geweke_test

validation.geweke_test(
    kernel='simple',
    T0=15,
    N=8,
    K=2,
    p=1,
    spatial_W=None,
    spatial_w=None,
    alpha=None,
    X=None,
    y0_pre=None,
    m_iid=20000,
    m_mcmc=20000,
    burn=5000,
    a0=1.0,
    b0=1.0,
    step_rho=0.05,
    rho_support=None,
    beta_prior='horseshoe',
    g_fn=None,
    batch_size=None,
    alpha_level=0.05,
    bonferroni=True,
    seed=None,
    verbose=False,
)

Run the Geweke joint distribution test of the Step-2 sampler.

Defaults mirror the replication package’s Geweke driver: a T0 = 15 x N = 8 panel on a chain graph with w = e_1, K = 2 iid standard-normal covariates, p = 1 latent factor, and standardized synthetic weights drawn N(0, 0.4^2).

Parameters

Name	Type	Description	Default
kernel	('simple', 'production')	`"simple"` tests the appendix’s simplified model (comparable to the R package’s frozen table); `"production"` tests the sampler users actually run. A custom object implementing `draw_prior` / `simulate_data` / `transition` / `state_summary` / `extra_stats` (see :mod:`scspill.validation.kernels`) is accepted.	`"simple"`
T0	int	Panel and model dimensions (ignored for a custom kernel object).	`15`
N	int	Panel and model dimensions (ignored for a custom kernel object).	`15`
K	int	Panel and model dimensions (ignored for a custom kernel object).	`15`
p	int	Panel and model dimensions (ignored for a custom kernel object).	`15`
spatial_W	arrays	Overrides of the toy design; drawn/derived from `seed` when omitted.	`None`
spatial_w	arrays	Overrides of the toy design; drawn/derived from `seed` when omitted.	`None`
alpha	arrays	Overrides of the toy design; drawn/derived from `seed` when omitted.	`None`
X	arrays	Overrides of the toy design; drawn/derived from `seed` when omitted.	`None`
y0_pre	arrays	Overrides of the toy design; drawn/derived from `seed` when omitted.	`None`
m_iid	int	Draw counts of the two simulators and the transition burn-in.	`20000`
m_mcmc	int	Draw counts of the two simulators and the transition burn-in.	`20000`
burn	int	Draw counts of the two simulators and the transition burn-in.	`20000`
a0	sampler settings	Passed to the kernel (`beta_prior` is production-only).	`1.0`
b0	sampler settings	Passed to the kernel (`beta_prior` is production-only).	`1.0`
step_rho	sampler settings	Passed to the kernel (`beta_prior` is production-only).	`1.0`
rho_support	sampler settings	Passed to the kernel (`beta_prior` is production-only).	`1.0`
beta_prior	sampler settings	Passed to the kernel (`beta_prior` is production-only).	`1.0`
g_fn	callable	`g_fn(summary, Yc, y0_pre, Wn, wn) -> dict` replacing :func:`default_g_fn`.	`None`
batch_size	int	Batch length for the MCMC standard error (default `floor(sqrt(m))`).	`None`
alpha_level	float	Familywise test level.	`0.05`
bonferroni	bool	Bonferroni-adjust the critical value across statistics.	`True`
seed	int	Seed for all randomness (design draws included).	`None`
verbose	bool	Print stage progress.	`False`

Returns

Name	Type	Description
	GewekeReport	The per-statistic z table and the pass decision.

Notes

The successive-conditional simulator mixes slowly along two well-known directions, and an under-resolved run flags them as spurious failures:

the rho chain moves only as far per sweep as its data-conditional posterior allows, so informative designs (large T0 * N) make it diffuse slowly – keep the test panel small (e.g. T0=4, N=4);
with K > 0 and p > 0 simultaneously, the X beta and Eta Gamma mean components trade off along a ridge whose relaxation dominates the global data statistics – test the blocks in isolation first, and give joint configurations long chains with a large batch_size;
the production kernel’s half-Cauchy scale hierarchies are funnel-shaped and effectively untestable at feasible chain lengths (the reason the replication package only ever tested the simplified kernel, at two million draws).

A genuine incoherence shows up as a stable, sign-consistent z across seeds and scales; mixing artifacts flip sign and shrink as the chain grows.