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In estimation of distribution algorithms (EDAs), probability models hold accumulating evidence on the location of an optimum. Stochastic sampling drift has been heavily researched in EDA optimization but not in EDAs applied to genetic programming (EDA-GP). We show that, for EDA-GPs using probabilistic prototype tree models, stochastic drift in sampling and selection is a serious problem, inhibiting scaling to complex problems. Problems requiring deep dependence in their probability structure see such rapid stochastic drift that the usual methods for controlling drift are unable to compensate. We propose a new alternative, analogous to likelihood weighting of evidence. We demonstrate in a small-scale experiment that it does counteract the drift, sufficiently to leave EDA-GP systems subject to similar levels of stochastic drift to other EDAs.