Pulsed Arterial Spin Labeling (PASL) techniques potentially allow the absolute, non-invasive quantification of brain perfusion and arterial transit time. This can be achieved by fitting a kinetic model to the data acquired at a number of inversion time points (TI). The intrinsically low SNR of PASL data, together with the uncertainty in the model parameters, can hinder the estimation of the parameters of interest. Here, a two-compartment kinetic model is used to estimate perfusion and transit time, based on a Maximum a Posteriori (MAP) criterion. A priori information concerning the physiological variation of the multiple model parameters is used to guide the solution. Monte Carlo simulations are performed to compare the accuracy of our proposed Bayesian estimation method with a conventional Least Squares (LS) approach, using four different sets of TI points. Each set is obtained either with a uniform distribution or an optimal sampling strategy designed based on the same MAP criterion. We show that the estimation errors are minimized when our proposed Bayesian estimation method is employed in combination with an optimal set of sampling points. In conclusion, our results indicate that PASL perfusion and transit time measurements would benefit from a Bayesian approach for the optimization of both the sampling strategy and the estimation algorithm, whereby prior information on the parameters is used.