The observation of binary neutron star merger GW170817 provides the first constraint on the Hubble constant $H_0$ using bright counterpart standard siren method. For the case of a dark standard siren, where an electromagnetic counterpart is not identified, a statistical method with a galaxy catalog can be exploited to estimate Hubble constant. With multiple events, a combined posterior can be obtained using Bayesian framework. In this lunch talk, I will walk you through the Hubble constant inference via a series of mock data challenges from O2-like detectability simulation of hundreds of binary neutron star mergers, using both the counterpart and the statistical standard siren methods and with focuses on gravitational wave selection and electromagnetic selection effects. I will also talk about Hubble constant measurement with real gravitational wave detections from LIGO.
