The likelihood
For any pair of masses, the likelihood says how probable the data would be if those masses were the truth. When your model matches the hidden signal, what’s left over looks like pure noise, and the likelihood is high.
Explore · Inference
Be Bilby
There’s a gravitational wave hidden in this noise. Tune the two masses until your model fits, then watch a nested sampler do the job properly: find the answer, and work out how sure we can be.
Detector data · 2 seconds, whitened
The outline traces how loud the data are from moment to moment, and turns orange where they’re louder than noise alone. The hidden signal makes it flare near the merger; subtract the right model and the flare disappears from the residual.
Log likelihood, ln L
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All possible pairs of masses
- Your guesses
- Live points
- Worst, about to go
- Posterior
- The answer
- Lines of equal chirp mass
- Iteration
- 0
- Likelihood evaluations
- 0
- Possibilities left
- all
- Steps accepted
- –
- Evidence, ln Z
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The answer, with its uncertainty
Why bother with a clever sampler? Compute the likelihood at every point on an 80 × 80 grid and compare.
This page doesn’t run Bilby. It runs a small nested sampler written for this toy, in JavaScript, in your web browser. It uses the same basic algorithm as dynesty, the nested-sampling package most often used through Bilby for gravitational-wave analyses: a set of live points, where the lowest-likelihood point is repeatedly replaced by a new one found by a random walk that must beat it.
What’s going on
From noisy data to masses
Why the masses blur together
How quickly a chirp sweeps up in pitch depends mostly on one combination of the masses, the chirp mass. Many pairs of masses share the same chirp mass and give almost the same signal, so the answer is a thin curve rather than a single point.
Nested sampling
Start with guesses spread over every possibility. Repeatedly throw away the worst and replace it with a better one. The guesses close in on the answer, the space of possibilities shrinks in a known way, and the discarded guesses, weighted, become the posterior.
What real analyses add
Real signals have around fifteen parameters (spins, sky position, distance, orientation and more), detector noise that varies with frequency, two or three detectors, and carefully chosen priors. The same ideas still apply.
About this simulation
The data are 2 seconds of white Gaussian noise at 2,048 samples per second (as if the detector noise had already been whitened), with a binary-black-hole signal from the same illustrative model as Hear a chirp. The merger time is known; the signal’s amplitude and phase are fitted automatically, as a matched filter does, so only the two masses are left to find. Signals have a matched-filter signal-to-noise ratio of 60 (loud), 35 (typical) or 20 (faint); for comparison, GW150914 had a signal-to-noise ratio of about 24.
The prior is uniform in the two component masses between 10 and 80 solar masses, with mass 1 the heavier. The nested sampler uses 200 live points; each replacement comes from a 20-step random walk that must stay above the worst live point’s likelihood, with steps shaped by the spread of the live points. It stops when the remaining live points could change ln Z by less than 0.1.
Bilby is an open-source Bayesian inference library used across gravitational-wave astronomy. The sampler on this page isn’t Bilby, and doesn’t use its code: it’s a simplified nested sampler written for this toy, following the same basic algorithm as dynesty, the nested sampler most often used through Bilby.