How specific statistical priors do we maintain? While it is known that past stimulus statistics influences later perceptual decisions, it is unclear how such effects would interact and influence decisions across different spatial locations. To test this, we used a visual discrimination paradigm with two target locations, and two abstract shapes that could appear in varying levels of Gaussian noise. The stimulus appearance probabilities shifted from the training block (always balanced) to the test block (unbalanced). In each trial, participants reported via fixation which of the two locations the stimulus would likely to appear, and using a touchpad, they chose which shape was presented. In the test of Exp. 1, object A was equally more frequent at both locations. In the test of Exp. 2, object A was more frequent at one location, but less frequent at the other location. In Exp. 1, strong priors emerged after the shift, as if participants were compensating to maintain the overall training probabilities. In contrast, in Exp. 2, participants followed the shift in appearance probabilities with their responses. This suggests that only simple priors emerge automatically, with more complex statistics, averaging might cause visual decisions to follow local probabilities more accurately.