We begin by considering uncertainty due to the fact that the target can appear in any one of
N locations within an alternative. This results in
N target vectors that contain the target at different locations. We therefore add a subscript to the target vector,
t i (
i = 1, …,
N), where
i indicates the location of the target within the alternative. The likelihood that a particular alternative contains the target is the sum of the likelihoods of the target across all locations in the alternative. This generalizes
Equation A4 to
Because there are also multiple potential distractor features for a given alternative (
D), the model needs to sum across all possible distractor features in addition to the possible target locations. This adds another subscript to both the target vector variable,
t ij, and to our distractor vector variable,
d j. For example, for a given target feature value of
F Targ, the target vector
t 12 = [
F Targ,
F 2,
F 2,
F 2], and distractor vectors are represented by
d 2 = [
F 2,
F 2,
F 2,
F 2]. When distractor uncertainty is accounted for, the likelihood in
Equation A5 is generalized to
This equation is representative of the likelihood in the target-known search where
F Targ is known to the observer. For an oddity search, there is also uncertainty as to the target feature value. We incorporate this additional uncertainty by adding an additional subscript,
k, to the target vector, which indicates the feature value of the target. For an alternative with four possible locations, a feature vector
t 213 = [
F 1,
F 3,
F 1,
F 1]. Note that the feature value of the target cannot be the same as the distractor, and hence,
k ≠
j. The target and distractor feature values are otherwise independent, and hence, any pairing of feature values as target/distractor is equally likely although it is straightforward to generalize this as well. The model must now sum across all target feature values (
V values) in addition to the other components shown in
Equation A6,
We now describe the implementation of this model with Gaussian densities.