Learning Bayesian Posteriors with Neural Networks for Gravitational-Wave Inference.

We seek to achieve the holy grail of Bayesian inference for gravitational-wave astronomy: using deep-learning techniques to instantly produce the posterior p(θ|D) for the source parameters θ, given the detector data D. To do so, we train a deep neural network to take as input a signal + noise dataset (drawn from the astrophysical source-parameter prior and the sampling distribution of detector noise), and to output a parametrized approximation of the corresponding posterior. We rely on a compact representation of the data based on reduced-order modeling, which we generate efficiently using a separate neural-network waveform interpolant [A. J. K. Chua, C. R. Galley, and M. Vallisneri, Phys. Rev. Lett. 122, 211101 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.211101]. Our scheme has broad relevance to gravitational-wave applications such as low-latency parameter estimation and characterizing the science returns of future experiments.

Reduced-Order Modeling with Artificial Neurons for Gravitational-Wave Inference.

Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms are first represented as weighted sums over reduced bases (reduced-order modeling); we then train artificial neural networks to map gravitational-wave source parameters into basis coefficients. Statistical inference proceeds directly in coefficient space, where it is theoretically straightforward and computationally efficient. The neural networks also provide analytic waveform derivatives, which are useful for gradient-based sampling schemes. We demonstrate fast and accurate coefficient interpolation for the case of a four-dimensional binary-inspiral waveform family and discuss promising applications of our framework in parameter estimation.

Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors.

We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ∼ 10-5 - 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger.

Beyond the fisher-matrix formalism: exact sampling distributions of the maximum-likelihood estimator in gravitational-wave parameter estimation.

Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise realizations, as well as the leading-order width of the posterior probability, but it is limited to high signal strengths often not realized in practice. By contrast, Monte Carlo Bayesian inference provides the full posterior for any signal strength, but it is too expensive to repeat for a representative set of noises. Here I describe an efficient semianalytical technique to map the exact sampling distribution of the maximum-likelihood estimator across noise realizations, for any signal strength. This technique can be applied to any estimation problem for signals in additive Gaussian noise.