Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking mechanism. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism. Specifically, we formulate the problem in terms of maximum likelihood estimation, and show that the computational problem of optimizing this cost function is tractable. Our main contribution is an algorithm and a proof that this algorithm is guaranteed to find the global optimum. We demonstrate the effectiveness of our estimator with numerical simulations.