Jonathan Gair leads a research group on "Data
Analysis". His research is in the development and application of new
methodology for gravitational wave data analysis and science exploitation. He
is playing a leading role within the LIGO/Virgo collaboration in deriving
constraints on cosmological parameters, such as the local expansion rate of the
Universe (the Hubble constant), from gravitational wave observations. He is also
heavily involved in the development of data analysis tools for, and assessing
the potential scientific impact of, the planned ESA-led space-based
gravitational wave detector LISA and currently chairs the LISA Science Group
which oversees that activity. Jonathan Gair also has completed research
projects connected to gravitational wave detection with pulsar timing and
astrometric measurements, and on the development of computationally efficient
techniques for parameter inference.
Cosmological and Astrophysical Inference
Observations of gravitational wave sources have huge potential to tell us about the astrophysical populations of sources that are the progenitors of the events, and can be used as probes of cosmology and fundamental physics. My research explores the scientific questions that these observations can answer, develops methods for answering those questions and puts these into practice on our new data sets.
Gravitational wave sources are standard sirens, in the sense that the intrinsic amplitude of the source can be inferred very accurately from measurements of the phase evolution of the source. The apparent amplitude of the source then gives an accurate measurement of distance without any need to calibrate to the local distance ladder. If the redshift of the source, i.e., the rate at which it is moving away from us due to the expansion of the Universe, can be inferred, these observations provide a probe of the expansion history of the Universe that in turn reveals the composition of the Universe on large scales. We have done such measurements using redshifts derived from electromagnetic counterparts to binary neutron star mergers  and statistically using redshifts in published catalogues of galaxies . The main research question for the future is to assess the size of systematic errors in these measurements which will become increasingly important as the precision of the measurements improves with future observations.
Estimating the rate of different types of astrophysical event is essential for understanding astrophysical populations and in predicting for the future. Rate estimation is complicated by selection effects, i.e., the fact that detectors of limited sensitivity cannot observe all events, and by possible confusion in the list of triggers between real signals and instrumental transients. Unbiased rate estimates requires developing and using robust statistical tools to handle these effects [5,6]. Combining rate estimation with astrophysical and cosmological parameter inference is an active topic of research.
Following the merger between two galaxies, the black holes that are ubiquitously found in the centres of galaxies are expected to merge after some delay, and in the right mass range these mergers can be observed in gravitational waves by the space-based gravitational wave detector LISA. Galaxy mergers in the early Universe are a direct probe of the formation of large scale structure and hence a key tracer of cosmology. LISA has a unique potential to extract this information [11,15]. We are currently interested in developing techniques to convert LISA’s observations into statements about the physical parameters that characterise the state of the early Universe.
Gravitational wave sources are a unique probe of the theory of general relativity in a highly relativistic and non-linear regime and testing GR with LIGO and LISA observations is an active area of research . The observation of extreme-mass-ratio inspirals (EMRIs) with LISA can provide a precise map of the spacetime structure in the vicinity of a massive black hole, and hence test the fact that these are described by the Kerr metric, as expected in GR. While many phenomenological or theory-specific tests have been proposed, there is as yet no systematic framework to characterise any potential deviations.
Computationally efficient inference
Scientific inference on gravitational wave observations relies on the availability of models of potential signals. Typically it is very expensive computationally to generate these models using the most sophisticated and accurate techniques, which makes the best models unsuitable for inference calculations that typically need hundreds of thousands of waveform evaluations. To make inference practical we require phenomenological or “kludge” models that capture the key physical features of the waveforms at much lower computational cost. For LISA EMRI events such models can be constructed by adding radiative effects onto geodesic motion [4,17], but at present these do not get us close enough to the true parameters of the signal so further development is needed.
Another approach to efficient inference is reduced order modelling. This relies on building a compressed basis for the space of waveform models and basing inference on that reduced basis using a technique known as reduced order quadrature. These reduced order quadrature methods can accelerate inference on compact binary signals by an order of magnitude . A new reduced order model is required for each new waveform model and detector, so these methods are constantly being developed and improved.
Data analysis methodology
Extracting science from gravitational wave observations relies on sophisticated statistical and computational techniques to identify candidate signals in the data and extract their parameters. Different detectors pose different challenges. For LIGO the challenge is to identify rare and short-lived signals in long data sets dominated by instrumental noise . For LISA the challenge is to disentangle many thousands of signals of different types that overlap in time and frequency and can last for many years. There are additional challenges associated with uncertainties in the instrumental noise. At present many of the challenges for LISA data analysis are unsolved. EMRIs pose a p[articular challenge because of the large parameter space pf possible signals and relative complexity of the waveforms. Nearby events can be found using model-free methods , but these don’t perform well in the face of source confusion. Techniques that identify many individual parts of the signal and then combine this information perform better  but currently rely too much on specific details of the signals. Developing these methods into a robust algorithm for LISA data analysis is work in progress, as is the development of methods for handling instrumental artefacts and for carrying out a final global fit of all sources simultaneously.
Pulsar timing arrays are sensitive to gravitational waves at nanohertz frequencies generated by very massive black hole binary mergers. PTA analysis poses challenges due to poorly understood red noise properties in individual pulsars in the array, uneven sampling of the data and continuously changing instrumental properties. The first source PTAs are expected to observe is the stochastic background of gravitational waves from the population of unresolved massive black hole mergers. In  we developed an approach for phase-coherent mapping of such a background. Such mapping will extract the maximum possible information from future PTA observations. Astrometric measurements of stellar positions with satellites such as Gaia also have the potential to detect gravitational waves at nanohertz frequencies and future astrometric satellites should provide complementary information to PTAs .
Given the computational expense of modelling gravitational wave signals accurately, inference must be robust to residual uncertainties in the phenomenological models used. One way to ensure this is to include additional parameters in the waveform model that encapsulate these uncertainties and marginalise over them when constructing final posterior distributions for the parameters of interest. One approach to this is to use Gaussian process regression , but other approaches such as machine learning are now being explored.
 Soares-Santos, M, …, Gair, J R, et al., 2019, First Measurement of the Hubble Constant from a Dark Standard Siren using the Dark Energy Survey Galaxies and the LIGO/Virgo Binary–Black-hole Merger GW170814, Astrophys. J. 876 L7.
 Mihaylov, D P, Moore, C J, Gair, J R, Lasenby, A, and Gilmore, G, 2018, Astrometric Effects of Gravitational Wave Backgrounds with non-Einsteinian Polarizations, Phys. Rev. D 97 124058
 Abbott, B P, ..., Gair, J R, et al., 2017, A gravitational-wave standard siren measurement of the Hubble constant, Nature Lett. 551 85.
 Chua, A J K, Moore, C J, and Gair, J R, 2017, The Fast and the Fiducial: Augmented kludge waveforms for detecting extreme-mass-ratio inspirals, Phys. Rev. D 96, 044005.
 Abbott, B P, ..., Gair, J R, et al., 2016, The Rate of Binary Black Hole Mergers Inferred from Advanced LIGO Observations Surrounding GW150914, Astrophys. J. Lett. 833, 1.
 Abbott, B P, ..., Gair, J R, et al., 2016, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116, 061102.
 Moore, C J, and Gair, J R, 2014, Novel method for incorporating model uncertainties into gravitational wave parameter estimates, Phys. Rev. Lett. 113 251101.
 Gair, J R, Romano, J D, Taylor, S R, and Mingarelli, C M F, 2014, Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays, Phys. Rev. D 90 082001.
 Canizares, P, Field, S E, Gair, J R, and Tiglio, M, 2013, Gravitational wave parameter estimation with compressed likelihood evaluation, Phys. Rev. D 87, 124005.
 Gair, J R, Vallisneri, M, Larson, S L, and Baker, J G, 2013, Testing General Relativity with Low-Frequency, Space-Based Gravitational Wave Detectors, Living Reviews in Relativity 16, 7.
 Sesana, A, Gair, J R, Berti, E and Volonteri, M, 2011, Reconstructing the massive black hole cosmic history through gravitational waves, Phys. Rev. D 83 044036.
 Feroz, F, Gair, J R, Hobson, M P and Porter, E K, 2009, Use of the MultiNest algorithm for gravitational wave data analysis, Class. Quantum Grav. 26 215003.
 Gair, J R and Porter, E K, 2009, Cosmic Swarms: A search for Supermassive Black Holes in the LISA data stream with a Hybrid Evolutionary Algorithm, Class. Quantum Grav. 26 225004.
 Babak, S, Gair, J R and Porter, E K, 2009, An algorithm for detection of extreme mass ratio inspirals in LISA data, Class. Quantum Grav. 26, 135004.
 Gair, J R, 2009, Probing black holes at low redshift using LISA EMRI observations, Class. Quantum Grav. 26, 094034.
 Gair, J R and Jones, G J, 2007, Detecting extreme mass ratio inspiral events in LISA data using the Hierarchical Algorithm for Clusters and Ridges (HACR), Class. Quantum Grav. 24, 1145.
 Gair, J R and Glampedakis, K, 2006, Improved approximate inspirals of test-bodies into Kerr black holes, Phys. Rev. D73 064037.
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