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Gravitational microlensing events with high peak magnifications provide amuch enhanced sensitivity to the detection of planets around the lens star.However, estimates of peak magnification during the early stages of an event bymeans of chi^2 minimization frequently involve an overprediction, makingobserving campaigns with strategies that rely on these predictions inefficient.  I show that a rudimentary Bayesian formulation, incorporating the knownstatistical characteristics of a detection system, produces much more accuratepredictions of peak magnification than chi^2 minimisation. Implementation ofthis system will allow efficient follow-up observing programs that focus solelyon events that contribute to planetary abundance statistics.Comment: Accepted by ApJ. 19 pages, incl 7 figures and 2 table

Early Estimation of Microlensing Event Magnifications