You might be wondering how closely our simulation matches the facts about perception of the dress. In general, many studies (Lafer-Sousa et al. 2015, Toscani et al. 2017, Witzel et al. 2017)) have shown that assumptions about the illumination in the picture are a crucial factor in determining how a given person will interpret it; in our simulation we encoded these assumptions through the likelihood term. Some studies, such as the one discussed earlier about early birds vs. night owls (Wallisch 2017) support our experience-based account for why different people make different assumptions about the illumination. However, other studies suggest that assumptions about the illumination are not just significantly associated with experience by also with innate biological factors such as pupil diameter (Vemuri et al. 2016) or macular pigment optical density (Rabin et al. 2016). Thus, a more accurate model of the perception of the dress would also have to factor in these innate biological factors.
All of the studies we've mentioned have focused on the likelihood term of our Bayesian framing of the problem; none have discussed the role of the prior probabilities. This is probably because most people have similar prior probabilities for white and gold vs. black and blue dresses; that is, people assume that it is equally likely for a dress to be white and gold as it is for it to be black and blue, since your experience with dresses usually teaches you that dresses can come in all sorts of colors. Thus, in this scenario, the prior probabilities end up being largely irrelevant.
Are there cases where the prior probabilities do matter? Indeed there are! One example is the perception of 3D objects. All objects in the real world are three-dimensional, yet we only see them as two-dimensional projections of their three-dimensional shapes. For a given two-dimensional image, there are infinitely many three-dimensional shapes that could have generated that image. For example, all three images below look the same, but by dragging the shapes to rotate them you can see that they have in fact been generated from very different shapes:
Bayesian methods can very successfully model the perception of 3D shapes from ambiguous 2D images such as these (Kersten and Yuille (2003)). In the examples above, all three shapes have equal likelihoods of generating this image (the likelihoods might actually be a bit different, since the one on the left has more possible orientations that lead to this image than the others, but we can ignore that fact for our purposes). However, most people would probably interpret this image as representing a cube rather than the two stranger images represented here. This fact can be attributed to the viewers' prior probabilities of different shapes: Viewers assume that cubes are more likely to exist in the world than the other two shapes are, so they view the image as a cube.
3D cube rendering based on this example: http://codentronix.com/2011/05/10/html5-experiment-a-rotating-solid-cube/