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Register a new userLabel Switching Problem in Bayesian Analysis for Gravitational Wave Astronomy
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Riccardo Buscicchio
Publication date
2019
fields
Physics
and research's language is
English
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The label switching problem arises in the Bayesian analysis of models containing multiple indistinguishable parameters with arbitrary ordering. Any permutation of these parameters is equivalent, therefore models with many such parameters have extremely multi-modal posterior distributions. It is difficult to sample efficiently from such posteriors. This paper discusses a solution to this problem which involves carefully mapping the input parameter space to a high dimensional hypertriangle. It is demonstrated that this solution is efficient even for large numbers of parameters and can be easily applied alongside any stochastic sampling algorithm. This method is illustrated using two example problems from the field of gravitational wave astronomy.
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Gravitational wave (GW) detection is now commonplace and as the sensitivity of the global network of GW detectors improves, we will observe $mathcal{O}(100)$s of transient GW events per year. The current methods used to estimate their source parameters employ optimally sensitive but computationally costly Bayesian inference approaches where typical analyses have taken between 6 hours and 5 days. For binary neutron star and neutron star black hole systems prompt counterpart electromagnetic (EM) signatures are expected on timescales of 1 second -- 1 minute and the current fastest method for alerting EM follow-up observers, can provide estimates in $mathcal{O}(1)$ minute, on a limited range of key source parameters. Here we show that a conditional variational autoencoder pre-trained on binary black hole signals can return Bayesian posterior probability estimates. The training procedure need only be performed once for a given prior parameter space and the resulting trained machine can then generate samples describing the posterior distribution $sim 6$ orders of magnitude faster than existing techniques.
This paper reviews gravitational wave sources and their detection. One of the most exciting potential sources of gravitational waves are coalescing binary black hole systems. They can occur on all mass scales and be formed in numerous ways, many of which are not understood. They are generally invisible in electromagnetic waves, and they provide opportunities for deep investigation of Einsteins general theory of relativity. Sect. 1 of this paper considers ways that binary black holes can be created in the universe, and includes the prediction that binary black hole coalescence events are likely to be the first gravitational wave sources to be detected. The next parts of this paper address the detection of chirp waveforms from coalescence events in noisy data. Such analysis is computationally intensive. Sect. 2 reviews a new and powerful method of signal detection based on the GPU-implemented summed parallel infinite impulse response filters. Such filters are intrinsically real time alorithms, that can be used to rapidly detect and localise signals. Sect. 3 of the paper reviews the use of GPU processors for rapid searching for gravitational wave bursts that can arise from black hole births and coalescences. In sect. 4 the use of GPU processors to enable fast efficient statistical significance testing of gravitational wave event candidates is reviewed. Sect. 5 of this paper addresses the method of multimessenger astronomy where the discovery of electromagnetic counterparts of gravitational wave events can be used to identify sources, understand their nature and obtain much greater science outcomes from each identified event.
On a time scale of years to decades, gravitational wave (GW) astronomy will become a reality. Low frequency (nanoHz) GWs are detectable through long-term timing observations of the most stable pulsars. Radio observatories worldwide are currently carrying out observing programmes to detect GWs, with data sets being shared through the International Pulsar Timing Array project. One of the most likely sources of low frequency GWs are supermassive black hole binaries (SMBHBs), detectable as a background due to a large number of binaries, or as continuous or burst emission from individual sources. No GW signal has yet been detected, but stringent constraints are already being placed on galaxy evolution models. The SKA will bring this research to fruition. In this chapter, we describe how timing observations using SKA1 will contribute to detecting GWs, or can confirm a detection if a first signal already has been identified when SKA1 commences observations. We describe how SKA observations will identify the source(s) of a GW signal, search for anisotropies in the background, improve models of galaxy evolution, test theories of gravity, and characterise the early inspiral phase of a SMBHB system. We describe the impact of the large number of millisecond pulsars to be discovered by the SKA; and the observing cadence, observation durations, and instrumentation required to reach the necessary sensitivity. We describe the noise processes that will influence the achievable precision with the SKA. We assume a long-term timing programme using the SKA1-MID array and consider the implications of modifications to the current design. We describe the possible benefits from observations using SKA1-LOW. Finally, we describe GW detection prospects with SKA1 and SKA2, and end with a description of the expectations of GW astronomy.
This is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples are drawn from gravitational-wave astronomy, though we endeavor for the presentation to be understandable to a broader audience. We begin with a review of the fundamentals: likelihoods, priors, and posteriors. Next, we discuss Bayesian evidence, Bayes factors, odds ratios, and model selection. From there, we describe how posteriors are estimated using samplers such as Markov Chain Monte Carlo algorithms and nested sampling. Finally, we generalize the formalism to discuss hyper-parameters and hierarchical models. We include extensive appendices discussing the creation of credible intervals, Gaussian noise, explicit marginalization, posterior predictive distributions, and selection effects.
The Laser Interferometer Space Antenna (LISA) will open three decades of gravitational wave (GW) spectrum between 0.1 and 100 mHz, the mHz band. This band is expected to be the richest part of the GW spectrum, in types of sources, numbers of sources, signal-to-noise ratios and discovery potential. When LISA opens the low-frequency window of the gravitational wave spectrum, around 2034, the surge of gravitational-wave astronomy will strongly compel a subsequent mission to further explore the frequency bands of the GW spectrum that can only be accessed from space. The 2020s is the time to start developing technology and studying mission concepts for a large-scale mission to be launched in the 2040s. The mission concept would then be proposed to Astro2030. Only space based missions can access the GW spectrum between 10 nHz and 1 Hz because of the Earths seismic noise. This white paper surveys the science in this band and mission concepts that could accomplish that science. The proposed small scale activity is a technology development program that would support a range of concepts and a mission concept study to choose a specific mission concept for Astro2030. In this white paper, we will refer to a generic GW mission beyond LISA as bLISA.
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