Abstract: We compute upper limits on the nanohertz-frequency isotropic stochastic gravitational wave background (GWB) using the 9 year data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration. Well-tested Bayesian techniques are used to set upper limits on the dimensionless strain amplitude (at a frequency of 1 yr(exp -1) for a GWB from supermassive black hole binaries of A(sub gw) less than 1.5 x 10(exp -15). We also parameterize the GWB spectrum with a b…