Inference Methods¶

bayRing supports three inference paths:

[Inference]
method = Nested-sampler

Allowed values are Nested-sampler, Minimization and Linear-inversion.

Likelihood¶

The inference model compares a complex NR waveform d with a complex model h(theta). The residual is:

\[r(\theta) = d - h(\theta).\]

For the default Gaussian likelihood, real and imaginary residuals are weighted by the corresponding real and imaginary parts of the NR error vector:

\[\log L(\theta) = -\frac{1}{2}\sum_i \left[ \left(\frac{\mathrm{Re}[r_i(\theta)]}{\mathrm{Re}[\sigma_i] + \epsilon}\right)^2 + \left(\frac{\mathrm{Im}[r_i(\theta)]}{\mathrm{Im}[\sigma_i] + \epsilon}\right)^2 \right],\]

where epsilon = 1e-16 avoids division by zero. This is a diagonal time-domain likelihood on the selected NR samples. PSD/ACF settings are used later by mismatch and optimal-SNR diagnostics, not by this inference likelihood.

Priors And Bounds¶

Default bounds are model dependent and are defined in bayRing.inference.read_default_bounds. Override a bound in [Priors]:

[Priors]
ln_A_220-min = -12.0
ln_A_220-max = 0.0
phi_220-min = 0.0
phi_220-max = 6.283185307179586

Fix a parameter with:

[Priors]
fix-ln_A_220 = -5.0
fix-phi_220 = 1.0

The fixed-value syntax removes that parameter from the free parameter list. The waveform model still sees the value through the fixed-parameter override.

Non-Rectangular Prior Constraints¶

Some constraints are enforced in addition to simple rectangular bounds:

Model feature	Constraint
`Damped-sinusoids`	Frequencies are ordered by mode index.
Kerr tails	Tail exponents are ordered relative to the fitted NR multipole tail.

Nested sampling applies these constraints in log_prior by returning -inf when the constraint is violated. Minimization adds large penalty residuals so the least-squares objective respects the same shape.

Choosing A Method¶

Goal	Recommended method
Quick check of a nonlinear model	`Minimization`
Fast Kerr amplitude extraction	`Linear-inversion` if the template is `Kerr` and all free parameters are paired amplitudes/phases.
Posterior intervals and evidence	`Nested-sampler`
Production model comparison	`Nested-sampler` with raised `nlive`/`maxmcmc` and stability checks.
Debugging priors and start times	`Minimization` followed by a nested-sampler run if the solution is physically meaningful.

Point-estimate methods are excellent diagnostics, but they do not replace a posterior calculation when uncertainties, prior-volume effects or evidences matter.