main.tex

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\begin{document}

% \title{Binary black hole parameter estimation with Stein variational inference}
\title{Notes on likelihood heterodyning}

\author[1]{Alex Leviyev}
% \author[2]{Joshua Chen}
% \author[3]{Yifei Wang}
\author[4]{Francesco Iacovelli}
% \author[4]{Michele Mancarella}
% \author[2]{Omar Ghattas}
% \author[3]{Qiang Liu}
\author[1]{Aaron Zimmerman}
\affil[1]{Center for Gravitational Physics, University of Texas at Austin}
% \affil[2]{Oden Institute, University of Texas at Austin}
% \affil[3]{Department of Electrical Engineering, Stanford University}
% \affil[3]{Department of Computer Science, University of Texas at Austin}
\affil[4]{D\'{e}partement de Physique Th\'{e}orique and Gravitational Wave Science Center, Universit\'{e} de Gen\`{e}ve}
\date{\today}
\maketitle

\begin{abstract}
This is a set of notes which explores in more detail the strategy of reducing the computational cost of evaluating the gravitational wave likelihood with a strategy known as heterodyning.
Our aim is to provide concrete results and algorithms to supplement the ideas presented in the original paper.
Additionally, we discuss the extension of these ideas in calculating the gradient, and the Fisher information.
% is an interacting particle MCMC method whose proposals correspond to quasi-Newton optimization over constrained spaces,


% Since their original detection in 2016, gravitational waves have provided an unprecedented method to study neutron stars, black holes, and strong field gravity.
% As such detections become routine, it is imperative that signals be processed in a timely manner without undue computational burden.
% In this paper, we investigate the benefits of incorporating second order information into the parameter estimation process.
% Specifically, the standard Gaussian noise model used for gravitational wave parameter estimations allows one to use a computationally inexpensive, positive-definite surrogate to the Hessian of the log-likelihood (the Fisher-information) to perform quasi-Newton descent.
% We demonstrate that using an algorithm known as Stein variational Newton (SVN) as implemented in \texttt{sSVN}\footnote{\url{https://github.com/leviyevalex/sSVN}} reduces (t.b.d) the number of waveform evaluations for a binary black hole merger (GW170817) by two orders of magnitude compared to the state of the art \texttt{Dynesty}\footnote{\url{https://github.com/joshspeagle/dynesty}} library.
% The \texttt{gwfast}\footnote{\url{https://github.com/CosmoStatGW/gwfast}} library is used to construct a detector network likelihood in pure Python, which then allows for fast and accurate algorithmic differentiation of the likelihood via \texttt{JAX}\footnote{\url{https://github.com/google/jax}}.
\end{abstract}
\input{notes}
% \input{1-intro}
% \input{2-background}
% \input{3-contributions}
% \input{4-numerics}
% \input{5-conclusion}

\appendix
\bibliographystyle{amsplain}
\bibliography{ref.bib}

\input{app}
\end{document}