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We perform Bayesian model selection with parameter estimation to identifypotentially lensed gravitational-wave images from the second observing run (O2)of Advanced LIGO and Advanced Virgo. Specifically, we compute the Bayesianevidence for a pair of events being lensed or not lensed (unlensed) usingnested sampling. We consider the discrete coalescence phase shifts that can beinduced if the gravitational-wave signal interacts with the lens caustics inthe model selection. We find that the pair of events, GW170104 and GW170814with a $\pi/2$ coalescence phase shift, has a significant Bayes factor($B^L_{U}$ $\sim 1.98 \times 10^4$) favoring the lensing hypothesis. However,after taking into account the long time delay of approximately 7 months betweenevents, the timing Bayes factor is significantly small ($B_t \sim8.7\times10^{-2}$). The prior probability for detecting strongly lensed pairsat O2 sensitivity are exceedingly small for both galaxy and galaxy clusterlensing. Combining the lensing and timing Bayes factors with the prior odds onlensing gives an odds ratio of $O^L_{U} \sim 20$. However, the model dependenceof the timing and prior odds factors does not provide strong evidence todemonstrate that the pair is strongly lensed.

Identifying strong gravitational-wave lensing during the second observing run of Advanced LIGO and Advanced Virgo