We develop a new method of modeling microlensing events based on a Monte Carlo simulation that incorporates both a Galactic model and the constraints imposed by the observed characteristics of the event .
The method provides an unbiased way to analyze the event especially when parameters are poorly constrained by the observed lightcurve .
We apply this method to search for planetary companions of the lens in OGLE-2003-BLG-423 , whose maximum magnification A _ { max } = 256 \pm 43 ( or A _ { max } = 400 \pm 115 from the lightcurve data alone ) is the highest among single-lens events ever recorded .
The method permits us , for the first time , to place constraints directly in the planet-mass/projected-physical-separation plane rather than in the mass-ratio/Einstein-radius plane as was done previously .
For example , Jupiter-mass companions of main-sequence stars at 2.5 AU are excluded with 80 % efficiency .