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The ringdown of the gravitational-wave signal from a merger of two blackholes has been suggested as a probe of the structure of the remnant compactobject, which may be more exotic than a black hole. It has been pointed outthat there will be a train of echoes in the late-time ringdown stage fordifferent types of exotic compact objects. In this paper, we present atemplate-based search methodology using Bayesian statistics to search forechoes of gravitational waves. Evidence for the presence or absence of echoesin gravitational-wave events can be established by performing Bayesian modelselection. The Occam factor in Bayesian model selection will automaticallypenalize the more complicated model that echoes are present ingravitational-wave strain data because of its higher degree of freedom to fitthe data. We find that the search methodology was able to identifygravitational-wave echoes with Abedi et al.'s echoes waveform model about 82.3%of the time in simulated Gaussian noise in the Advanced LIGO and Virgo networkand about 61.1% of the time in real noise in the first observing run ofAdvanced LIGO with $\geq 5\sigma$ significance. Analyses using this method areperformed on the data of Advanced LIGO's first observing run, and we find nostatistical significant evidence for the detection of gravitational-waveechoes. In particular, we find $<1\sigma$ combined evidence of the three eventsin Advanced LIGO's first observing run. The analysis technique developed inthis paper is independent of the waveform model used, and can be used withdifferent parametrized echoes waveform models to provide more realisticevidence of the existence of echoes from exotic compact objects.

Template-based Gravitational-Wave Echoes Search Using Bayesian Model Selection