One of the broad aims of my work is to apply the approach of Bayesian Decision Theory to attentional phenomena. In this particular paper, published back in 2009, I examined one specific aspect of the approach: the decision rule.
Described very succinctly Bayesian Decision Theory consists of two main steps. Firstly, we make an inference about the state of the world. This itself involves combining noisy sensory observations and our expectations about what is more or less likely to be the case. The second step, is the decision rule. It describes how we translate that guess about the state of the world into an action.
In order to examine the decision rule, I used a specific covert attentional task. A detection task was run: people had to indicate if a vertical line was present or absent. This sounds easy, but it was actually pretty hard because the lines were small and flashed up briefly. In addition, while the target object was a vertical line, there were distractor lines, and on average these were also vertical, but on any given trial their orientation was jittered with various degrees of external noise. This means that it is impossible to perfectly detect targets, and it provides insight into the decision rule. In short, the first step was to infer the orientations of the lines displayed on a screen, and the second step was to decide whether to respond ‘present’ or ‘absent’.
One decision rule, the MAX rule, states that people should compare the most (i.e. maximum) orientation with a threshold orientation and indicate ‘present’ if the threshold is exceeded. This is in fact an optimal decision rule if the uncertainty that people have about the orientation of targets and distracters are equal. However, because of the added external noise (in this distracter heterogeneity experiment) this was not the case. So did people stick with the MAX rule, and achieve sub-optimal performance, or did they use another decision rule which allowed the best possible detection performance?
It turns out that people did not use the MAX rule, and instead they seemed to use a more optimal MAP rule. This maximum a posteriori rule is very similar to the MAX rule, but instead of comparing the maximum orientation to a threshold, people acted as follows: People seemed to evaluate the probability that the target was present, and if this probability exceeded a threshold, then they indicated ‘present’.
Vincent, B. T., Baddeley, R. J., Troscianko, T., & Gilchrist, I. D. (2009). Optimal feature integration in visual search. Journal of Vision, 9(5):15, 1-11.
UPDATE 1: The basic line of reasoning was supported in this following paper in Nature Neuroscience which used an almost identical experiment, but which explored a wider range of issues.
Ma, W. J., Navalpakkam, V., Beck, J. M., Berg, R. V. D., & Pouget, A. (2011). Behavior and neural basis of near-optimal visual search. Nature Neuroscience, 14(6), 783–790.