Pulsar timing arrays (PTAs), which are currently operating around the world and achieving remarkable sensitivitiesin the ~1-100 nHz band, will observe supermassive black holes (SMBHs) at redshifts z < ~1. Until now, all estimates of the anticipated signal strength of these sources have relied primarily on simulations to predict the relevant merger rates. I will present results from acompletely new approach, which combines observational data and a fully self-consistent numerical evolution of the galaxy mass function. This method, which we will argue is superior to past estimates in several key ways, predicts a merger rate for massive galaxies that is ~10 times larger than that implied by previous calculations. I will explain why previous methods applied to this problem may systematically underestimate this merger rate, and one way in which
our method may overestimate the rate, so that our approach has complementary systematic uncertainties in the worst case, and is an overall improvement in the best case. Finally, I will show that the new rate implies a range of possible signal strengths that is already in mild tension with PTA observations, with our model predicting a detection at the 95% confidence level as early as 2016. This could make PTAs the first
instruments to directly detect gravitational waves, and will provide unprecedented information about the dynamics of merging galaxies, and merging bulges and supermassive black holes within those galaxies.