Enabling new sampling strategies for continuous-wave analyses by integrating Bilby into PyFstat

Author(s)

Ferrer-Martinez, Maria-Antonia, Keitel, David

Abstract

Continuous-wave searches for rotating neutron stars usually cover wide parameter spaces and produce a large number of candidate signals. Stochastic sampling methods therefore play an important role in candidate follow-up and parameter estimation. We present the integration of the Bayesian inference library BILBY into the open-source continuous-wave analysis package PyFstat, enabling access to the broad range of stochastic samplers available through BILBY while preserving the existing PyFstat analysis infrastructure. The implementation is validated through injection studies in Gaussian noise for two representative single-stage follow-up configurations: candidates from a directed search and candidates from an all-sky search. Using the nested sampler DYNESTY, we obtain detection efficiencies consistent with the theoretical sensitivity predictions. In this setup, DYNESTY performs comparably to the existing PTEMCEE-based implementation of PyFstat for the directed case, and also provides an effective single-stage approach for the all-sky candidate follow-up considered here, where we did not identify a PTEMCEE setup with similar recovery performance. Percentile-percentile tests for DYNESTY further show well-calibrated credible intervals, demonstrating reliable parameter estimation. While a full exploration of DYNESTY settings, multi-stage setups, and other samplers is left for future work, these results demonstrate that this flexible and publicly available framework opens useful new possibilities for Bayesian continuous-wave analyses.

Figures

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Detection efficiency as a function of sensitivity depth for the directed follow-up. Markers show the measured efficiencies obtained with \dynesty{} and \ptemcee{} using the sampler settings described in the text; the overlapping solid and dashed curves show the theoretical sensitivity estimates.

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Detection efficiency as a function of sensitivity depth for the all-sky follow-up. Markers show the measured efficiencies obtained with \dynesty{} using \texttt{nlive}=1500; the overlapping solid and dashed curves show the theoretical sensitivity estimates.

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\Acs{pp} plots obtained from 100 injections at depth $D=125$ using the \dynesty{} sampler for the directed follow-up (left) and the all-sky follow-up (right). The shaded regions show the expected 1-, 2- and 3-$\sigma$ statistical fluctuations for perfectly calibrated posteriors. The Fisher-combined $p$-values over the plotted parameters are 0.47 for the directed follow-up and 0.82 for the all-sky follow-up.

Caption

\Acs{pp} plots obtained from 100 injections at depth $D=125$ using the \dynesty{} sampler for the directed follow-up (left) and the all-sky follow-up (right). The shaded regions show the expected 1-, 2- and 3-$\sigma$ statistical fluctuations for perfectly calibrated posteriors. The Fisher-combined $p$-values over the plotted parameters are 0.47 for the directed follow-up and 0.82 for the all-sky follow-up.

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\Acs{pp} plot obtained from 100 injections at depth $D=100$ using the \ptemcee{} sampler for the directed follow-up. The shaded regions show the expected 1-, 2- and 3-\(\sigma\) statistical fluctuations for perfectly calibrated posteriors. The Fisher-combined $p$-value is $1.6\times10^{-12}$.

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Detection efficiency as a function of sensitivity depth for different values of \texttt{nlive} for the directed follow-up (left) and the all-sky follow-up (right). Markers indicate the measured recovery fractions from fixed-orientation injection studies, with error bars showing the binomial statistical uncertainty. The curves show the corresponding semi-analytic and \texttt{cows3} sensitivity estimates for each configuration. This comparison is used to select the reference \texttt{nlive} values adopted in the main text.

Caption

Detection efficiency as a function of sensitivity depth for different values of \texttt{nlive} for the directed follow-up (left) and the all-sky follow-up (right). Markers indicate the measured recovery fractions from fixed-orientation injection studies, with error bars showing the binomial statistical uncertainty. The curves show the corresponding semi-analytic and \texttt{cows3} sensitivity estimates for each configuration. This comparison is used to select the reference \texttt{nlive} values adopted in the main text.

Caption

Comparison of different \dynesty{} walk strategies for the directed follow-up. Left: detection efficiency as a function of sensitivity depth for the \texttt{acceptance-walk}, \texttt{act-walk}, and \texttt{rwalk} sampling methods. Right: median runtime as a function of sensitivity depth for the same configurations. Error bars show the full range of measured runtimes at each depth, from the fastest to the slowest completed run. The \texttt{act-walk} and \texttt{rwalk} configurations recover detection efficiencies consistent with the theoretical predictions, while \texttt{acceptance-walk} shows a modest reduction in recovery efficiency.

Caption

Comparison of different \dynesty{} walk strategies for the directed follow-up. Left: detection efficiency as a function of sensitivity depth for the \texttt{acceptance-walk}, \texttt{act-walk}, and \texttt{rwalk} sampling methods. Right: median runtime as a function of sensitivity depth for the same configurations. Error bars show the full range of measured runtimes at each depth, from the fastest to the slowest completed run. The \texttt{act-walk} and \texttt{rwalk} configurations recover detection efficiencies consistent with the theoretical predictions, while \texttt{acceptance-walk} shows a modest reduction in recovery efficiency.

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Detection efficiency as a function of sensitivity depth for the O4a-timestamp Gaussian-noise datasets, for the fixed-sky (left) and all-sky (right) follow-ups. Markers indicate the measured detection efficiencies for $\texttt{nlive}=450$, $1000$, and $1500$, while the solid and dashed curves show the corresponding semi-analytic and \texttt{cows3} sensitivity estimates, respectively.

Caption

Detection efficiency as a function of sensitivity depth for the O4a-timestamp Gaussian-noise datasets, for the fixed-sky (left) and all-sky (right) follow-ups. Markers indicate the measured detection efficiencies for $\texttt{nlive}=450$, $1000$, and $1500$, while the solid and dashed curves show the corresponding semi-analytic and \texttt{cows3} sensitivity estimates, respectively.

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Normalized centered offsets, as defined in Eq.~\eqref{eq:normalized-posterior-offset}, for the \dynesty{} directed follow-up at $\mathcal{D}=145$. The redsolid vertical lines mark zero, the gray dashed lines mark the bounds $z_{90}=\pm1$, and the blak dotted lines mark the median offsets. The empirical coverages of the nominal 90\% credible intervals are 0.87 for $f$ and 0.86 for $\dot f$.

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Normalized centered offsets, as defined in Eq.~\eqref{eq:normalized-posterior-offset}, for the \dynesty{} all-sky follow-up at $\mathcal{D}=120$. The red solid vertical lines mark zero, the gray dashed lines mark the bounds $z_{90}=\pm1$, and the blackdotted lines mark the median offsets. The empirical coverages of the nominal 90\% credible intervals are 0.90 for $f$, 0.93 for $\dot f$, 0.93 for $\alpha$, and 0.92 for $\delta$.