

Notes

Posterior contraction measures the reduction in uncertainty from the prior to the posterior. Values close to 1 indicate strong contraction (high reduction in uncertainty), while values close to 0 indicate low contraction.