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## Likelihood differences
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The relative binning (heterodyned) likelihood ([Zackay _et al._](https://arxiv.org/abs/1806.08792)) offers a method to accelerate the likelihood for arbitrary frequency-domain models.
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While it is more widely applicable than ROQ bases, more care must be taken with tuning.
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Compute likelihood difference for
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For this review, we have focused on demonstrating two things:
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- when a good fiducial point is provided, the results obtained with this approximation are high fidelity.
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- when a bad fiducial point is used, or the approximation otherwise fails, we can identify this in a programmatic way.
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To establish this, we importance sample the results obtained with relative binning using the regular likelihood.
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If the mismatches, defined as the log of the absolute difference between (natural) log-likelihoods obtained with the two methods are small, the approximation is good.
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By rejection sampling using the weights (true vs approximate likelihood ratios), we can find the fraction of samples obtained.
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If the rejection sampling efficiency is small, then we can say that the approximation failed and we should repeat with a more robust method.
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## [Unit testing](https://git.ligo.org/lscsoft/bilby/-/blob/master/test/gw/likelihood/relative_binning_test.py)
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## [Unit testing](https://git.ligo.org/lscsoft/bilby/-/blob/master/test/gw/likelihood/relative_binning_test.py)
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| ... | @@ -42,6 +50,17 @@ For some successful cases, the mean ln likelihood is > 0.1 in the tails, however |
... | @@ -42,6 +50,17 @@ For some successful cases, the mean ln likelihood is > 0.1 in the tails, however |
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The fiducial BNS injection has been analyzed with the relative binning likelihood.
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The fiducial BNS injection has been analyzed with the relative binning likelihood.
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In all cases, we see good agreement with the ROQ-likelihood runs and good resampling efficiency.
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In all cases where a suitable starting point was provided, we see good agreement with the ROQ-likelihood runs and good resampling efficiency.
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Here is the distribution of likelihood mismatches for two identical analyses of the fiducial BNS signal with a processing spin prior with magnitudes up to 0.4 and tidal deformability up to 5000.
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The legend entries show the fraction of samples surviving rejection sampling.
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It is very close to 1.
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By accident, we performed some runs with fiducial parameters that are a very bad fit to the actual signal.
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In this case, we found that the rejection sampling efficiency was very small with large mismatches.
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*TODO*: add figures and numbers here |
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While we did not perform large-scale testing in this regime. These findings are consistent with the tests with the NSBH waveform model that we can get good results in a representative use case and identify bad results. |
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