Similitude is a intriguing approach in engineering vibroacoustics, which makes use of scaling laws. These scaling laws enable to predict the dynamic response of an original system by using the information obtained from a similar one, that is defined as avatar or replica according to the partial or complete degree of similitude.Potential applications range from simple plates and beams, to complex systems like gearboxes and help avoid costly measurements on large or small structures, since the results of one structure can be generalized between similar structures. While traditional similitude theory relies on deterministic models with fixed parameters, real-world systems often exhibit uncertainty, necessitating models that incorporate this variability. A common approach is to model parameter uncertainty, often quantified through Bayesian inference, using random variables with distributions obtained via Markov Chain Monte Carlo (MCMC) methods. This work investigates the inherent parameter uncertainty in a vibrating plate and examines how uncertainty in an avatar model influences scaling behaviour in the parent structure. The study compares uncertainty in the responses of both parent and avatar structures, ultimately describing how parameter uncertainty scales between them.