Mismatch & SNR Diagnostics¶

After inference, bayRing computes waveform mismatch and optimal-SNR diagnostics using a detector-scaled strain, an ASD/PSD file and an autocorrelation function. These diagnostics live in the post-processing path. They are separate from the diagonal NR-error likelihood used during inference.

Physical Scaling¶

The NR waveform is dimensionless. For mismatch and SNR diagnostics, it is scaled to a source with remnant mass M and luminosity distance dL:

\[h_{\mathrm{phys}}(t) = \frac{G M_\odot M}{c^2\,d_L\,\mathrm{Mpc}}\, h_{\mathrm{NR}}(t).\]

The parameters are set in [Mismatch-GW-parameters]:

[Mismatch-GW-parameters]
M = 60
dL = 410
ra = 1.375
dec = -0.2108
psi = 2.659

ra, dec and psi are used with LAL antenna-response utilities when building plus/cross diagnostics.

PSD And ACF Inputs¶

The diagnostic section starts from an ASD file:

[Mismatch-PSD-settings]
asd-path = /path/to/asd.txt

If asd-path is empty, the helper routines can use their default public ASD path. The PSD/ASD is interpolated, optionally smoothed at the frequency edges, and transformed into an autocorrelation function used for time-domain inner products.

Smoothing Controls¶

PSD edge smoothing is controlled by:

[Flags]
apply_window = 1
C1_flag = 1

[Mismatch-PSD-settings]
direction = below-and-above
window_DX = 0.8
window_SX = 0.8
steepness = 7.0
saturation_DX = 1.0
saturation_SX = 1.0

direction selects which PSD edge is smoothed:

Value	Meaning
`below`	Smooth the low-frequency edge.
`above`	Smooth the high-frequency edge.
`below-and-above`	Smooth both edges.

The *_max and n_* settings define a grid over smoothing parameters. For example:

window_DX = 0.8
window_DX_max = 10.0
n_window_DX = 4

asks the post-processing loop to evaluate several low-frequency smoothing window values between the minimum and maximum.

Time-Domain Inner Product¶

The diagnostic inner product uses the truncated ACF on the NR time interval. For a residual or waveform vector x, the whitened norm is computed through a Toeplitz solve:

\[\|x\|_C^2 = x^T C^{-1} x,\]

where C is the Toeplitz covariance matrix implied by the ACF. The code uses scipy.linalg.solve_toeplitz for the time-domain norm.

The mismatch between NR and model waveforms has the usual normalized form:

\[\mathcal{M} = 1 - \frac{(h_{\mathrm{NR}},h_{\mathrm{model}})} {\sqrt{(h_{\mathrm{NR}},h_{\mathrm{NR}}) (h_{\mathrm{model}},h_{\mathrm{model}})}}.\]

The optimal SNR diagnostic is:

\[\rho_{\mathrm{opt}} = \sqrt{(h,h)}.\]

Percentile Waveforms¶

For posterior samples, the plotting utilities construct model-waveform percentiles. The default mismatch/SNR files use the configured summary percentiles and plot percentiles from bayRing.postprocess:

summary_percentiles = (5, 50, 95)
plot_percentiles = (50,)

For point-estimate methods, bayRing writes a Gaussian approximation to Algorithm/posterior.dat so the same percentile-based machinery can be used.

Output Files¶

Mismatch and SNR text files are written under:

outdir/Algorithm/Mismatch/

File names encode mass, distance, start time, window settings and FFT length, for example:

Mismatch_M_60_dL_410_t_s_30.0M_wDX_0.8Hz_wSX_0.8Hz_k_7.0_satDX_1.0_satSD_1.0_NFFT_4096.txt
Optimal_SNR_M_60_dL_410_t_s_30.0M_wDX_0.8Hz_wSX_0.8Hz_k_7.0_satDX_1.0_satSD_1.0_NFFT_4096.txt

Each file stores confidence interval or percentile labels, the strain component and the corresponding mismatch or SNR value.

Sanity Plots¶

Enable diagnostic plots with:

[Flags]
mismatch_section_plot_flag = 1

Depending on the smoothing direction, plots are placed under one of:

Algorithm/Mismatch/Left_smoothing/
Algorithm/Mismatch/Right_smoothing/
Algorithm/Mismatch/Both_edges_smoothing/

These plots are useful when tuning window widths, steepness, saturation and FFT length. Inspect them whenever changing PSD settings; a numerically smooth ACF is not guaranteed by a syntactically valid configuration.

Frequency-Domain Checks¶

Set:

[Flags]
compare_TD_FD = 1

to request frequency-domain comparison outputs where implemented. This is a diagnostic check on the PSD/ACF and time/frequency-domain treatments. It is not a different inference likelihood.

Common Failure Modes¶

Too long a time interval for the smoothing edge: The code checks t_end - t_start < 1/(f_min + window_DX) when smoothing below the band. If violated, reduce the time interval or change the PSD smoothing settings.
Ill-conditioned ACF: Inspect the PSD edge smoothing and FFT length. Enable mismatch_section_plot_flag and compare condition-number plots.