... | ... | @@ -4,7 +4,22 @@ A page for reviewing the evidence calculation produced by bilby. |
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## Analytical likelihood
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To review the evidence calculation using bilby (in particular using the `dynesty` sampler) it can be used to sample from a probability distribution with a known normalisation. In the review of LALInference this consisted of checking the evidence calculation using [two distributions](https://www.lsc-group.phys.uwm.edu/ligovirgo/cbcnote/LALInferenceReviewAnalyticGaussianLikelihood): i) a 15D multivariate Gaussian distribution, and ii) a bi-modal multivariate Gaussian distribution. These same distribution are coded up in bilby in [`15d_gaussian.py`](https://git.ligo.org/lscsoft/bilby/blob/master/examples/core_examples/15d_gaussian.py) and have been tested on [this page](https://git.ligo.org/lscsoft/bilby_pipe/-/wikis/O3-review/15D_Gaussian).
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To review the evidence calculation using bilby (in particular using the `dynesty` sampler) it can be used to sample from a probability distribution with a known normalisation. In the review of LALInference this consisted of checking the evidence calculation using [two distributions](https://www.lsc-group.phys.uwm.edu/ligovirgo/cbcnote/LALInferenceReviewAnalyticGaussianLikelihood): i) a 15D multivariate Gaussian distribution, and ii) a bi-modal multivariate Gaussian distribution. Equivalent distributions are implemented in bilby in [`15d_gaussian.py`](https://git.ligo.org/lscsoft/bilby/blob/master/examples/core_examples/15d_gaussian.py) and have been tested on [this page](https://git.ligo.org/lscsoft/bilby_pipe/-/wikis/O3-review/15D_Gaussian).
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A more extensive review has been performed using [this repository](https://git.ligo.org/moritz.huebner/evidence_review).
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While this review is meant to evaluate the performance of `dynesty`, it was trivial to redo the tests with other nested sampling packages.
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Thus, all tests have been performed using `bilby==0.6.5`, `cpnest==0.9.7`, `dynesty==1.0.1`, `Multinest=3.10`, `nestle==0.2.0`, `Polychord==1.15.1`
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### Convergence to analytical evidence
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As we increase the number of live points, stochastic and systematic errors should decrease and the mean value of the evidence should converge to the analytically known evidence. We choose to perform 100 runs with 32, 64, 128, ..., 4096 livepoints with the analytical likelihood both in the unimodal and bimodal case.
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![all_samplers_review_unimodal_summary](uploads/3904f7c48207f4abab73505ad4ef6fbc/all_samplers_review_unimodal_summary.png)
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![all_samplers_review_bimodal_summary](uploads/dfb698950ab60945b6c869a8544d8096/all_samplers_review_bimodal_summary.png)
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### Empirical evidence uncertainties vs. K-L-divergence uncertainties
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Review items:
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