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#### Gravitational-wave parameter estimation with autoregressive neural network flows

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##### Fulltext (public)

2002.07656.pdf

(Preprint), 2MB

PhysRevD.102.104057.pdf

(Publisher version), 2MB

##### Supplementary Material (public)

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##### Citation

Green, S., Simpson, C., & Gair, J. (2020). Gravitational-wave parameter estimation
with autoregressive neural network flows.* Physical Review D,* *102*:
104057. doi:10.1103/PhysRevD.102.104057.

Cite as: http://hdl.handle.net/21.11116/0000-0007-97D1-2

##### Abstract

We introduce the use of autoregressive normalizing flows for rapid
likelihood-free inference of binary black hole system parameters from
gravitational-wave data with deep neural networks. A normalizing flow is an
invertible mapping on a sample space that can be used to induce a
transformation from a simple probability distribution to a more complex one: if
the simple distribution can be rapidly sampled and its density evaluated, then
so can the complex distribution. Our first application to gravitational waves
uses an autoregressive flow, conditioned on detector strain data, to map a
multivariate standard normal distribution into the posterior distribution over
system parameters. We train the model on artificial strain data consisting of
IMRPhenomPv2 waveforms drawn from a five-parameter $(m_1, m_2, \phi_0, t_c,
d_L)$ prior and stationary Gaussian noise realizations with a fixed power
spectral density. This gives performance comparable to current best
deep-learning approaches to gravitational-wave parameter estimation. We then
build a more powerful latent variable model by incorporating autoregressive
flows within the variational autoencoder framework. This model has performance
comparable to Markov chain Monte Carlo and, in particular, successfully models
the multimodal $\phi_0$ posterior. Finally, we train the autoregressive latent
variable model on an expanded parameter space, including also aligned spins
$(\chi_{1z}, \chi_{2z})$ and binary inclination $\theta_{JN}$, and show that
all parameters and degeneracies are well-recovered. In all cases, sampling is
extremely fast, requiring less than two seconds to draw $10^4$ posterior
samples.