Parameter-estimation results
Reviewed 20 October 2026. These are restricted two-parameter numerical validation experiments, with all other source and detector parameters fixed. They test whether the implemented likelihood, prior, waveform adapter and sampler recover the intended posterior. They do not establish full-dimensional inference or physical waveform accuracy.
What the experiments test
Parameter estimation (PE) infers a probability distribution for source parameters from data. The posterior combines a waveform-based likelihood with a prior. In these experiments, the injected parameters are known, so numerical recovery can be checked against a separately integrated posterior.
The validation has three distinct stages:
- Reference posterior: refine numerical integration over the complete declared prior. Check the joint density, normalization, marginal probabilities and quantiles. In the completion study, also check common-data Torch/JAX agreement and independent quadrature/CDF calculations.
- Sampler validation: compare actual retained NUTS draws with an accepted reference. Check mixing, effective sample size, Monte Carlo uncertainty, divergences, marginal probabilities and joint posterior structure.
- Ensemble calibration: recover independently generated truths and matched noise across the declared 50-case ensemble. Assess coverage with finite-ensemble simultaneous uncertainty, keeping failed and missing cases in the denominator.
A stage passes only its own frozen checks. A completed process, smooth-looking posterior or injected truth inside one credible interval is insufficient. Zero-noise recovery retains PSD weighting but does not test noisy coverage. Fixed-truth noise repeats also do not constitute a prior-drawn calibration ensemble. See the protocol.
Current results
The original 30 September grid study evaluated 29 waveform/API entries in each frontend: 28 supported waveform scopes and one component-only entry. Each frontend recorded 18 converged grid baselines, 10 unresolved results and one blocked component. Those historical outcomes remain unchanged by later studies.
The completion study has accepted common-data zero-noise references for four models and 17 unique model/condition/frontend sampler records, comprising 272,000 retained draws. These records span four models; they are not 17 qualified waveforms. Rechecking the same record adds no new case or ensemble event. No supported model has completed the entire expanded campaign or its 50-case calibration stage: 0/28.
| Model | Accepted paired zero-noise reference | Accepted individual fixed-noise reference pairs | Accepted Torch sampler cases | Accepted JAX sampler cases |
|---|---|---|---|---|
| IMRPhenomD | Yes | 4 | Zero + fixed 000–003 | Fixed 001, 003 |
| IMRPhenomPv2 | Yes | 4 | Zero | Zero + fixed 000 |
| MemoryWaveform | Yes | 4 | Zero + fixed 000–003 | None |
| NewtonianEccentricEMRI | Yes | None | Zero | Zero |
“Paired” means Torch and JAX analyze common data under the matched prior and likelihood. A sampler case is one frontend's accepted run for one condition; four chains do not count as four cases. Memory's four individual noisy references are accepted, while the combined four-case stage remains incomplete. Historical pilot samples are reported separately and are not added to these counts.
Newtonian's accepted Torch zero-noise case uses four chains, 1,000 warmup steps
and 4,000 retained draws per chain, target acceptance 0.95 and maximum depth 8.
The free parameters are p0 and e0, with independent uniform priors
p0 ∈ [15.5, 16.5], e0 ∈ [0.1, 0.3] and injected values (16, 0.2).
All original sampler gates pass: maximum rank/folded R-hat 1.0029, minimum bulk
ESS 2,688.9, minimum tail ESS 2,884.5, zero retained divergences, and all six
marginal-CDF and nine joint Rosenblatt checks. One warmup divergence is reported
separately. This qualifies that bounded zero-noise sampler case only.
Unresolved results and incomplete stages
| Waveform/API scope | Interpretation of the current evidence |
|---|---|
| TaylorF2, TaylorF2_HM, TaylorF2_Eccentric; IMRPhenomHM, IMRPhenomXAS, IMRPhenomXHM | Original Torch/JAX grid baselines converged. The stricter completion references and sampler/calibration stages are not accepted. |
| IMRPhenomP, IMRPhenomXPNR | Original grids converged; no accepted completion reference or sampler. |
| IMRPhenomXP, IMRPhenomXPHM | Original grids converged. Additional convention/option checks remain unresolved; these do not erase the historical grid outcome. |
| IMRPhenomD_NRTidal | The separate refined-reference and Torch zero-noise NUTS pilots passed. Compiled noisy references accepted 3/4 cases; fixed 002 and a compiled precision check remain unresolved. The original rectangular-grid outcome is still unresolved. |
| IMRPhenomD_NRTidalv2 | Original grid and later independent CDF convergence remain unresolved. No accepted completion reference or sampler. |
| IMRPhenomNSBH | The separate 3841-by-3841 supplement passes both required consecutive refinements, frontend parity and Gauss quadrature. Independent CDF convergence still fails, so the reference is not accepted. |
| IMRPhenomT | Construction and derivative prerequisite checks pass. The completion reference and samplers are not accepted; its original grid result remains unresolved. |
| IMRPhenomTHM | No accepted completion reference or sampler; original grid convergence remains unresolved. |
| IMRPhenomTP, IMRPhenomTPHM | Reference convergence and onset/branch behavior remain unresolved. |
| IMRPhenomXPHMSpinTaylor | Original credible-interval-width refinement failed; additional parity and optimizer checks remain unresolved. |
| EMRIKludge | Later refinement has only one consecutive pass where two are required. No accepted completion reference or sampler. |
| ContinuousWave | Refinement and independent quadrature remain unresolved. |
| KerrRingdown, KerrRingdownDirect | Original grids converged; no accepted completion reference or sampler. |
| SEOBNRv4_ROM | Original grids converged with the required external ROM data; no accepted completion reference or sampler. |
| ParameterizedPostEinstein | Original grids converged; later reference-density and matched-noise checks remain unresolved. |
| TEOBResumSHamiltonian | A Hamiltonian component without a public waveform API; excluded from the 28 supported waveform PE scopes. |
For NSBH, the final independent CDF refinement changes a cut probability by 0.00343784, above its frozen 0.0002 limit. The three second-mass quantile checks also fail their required integration-uncertainty margins. Stable normalization and a passing grid do not remove these failed checks. This is unresolved numerical reference integration, not evidence by itself of a physical waveform error.
What a pass means
| Evidence | Supported conclusion | Outside its scope |
|---|---|---|
| Converged bounded grid | Numerical posterior integration met the stated checks for that experiment | All parameter values, all priors or every waveform option |
| Accepted sampler case | Its retained draws agree with the accepted reference within the frozen mixing and uncertainty checks | Every chain length, other datasets or full-dimensional PE |
| Torch/JAX common-data agreement | The two implementations agree for the tested data, options and posterior | Independent physical accuracy; shared errors can remain |
| Prior-drawn noisy calibration | Coverage under the assumed generative model, once the declared ensemble passes | Real-noise robustness or physical-model accuracy |
These are primarily same-model injection-and-recovery experiments. Independent physical injections, such as appropriately characterized numerical-relativity signals, are needed to measure waveform-model bias. Existing mathematical, implementation and physical-accuracy failures retain their separate status in the waveform qualification dashboard. Prior-limited or prior-dominated posteriors must also retain those labels even when numerical integration converges.
Evidence and use
The compact current results list all 29 inventory entries, the 17 accepted sampler records, review identifiers and SHA256 bindings. The original grid receipt retains the frozen case options, priors, measured values and original outcomes. Bulk chains, arrays and full reproduction records are retained externally; their hashes identify the reviewed data, and no public bulk download is implied.
The earlier common-data pilot, Torch sampler pilot, initial noisy study and compiled noisy references retain their own dated settings and outcomes. They are separate experiments. For practical inference, start with the PE guide and IMRPhenomD example.