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Result Types

Named tuples returned by testing and diagnostic functions.

TestResult

Bases: NamedTuple

Result of a two-sample permutation hypothesis test.

Returned by :func:~divergence.two_sample.permutation_test and related testing functions. Fields can be accessed by name or by index.

Attributes:

Name Type Description
statistic float

The observed test statistic computed on the original (unpermuted) samples.
p_value float

The permutation p-value: the fraction of permuted statistics that are at least as extreme as the observed statistic.
null_distribution ndarray

Array of test-statistic values computed under each permutation of the sample labels, representing the null distribution.

ChainKSDResult

Bases: NamedTuple

Result of per-chain kernel Stein discrepancy analysis.

Returned by :func:~divergence.bayesian.chain_ksd. Each field corresponds to KSD values computed on different subsets of the MCMC output. Small values indicate that the chain's empirical distribution is close to the target.

Attributes:

Name Type Description
ksd_per_chain ndarray

KSD value for each chain, shape (n_chains,).
ksd_split_first ndarray or None

KSD for the first half of each chain, shape (n_chains,). None if split=False was specified.
ksd_split_second ndarray or None

KSD for the second half of each chain, shape (n_chains,). None if split=False was specified.
ksd_pooled float

KSD computed from all chains pooled together.

ChainTestResult

Bases: NamedTuple

Result of pairwise two-sample tests between MCMC chains.

Returned by :func:~divergence.bayesian.chain_two_sample_test. Provides calibrated p-values for the null hypothesis that each pair of chains samples from the same distribution.

Attributes:

Name Type Description
p_value_matrix ndarray

Pairwise p-values, shape (n_chains, n_chains). Diagonal entries are 1.0 (a chain is identical to itself).
statistic_matrix ndarray

Pairwise test statistics, shape (n_chains, n_chains). Diagonal entries are 0.0.
min_p_value float

Minimum off-diagonal p-value across all chain pairs. The most evidence of distributional discrepancy.
any_significant bool

Whether any chain pair has a p-value below 0.05.

MixingDiagnostic

Bases: NamedTuple

Result of transfer-entropy-based mixing diagnostics.

Returned by :func:~divergence.bayesian.mixing_diagnostic. Uses transfer entropy to detect non-stationarity within chains and spurious dependence between chains.

Attributes:

Name Type Description
stationarity_te ndarray

Transfer entropy from the first half to the second half of each chain, shape (n_chains,). Low values indicate stationarity; elevated values suggest the chain has not yet reached its stationary distribution.
cross_chain_te ndarray

Transfer entropy between consecutive chain pairs, shape (n_chains - 1,). Low values indicate independence between chains; elevated values suggest shared non-stationarity or coupling artifacts.