The trust map

trust_lookup reports what a pre-registered simulation study measured about this estimator in a regime like yours. It is separate from FitResult.reliable, which describes one fit. The study is called h6-v1; its design was frozen at the git tag H6-preregistration before any cell ran.

import hawkes_engine as he

answer = he.trust_lookup(N=2000, rho_hat=0.3028, beta=1.0, T=1722.6)
print(answer.status, answer.cell, answer.distance)

N is the number of events, rho_hat the fitted branching ratio, beta the smallest fitted decay rate, T the observation window, and resolution the timestamp resolution in the units of T (0 for exact times).

The three outcomes

status is one of:

"measured". The query lies inside the measured box. coverage gives, for each block (mu, alpha, beta, all), the share of nominal-95% intervals that covered the truth in the nearest cell over 2000 replications, with its Monte Carlo standard error. A fit that returned no standard error counts as a miss. q gives the ratio of mean reported standard error to empirical standard deviation per block, with a bootstrap standard error; below 1 means the reported standard errors were too small.

"unknown". The query is outside the box, and no number is given. The lookup does not extrapolate, because the study cannot say what happens beyond what it ran.

"estimator undefined in this regime". The nearest cell is one where most fits returned no standard error, or the window held too few decay times for \(\beta\) to be identified. No coverage is reported.

The measured box

Two types (plus a four-type satellite of 8 cells), pair decay, \(\rho \le 0.95\), \(200 \le N \le 50\,000\), \(\beta\delta \le 0.13\) (where \(\delta\) is the timestamp resolution), and \(\beta_{\min}T\) inside the range the grid spans. Anything else returns "unknown" with a note saying which bound was crossed. The map has 128 cells; each was run at one fixed parameter set (studies/theta0.json), so the map describes those parameters at that \((N, \rho, \beta T)\), not every process with the same summary numbers.

How to read `distance`

distance is the Euclidean distance to the nearest cell in grid-step units over \((\log_{10} N,\ \rho,\ r,\ \log_{10}\beta_{\min}T)\), each axis divided by a typical step. 0 is a grid point and 1 is about one step away. The lookup answers however large the distance is. It does not refuse a far-away cell, so a "measured" status with a distance of 2 describes a cell two steps from your regime.

The six hypotheses

The study pre-registered six hypotheses. The table is generated from studies/results/analysis/hypotheses.json when this page is built. Where the admissible readings of a standard error disagreed, the label is the least favourable one any of them gave.

Hypothesis	Status	T	tau	SE	z	p	Holm	Final label
H6.1	exploratory	0.2325	0.05	0.0367	4.98	3.25e-07	outside family	confirmed (exploratory)
H6.2	exploratory	0.171	0.9	0.00842	86.59	<1e-300	outside family	confirmed (exploratory)
H6.3	confirmatory	0.01672	0	0.00589	2.84	0.00224	step 3, 0.025 met	not confirmed
H6.4	confirmatory	-1.696e+07	0.01	3.5e+06	-4.85	1	step 4, 0.05 missed	not confirmed
H6.5	confirmatory	0.7791	1	0.0114	19.35	1.08e-83	step 2, 0.01667 met	confirmed
H6.6	confirmatory	0.7751	0.02	0.0112	67.24	<1e-300	step 1, 0.0125 met	confirmed

H6.5, confirmed. The reported standard errors understate sampling spread. This is the headline result.
H6.6, confirmed but mostly mechanical. The reliable verdict separates coverage because 96.4 percent of unreliable replications carry no standard error, and a replication without one counts as a miss. Among replications that do carry one, a post hoc check gives a separation of about +0.07 +/- 0.04. The verdict marks fits that produced an interval; it does not detect an interval that is wrong.
H6.3, not confirmed. Coverage does not fall monotonically toward criticality.
H6.4, not confirmed. Timestamp quantisation moved the decay estimate downward at \(N \ge 10\,000\), the opposite of the hypothesis.
H6.1 and H6.2, confirmed (exploratory). They replicate a direction found before the study was designed, so they are labelled exploratory and carry no headline.

The paper draft is generated from the same analysis: paper/draft.md. The submission version, with every number generated from the same outputs, is paper/main.tex.

Using the map from a fit

fit(..., se_method="auto") reads this map for you. After the fit it looks the regime up and decides: where an estimated block’s two-standard-error interval around the measured q excludes 1 it switches to the bootstrap, where the map has no measurement it keeps the Hessian interval and says it is uncalibrated, and where the map reports the estimator undefined it reports no interval. The result records which happened in se_source, se_note and auto. The policy is The se_method="auto" policy; the study that measured whether the switch helps is docs/preregistration_auto.md in the repository.