This paper presents an in-depth mathematical analysis of the Monte Carlo replica method,
commonly used in global fitting studies within the high-energy physics theory field.
For the first time, we offer a rigorous derivation of the parameter distributions resulting from this method, demonstrating that,
while they align with Bayesian posteriors in linear models, they deviate in non-linear cases.
We then numerically assess this discrepancy in a phenomenologically important context: fitting SMEFT Wilson coefficients.
Our findings reveal that when non-linearity plays a significant role, the uncertainty estimates for key quantities differ between the two approaches.