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To improve the accuracy of target selection for finger touch, we conceptualize finger touch input as an uncertain process, and derive a statistical target selection criterion, Bayesian Touch Criterion, by combining the basic Bayes' rule of probability with the generalized dual Gaussian distribution hypothesis of finger touch. The Bayesian Touch Criterion selects the intended target as the candidate with the shortest Bayesian Touch Distance to the touch point, which is computed from the touch point to the target center distance and the target size. We give the derivation of the Bayesian Touch Criterion and its empirical evaluation with two experiments. The results showed that for 2-dimensional circular target selection, the Bayesian Touch Criterion is significantly more accurate than the commonly used Visual Boundary Criterion (i.e., a target is selected if and only if the touch point falls within its boundary) and its two variants.