Towards a unified treatment of gravitational-wave data analysis

Abstract

We present a unified description of gravitational-wave data analysis that unites the templatebased analysis used to detect deterministic signals from well-modeled sources, such as binary-blackhole mergers, with the cross-correlation analysis used to detect stochastic gravitational-wave backgrounds. We also discuss the connection between template-based analyses and those that target poorly-modeled bursts of gravitational waves, and suggest a new approach for detecting burst signals.PACS numbers: 04.80. Nn, 04.30.Db, 07.05.Kf, 95.55.Ym Gravitational-wave data analysis is conventionally divided into three classes that depend on the nature of the signal: (i) well-modeled deterministic signals, such as those from compact binary inspirals; (ii) poorly-modeled deterministic signals, such as those from core-collapse supernovae; and (iii) stochastic signals, such as those from a phase transition in the early Universe. Here we will argue that this division is rather artificial and unnecessary, and suggest that a unified treatment can yield deeper insights. The elements needed to unify cases (i) and (ii) can be found in Refs. [1][2][3][4]. Here we provide a unification of cases (i) and (iii) using hierarchical Bayesian modeling [5].The motivation for developing a unified description of gravitational-wave data analysis is two-fold. First there is the pedagogical value of a coherent picture that emphasizes the common foundation of the disparate analysis techniques found in the literature, and second, the unified picture can provide a deeper understanding that may suggest new approaches. To illustrate the latter point we conclude our discussion by proposing a novel technique for detecting un-modeled "bursts" of gravitational waves.In the conventional picture, signals for which we have waveform templates are analyzed using a matched-filter statistic [6], un-modeled signals are characterized in terms of an excess power statistic [7], and stochastic signals are analyzed using a cross-correlation statistic between pairs of detectors [8]. The connection between the various forms of analysis is not immediately apparent, especially when described in a frequentist framework.In the case of un-modeled signals, the analyses usually focus on short duration "bursts" of gravitational-wave energy that are localized in a time-frequency representation of the data. The connection between a waveform template-based search and a burst search becomes apparent in the case of fully-coherent network analyses, where it becomes possible to solve for the gravitational-wave signal by either maximizing the likelihood [2] or locating regions of high posterior density [3,4]. To obtain meaningful results these analyses require constraints or pri-

Searching for gravitational-wave transients with a qualitative signal model: Seedless clustering strategies

“…Cornish and Romano have recently emphasized the connection between data analysis algorithms and the signal model for which they are optimal [26]. Following the logic of Refs.…”

“…Following the logic of Refs. [26,27], STOCHTRACK is an optimal search algorithm (in the limit that T ! 1) for the class of signals described by quadratic Bézier curves in spectrograms of GW power with durations greater than t min .…”

Mismodeling in gravitational-wave astronomy: The trouble with templates

“…This can greatly aid in separating signals from noise in the data, s(t), by demanding that the residuals, r(t) = s(t) − h(t), are consistent with our instrument noise model. The different classes of analyses can be classified by the strength of the priors [1], ranging from the weak signal priors used in burst searches [2][3][4][5][6][7][8] and stochastic searches [9][10][11][12][13][14][15], to the highly restrictive priors used in searches for binary mergers [16][17][18][19][20][21][22][23].…”

An introduction to Bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models

“…Note that π with no parentheses and no subscript is the mathematical constant, not a prior distribution. There is no square root in the normalisation factor because d is (typically) complex, which means that we are working with a twodimensional Gaussian-the Whittle likelihood (Whittle, 1951); see also Cornish & Romano (2013). This likelihood function reflects our assumption that the noise in gravitational-wave detectors is Gaussian 5 .…”