A single input single output MEMS parameter sensor is investigated as a candidate for a chemical nose application. MEMS are subject to and influenced by noise sources which are inherent as well as introduced by measurement electronics. A method for quantifying the precision of parameter estimation is applied for prediction of linear sensor resolution in the presence of noise. The dynamic range of linear sensors is bound by the noise floor and the onset of nonlinearity: as the noise increases the dynamic range is thus decreased. Nonlinear sensing techniques are embraced for large amplitude response. Focus is given to a parametric resonator, where the stiness of the structure is modulated near twice the resonant frequency. Statistical methods dene the probability for the parametric resonator to be in a large amplitude state, leading to its resolution. The results of these methods lead toward comparing the linear and nonlinear parameter sensing techniques.