Fig. 6.

Perception as retrospective Bayesian decoding in working memory. (A and B) Schematic illustration of the theory. The x and y axes represent the first and second orientations, respectively. θ’s and r’s stand for stimulus orientations and their working-memory representations, respectively. The red dot indicates the actual orientations in a trial of the 2-line condition. The blue circle in A and the blue dot in B indicate the distribution of the two lines’ memory representations and a specific sample from it, respectively, at the report times in the 2-line condition. The area of the blue circle in A under the diagonal is the portion of incorrect ordinal discrimination based on the memory representations. For the blue-dot sample in B, the green circle indicates its likelihood function, and the Bayesian prior of ordinal relationship eliminates the shaded green portion, shifting the means of the posterior distribution to the green dot. (C) Simulated joint distribution for the subject of Fig. 3A, with the estimate for the 53° line against that for the 50° line in the 2-line condition (light green dots). The actual data are shown as gray dots (same as the gray dots in Fig. 3A). The light blue dots indicate simulated samples of memory representations (see Perception as Retrospective Bayesian Decoding in Working Memory from High to Low Levels). (D) Relative distributions obtained from the joint distributions in C by projecting them along the negative diagonal line. The gray, light blue, and light green histograms represent the relative distributions from the observation, the memory representation, and the retrospective Bayesian decoding, respectively. The black, blue, and green arrows indicate the mean of these relative distributions. The blue arrow is at the 3° and occluded by the red arrow, whereas the green arrow exaggerates the angular difference similar to the observation (black arrow). Note that 10,000 simulated samples were used to define each simulated relative distribution well, but only 100 of them were randomly selected for the corresponding scatter plot of the simulated joint distribution to avoid clutter. (E) The aftereffects predicted by the retrospective Bayesian decoding against the observations across subjects. The open dots and crosses are results for the 50° and 53° stimulus orientations, respectively. (F) The angular differences predicted by the retrospective Bayesian decoding against the observations across subjects. The simulations underestimated the angular difference for 2 of the total 12 subjects; this discrepancy can be eliminated by introducing a free parameter (see Perception as Retrospective Bayesian Decoding in Working Memory from High to Low Levels). deg, degrees.