deletions | additions       diff --git a/spinni_appendix_section_Computational_cost__.tex b/spinni_appendix_section_Computational_cost__.tex  index b34258f..e2f82e4 100644  --- a/spinni_appendix_section_Computational_cost__.tex  +++ b/spinni_appendix_section_Computational_cost__.tex 
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\section{Computational cost}\label{ap:CPU}  Performing a fully spinning analysis is computationally expensive. The main computational cost is generating the SpinTaylorT4 waveform, which must be done each time the likelihood is evaluated at a different point in parameter space. Progress is being made in reducing the cost of generating waveforms and evaluating the likelihood \citep[e.g.,][]{Canizares_2013,P_rrer_2014}; employing \citep[e.g.,][]{Canizares_2013,P_rrer_2014}. Employing  reduced order modelling can speed up the non-spinning TaylorF2 analysis by a factor of $\sim 30$ \citep{Canizares_2015}. However, this This  is still to be done for a waveform that includes the effects of two unaligned spins. spins; however, progress has also been made in constructing frequency domain approximants using shifted uniform asymptotics, which can speed up generation of a waveform like SpinTaylorT4 by an order of magnitude \citep{Klein:2014bua}.  In figure \ref{fig:wall-time}, we present the approximate wall time taken for analyses comparable to those presented here. The low-latency \textsc{bayestar} and the high-latency fully spinning SpinTaylorT4 results are for the $250$ events considered here. The medium-latency non-spinning TaylorF2 results are from \citet{Berry_2014}; these are not for a different set of signals, but represent a similar population (in more realistic non-Gaussian noise), representing what we hope to achieve in reality.\footnote{We use the more reliably estimated figures for the \textsc{LALInference} runs.} The wall times for \textsc{bayestar} are significantly reduced compared to those in \citet{Berry_2014} because of recent changes to how \textsc{bayestar} integrates over distance \citep{SingerPrice2015}: the mean (median) time is $4.6~\mathrm{s}$ ($4.5~\mathrm{s}$) and the maximum is $6.6~\mathrm{s}$. We assume that $2000$ (independent) posterior samples are collected for both of the \textsc{LALInference} analyses. The number of samples determines how well we can characterize the posterior: $\sim2000$ is typically needed to calculate $\mathrm{CR}_{0.9}$ to $10\%$ accuracy \citep{DelPozzo_2015}. In practice, we may want to collect additional samples to ensure our results are accurate, but preliminary results could also be released when the medium-latency analysis has collected $1000$ samples, which would after half the time shown here with a maximum wall time of $5.87\times10^4~\mathrm{s} \simeq 16~\mathrm{hr}$. We see that the fully spinning analysis is significantly (here a factor of $\sim20$) more expensive than the non-spinning analysis, taking a mean (median) time of $1.36\times10^6~\mathrm{s} \simeq 16~\mathrm{days}$ ($9.96\times10^5~\mathrm{s} \simeq 12~\mathrm{days}$) and a maximum of $7.03\times10^6~\mathrm{s} \simeq 81~\mathrm{days}$. 
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