Once upon a time, predictions for the accuracy of inference on gravitational-wave signals relied on computationally inexpensive but often inaccurate techniques. Recently, the approach has shifted to actual inference on noisy signals with complex stoc
hastic Bayesian methods, at the expense of significant computational cost. Here, we argue that it is often possible to have the best of both worlds: a Bayesian approach that incorporates prior information and correctly marginalizes over uninteresting parameters, providing accurate posterior probability distribution functions, but carried out on a simple grid at a low computational cost, comparable to the inexpensive predictive techniques.
Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally c
haracterize this picture, the physical parameters of the system can be extracted more efficiently from the gravitational wave data, and interpreted more easily. We assess the performance of MCMC parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binarys spins and orbital angular momentum and (b) a time at which the detectors are most sensitive to the binarys gravitational wave emission. Using anticipated noise curves for the advanced-generation LIGO and Virgo gravitational wave detectors, we find that this careful choice of reference frame and reference time significantly improves parameter estimation efficiency for BNS, NS-BH, and BBH signals.
The Fisher Information Matrix (FIM) has been the standard approximation to the accuracy of parameter estimation on gravitational-wave signals from merging compact binaries due to its ease-of-use and rapid computation time. While the theoretical faili
ngs of this method, such as the signal-to-noise ratio (SNR) limit on the validity of the lowest-order expansion and the difficulty of using non-Gaussian priors, are well understood, the practical effectiveness compared to a real parameter estimation technique (e.g. Markov-chain Monte Carlo) remains an open question. We present a direct comparison between the FIM error estimates and the Bayesian probability density functions produced by the parameter estimation code lalinference_mcmc. In addition to the low-SNR issues usually considered, we find that the FIM can greatly overestimate the uncertainty in parameter estimation achievable by the MCMC. This was found to be a systematic effect for systems composed of binary black holes, with the disagreement increasing with total mass. In some cases, the MCMC search returned standard deviations on the marginalized posteriors that were smaller by several orders of magnitude than the FIM estimates. We conclude that the predictions of the FIM do not represent the capabilities of real gravitational-wave parameter estimation.
Globular clusters should be born with significant numbers of stellar-mass black holes (BHs). It has been thought for two decades that very few of these BHs could be retained through the cluster lifetime. With masses ~10 MSun, BHs are ~20 times more m
assive than an average cluster star. They segregate into the cluster core, where they may eventually decouple from the remainder of the cluster. The small-N core then evaporates on a short timescale. This is the so-called Spitzer instability. Here we present the results of a full dynamical simulation of a globular cluster containing many stellar-mass BHs with a realistic mass spectrum. Our Monte Carlo simulation code includes detailed treatments of all relevant stellar evolution and dynamical processes. Our main finding is that old globular clusters could still contain many BHs at present. In our simulation, we find no evidence for the Spitzer instability. Instead, most of the BHs remain well-mixed with the rest of the cluster, with only the innermost few tens of BHs segregating significantly. Over the 12 Gyr evolution, fewer than half of the BHs are dynamically ejected through strong binary interactions in the cluster core. The presence of BHs leads to long-term heating of the cluster, ultimately producing a core radius on the high end of the distribution for Milky Way globular clusters (and those of other galaxies). A crude extrapolation from our model suggests that the BH--BH merger rate from globular clusters could be comparable to the rate in the field.
Selection among alternative theoretical models given an observed data set is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian m
odel selection, but it suffers from a fundamental difficulty: it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the MCMC algorithm and convergence is correspondingly slow. Here we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose inter-model jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient global proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher-dimensional spaces efficiently.
