One of the main bottlenecks in gravitational wave (GW) astronomy is the high cost of Bayesian parameter estimation. One approach to this problem is Reduced Order Quadratures (ROQs), an application and data-specific quadrature rule that can be used to perform fast and accurate likelihood evaluations. Generation of an ROQ rule is carried out offline (before the data is known). First, a projection-based greedy algorithm identifies a basis whose span accurately approximates the parameterized functions defining a GW model. An empirical interpolation procedure is then applied to select ROQ nodes. The resulting quadrature rule's computational cost depends linearly on the number of basis functions, and the ROQ approximation error is bounded by the so-called greedy error (the model's Kolmogorov n-width) times a computable constant. This approximation error converges exponentially fast, thereby significantly accelerating likelihood evaluations and, consequently, an end-to-end inference run. This talk will summarize the key algorithms and software needed to build ROQ rules and survey the models for which ROQs have been built. New challenges and opportunities for ROQs for upcoming detectors will also be highlighted.
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