Kavli Affiliate: Salvatore Vitale
| First 5 Authors: Jack Heinzel, Jack Heinzel, , ,
| Summary:
The coming years of gravitational wave astrophysics promises thousands of new
detections, which can unlock fundamental scientific insights if the information
in each observation can be properly synthesized into a coherent picture.
State-of-the-art approaches often accomplish this with hierarchical Bayesian
inference. However, this typically relies on Monte Carlo approximations that
are already very expensive in current data, and may become prohibitively so in
the future. In this paper we show how this process can be understood from a
first-principles statistical approach. We derive an error estimator $hatE$
for quantifying the amount of information that is lost due to the Monte Carlo
approximation and recommend that this error is limited to no more than $hatE
lesssim 0.2$ bits for reliable inference. We also show that the hierarchical
likelihood estimator is biased but may be corrected. Finally, we show some
practical examples for inference on synthetic gravitational-wave population
inference, demonstrating that simple models with strong assumptions can be much
more stable to Monte Carlo uncertainty than those with weaker assumptions. We
also provide a textttpip-installable package textttpopulation-error with
which analysts can calculate the error statistics $hatE$.
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