This paper proposes an innovative method, named b-ntPET, for solving a competition model in PET. The model is built upon the state-of-the-art method called lp-ntPET. It consists in identifying the parameters of the PET kinetic model relative to a reference region that rule the steady state exchanges, together with the identification of four additional parameters defining a displacement curve caused by an endogenous neurotransmitter discharge, or by a competing injected drug targeting the same receptors as the PET tracer. The resolution process of lp-ntPET is however suboptimal due to the use of discretized basis functions, and is very sensitive to noise, limiting its sensitivity and accuracy. Contrary to the original method, our proposed resolution approach first estimates the probability distribution of the unknown parameters using Markov-Chain Monte-Carlo sampling, distributions from which the estimates are then inferred. In addition, and for increased robustness, the noise level is jointly estimated with the parameters of the model. Finally, the resolution is formulated in a Bayesian framework, allowing the introduction of prior knowledge on the parameters to guide the estimation process toward realistic solutions. The performance of our method was first assessed and compared head-to-head with the reference method lp-ntPET using well-controlled realistic simulated data. The results showed that the b-ntPET method is substantially more robust to noise and much more sensitive and accurate than lp-ntPET. We then applied the model to experimental animal data acquired in pharmacological challenge studies and human data with endogenous releases induced by transcranial direct current stimulation. In the drug challenge experiment on cats using [18F]MPPF, a serotoninergic 1A antagonist radioligand, b-ntPET measured a dose response associated with the amount of the challenged injected concurrent 5-HT1A agonist, where lp-ntPET failed. In human [11C]raclopride experiment, contrary to lp-ntPET, b-ntPET successfully detected significant endogenous dopamine releases induced by the stimulation. In conclusion, our results showed that the proposed method b-ntPET has similar performance to lp-ntPET for detecting displacements, but with higher resistance to noise and better robustness to various experimental contexts. These improvements lead to the possibility of detecting and characterizing dynamic drug occupancy from a single PET scan more efficiently.