GW Searches with the Viterbi Algorithm

The Viterbi algorithm is a dynamic programming algorithm that determines the most likely sequence of states from a larger set of possible sequences. By transforming the time-series GW data into a time-frequency spectrogram, and referencing each time-frequency bin of the spectrogram as a unique state, the Viterbi algorithm can be applied to identify the most likely time-frequency path a signal would take throughout the observation if one is present. One can then compare this track with those typical of noise-only data to determine whether a signal has been identified. The advantage of this approach is that the computational complexity of the algorithm scales linearly with the data size, whereas a fully-coherent template search (which is of optimal sensitivity) scales very rapidly with the observation duration to the point that an all-sky continuous GW search becomes computationally intractable. This algorithm may therefore be applied to provide a rapid (but fairly uncertain) estimate of source parameters, which may then be investigated with a targeted coherent search (which greatly reduces the number of required templates).

This has been successfully applied in the incoherent case by J. Bayley et. al. (2019), which applies the Viterbi algorithm to the power spectrogram (which is obtained by taking the magnitude of the complex Fourier output). My research aims to build upon this work, improving sensitivity and investigating variations in its application that may be applicable to specific problems in GW data analysis.

Phase-sensitive Viterbi

When the power spectrogram is produced using the complex Fourier spectrogram of the time-series data, all phase information is lost. This inherently leads to a loss in sensitivity, as signals exhibit phase continuity (whereas noise does not) which cannot be exploited using only the power spectrogram. Therefore, if one is able to extend the application of the Viterbi algorithm to the more general, complex case, a boost in sensitivity is expected. As part of my research, I am investigating how (and if) this may be achieved.

Subtraction Viterbi

Another way to apply Viterbi to GW data is to iteratively apply the algorithm to the spectrogram, and to subtract away a small fraction of the identified tracks. This has the effect of removing strong noise fluctuations from the spectrogram and slowly digging towards the noise floor of the data. This can also allow for the identification of multiple signals within a given spectrogram. This method may also be applicable to data contaminated by strong instrumental lines, with the subtraction algorithm eliminating the line before searching for possible signals.

MBH Population Inference with LISA

One of the primary mission goals of LISA is to probe the underlying distribution of the MBH population. This is made possible by LISA's sensitivity to low-frequency GW sources (in the 1e-5 to 1e-2 Hz range). One expected type of source is the Extreme Mass Ratio Inspiral (EMRI) - the orbital decay and inspiral of a compact object (with a mass on the order of a few solar masses) into an MBH. These sources are long-lived, typically spending years within LISA's sensitivity window, and are extremely informative about the various parameters of the system. Observations of these events can be combined in a Bayesian hierarchical inference framework to infer properties of the MBH population. By constraining the MBH population, we can restrict MBH formation and evolution models, with ramifications for galaxy formation and evolution as a whole due to the close relationship between galaxies and their central MBH.

This is not a straightforward task, however - the observations are subject to numerous selection effects, which must be accounted for, and astrophysical modelling is required to extend EMRI population studies to the more-general case of the overall MBH population. My work involves the construction of a hierarchical inference framework that properly treats these selection effects to obtain unbiased estimates of how well we expect to probe the MBH population parameters when LISA is launched. This will involve the application of the latest EMRI waveform models, using Fisher Information Matrices to simulate the posteriors of individual events, and astrophysical modelling in order to prescribe suitable population models.