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The inherent bias pathology of the maximum likelihood (ML) estimation methodis confirmed for models with unknown parameters $\theta$ and $\psi$ when MLE$\hat \psi$ is function of MLE $\hat \theta.$ To reduce $\hat \psi$'s bias thelikelihood equation to be solved for $\psi$ is updated using the model for thedata $Y$ in it. Model updated (MU) MLE, $\hat \psi_{MU},$ often reduces eithertotally or partially $\hat \psi$'s bias when estimating shape parameter $\psi.$For the Pareto model $\hat \psi_{MU}$ reduces also $\hat \psi$'s variance. Theresults explain the difference that puzzled R. A. Fisher, between biased $\hat\psi$ and the unbiased estimate he obtained for two models with the "2-stageprocedure". MUMLE's implementation is equivalent to the abandoned 2-stageprocedure thus justifying its use. MUMLE and Firth's bias correcting likelihoodare also obtained with the Minimum Message Length method thus motivating itsuse in frequentist inference and, more generally, model updating with a priordistribution.

MLE's bias pathology, Model Updated Maximum Likelihood Estimates and Wallace's Minimum Message Length method