**Iconic memory is best assessed with the partial report procedure in which an array of letters appears briefly on the screen and a poststimulus cue directs the observer to report the identity of the cued letter(s). Typically, 6–8 cue delays or 600–800 trials are tested to measure the iconic memory decay function. Here we develop a quick partial report, or qPR, procedure based on a Bayesian adaptive framework to estimate the iconic memory decay function with much reduced testing time. The iconic memory decay function is characterized by an exponential function and a joint probability distribution of its three parameters. Starting with a prior of the parameters, the method selects the stimulus to maximize the expected information gain in the next test trial. It then updates the posterior probability distribution of the parameters based on the observer's response using Bayesian inference. The procedure is reiterated until either the total number of trials or the precision of the parameter estimates reaches a certain criterion. Simulation studies showed that only 100 trials were necessary to reach an average absolute bias of 0.026 and a precision of 0.070 (both in terms of probability correct). A psychophysical validation experiment showed that estimates of the iconic memory decay function obtained with 100 qPR trials exhibited good precision (the half width of the 68.2% credible interval = 0.055) and excellent agreement with those obtained with 1,600 trials of the conventional method of constant stimuli procedure (RMSE = 0.063). Quick partial-report relieves the data collection burden in characterizing iconic memory and makes it possible to assess iconic memory in clinical populations.**

*partial-report superiority effect*. The effect demonstrates performance benefits from one form of visual sensory memory, the iconic memory. The relationship between observer's performance and cue delay is called the

*iconic memory decay function*.

*pc*(

*x*) is the probability of correctly reporting the cued letter at a target and cue onset asynchrony of

*x*;

*a*is the asymptotic performance level, often associated with residual information in short-term memory after iconic memory decays completely;

_{0}*a*

_{1}is the performance level when

*x =*0; and

*τ*is the time constant of iconic memory decay, the time it takes for the observer's partial-report superiority effect to drop to 37% of its initial level. In the beginning, the procedure defines (a) a three dimensional

*θ*= (

*a*

_{0},

*a*

_{1},

*τ*) parameter space that represents all potential observable iconic memory decay functions, and (b) a one-dimensional stimulus search space over a range of possible levels of target and cue onset asynchronies,

*x*.

*p*

_{t}_{= 0}(

*θ*), is defined as a three-dimensional joint probability distribution, in which each dimension corresponds to one parameter of the iconic memory decay function.

*t-*th trial, the prior distribution

*p*(

_{t}*θ*) is updated to the posterior distribution

*p*(

_{t}*θ*|

*x*,

*r*) with the observer's response

_{t}*r*(correct or incorrect) to a test with a cue delay of

_{t}*x*by Bayes rule: where

*θ*= (

*a*

_{0},

*a*

_{1},

*τ*) represents the parameters of the iconic memory decay function,

*p*(

_{t}*θ*) is the prior probability density function of

*θ*. The probability of a response

*r*in a given stimulus condition

_{t}*x*,

*p*(

_{t}*r*|

_{t}*x*), is estimated by weighting the empirical response probability by the prior: where

*p*(

*r*|

_{t}*θ*,

*x*) is the likelihood of observing response

*r*given

_{t}*θ*and cue delay

*x*;

*p*(

*r*= correct|

_{t}*θ*,

*x*) is computed with the iconic memory decay function (Equation 1);

*p*(

*r*= incorrect|

_{t}*θ*,

*x*) = 1 −

*p*(

*r*= correct|

_{t}*θ*,

*x*) .

*x*that would maximize the expected information gain about the parameters of the iconic memory decay function. Here, information is quantified by entropy, a measure of uncertainty associated with variables (Shannon, 1948). The qPR uses a one-step-ahead search strategy to search for the cue delay that would lead to the minimum expected entropy (Cobo-Lewis, 1997; Kontsevich & Tyler, 1999; Kujala & Lukka, 2006; Lesmes, et al., 2006). It first computes the expected posterior probability distributions for all possible cue delays. The entropy of the posterior is defined as:

*x =*0.11 s (bottom left panel) so that a cue delay of 0.11 s is tested in the first trial (top panel). After the 10th trial, qPR expects that the information gain after the 11th trial would be maximum at

*x =*0 s. The procedure therefore selects the stimulus with a cue delay of 0 s in the 11th trial.

*a*

_{0}values (from 0 to 0.5), 41 linearly spaced

*a*

_{1}values (from 0.5 to 1.0), and 40 log-linearly spaced

*τ*values (from 0.01 to 0.8 s). The broad parameter space ensures robust assessment of various populations and avoids effects of extreme values—the tendency to bias toward the center of the parameter space when the observer's true parameter values are close to the boundary of the space. The prior was set to a uniform distribution in the current study.

*a*

_{0}of the iconic memory decay function.

*pc*(

*x*), of the simulated observer was calculated for the selected cue delay

*x*(Equation 1). Observer's response in each trial was simulated by drawing a random number

*r*from a uniform distribution over the interval from 0 to 1. The response was labeled as correct if

*r*<

*pc*(

*x*), and incorrect otherwise. 1,000 simulated runs were conducted for each observer.

*i*-th trial can be calculated as: where

*P*

_{true}is the true parameter value, and

*P*is the parameter estimate obtained after the

_{ij}*i*-th trial in the

*j*-th simulation.

*i*-th trial can be calculated as

^{1}: where

*pc*is the estimated probability correct in the

_{ijk}*k*-th cue delay condition after

*i*trials obtained in the

*j*-th simulation and is the true probability correct.

*a*

_{0}, the average bias became less than 0.017 after 100 trials and 0.010 after 200 trials, and further decreased to 0.005 after 400 trials, 0.003 after 800 trials, and 0.001 after 1,600 trials. The average bias for

*a*

_{1}was −0.019 after 100 trials and −0.011 after 200 trials, and further decreased to −0.005 after 400 trials, −0.003 after 800 trials, and −0.001 after 1,600 trials. For

*τ*, the average bias was −0.013 after 100 trials and −0.003 after 200 trials, and decreased further to −0.0014 after 400 trials, −0.0015 after 800 trials, and −0.001 after 1,600 trials, all in log10 units. The average 68.2% HWCI of

*a*

_{0}started at 0.157 in the first trial, and decreased to 0.071 after 100 trials, 0.054 after 200 trials, and 0.020 after 1,600 trials. The average 68.2% HWCI of

*a*

_{1}started at 0.160 in the first trial, and decreased to 0.050 after 100 trials, 0.038 after 200 trials, and 0.014 after 1,600 trials. The average 68.2% HWCI of

*τ*started at 0.526 in the first trial, and decreased to 0.216 after 100 trials, 0.154 after 200 trials, and 0.051 after 1,600 trials, all in log10 units. Since the accuracy and precision after qPR 200 trials were reasonably good, we only present results from the first 200 trials in the rest of this article. The accuracy and precision of estimates of the parameters of the iconic memory decay function after 20, 50, 100, and 200 trials are summarized in Table 2.

*pc*is the true probability correct at the

_{i}*i*-th cue delay,

*n*is the number of trials tested at the

_{i}*i*-th cue delay. Here we assume that eight cue delays (

*I*= 8) are tested with the MCS method so that the total number of tested trials is

*n*× 8. The eight cue delays, 0, 0.03, 0.06, 0.14, 0.30, 0.65, 1.4, and 3.0 s, are selected based on a typical iconic memory procedure (Lu et al., 2005) and are the same as those used in the psychophysical validation experiment. A comparison between the standard deviation of the estimates from the MCS, the standard deviation of the estimates from the qPR, and the average 68.2% HWCI of the qPR is presented in Figure 8 and Table 4. To reach a 0.075 probability correct precision, the MCS requires 240–270 trials, while the qPR only needs about 50–90 trials. The qPR is 3–5 times more efficient than the MCS. In terms of testing time, using the qPR, an iconic memory decay function can be estimated with reasonable accuracy and precision in less than 10 min, which is considerably faster than the 1 hr of testing time with the conventional MCS.

_{i}*x*-coordinate of the center of the circle in trials 1–20, 21–50, 51–100, and 101–200. In the first 20 trials, the qPR intensively tests the shortest and longest cue delays to characterize

*a*

_{0}and

*a*

_{1}, with only a few trials on short cue delays (0.03–0.3 s). Then the stimulus sampling of the qPR spreads to short cue delays and progressively moves to the range around the true

*τ*value (0.2–0.4 s). The method does not frequently test cue delays greater than 0.5 s (except 3.0 s) throughout the whole experiment.

*i*-th cue delay of the

*j*-th run of the qPR procedure for the

*k*-th observer, and is the probability correct at the

*i*-th cue delay for the

*k*-th observer in the MCS procedure. The RMSE started at 0.149 after the first qPR trial and decreased to 0.063 after 100 qPR trials and to 0.049 after 200 qPR trials.

*a*

_{0},

*a*

_{1}, and

*τ*, were 0.14, 0.05, and 0.28 (log10 units) after 200 qPR trials, respectively. The average COR of probability correct was 0.15, 0.14, and 0.12 for the three observers. The Bland-Altman plots in the upper row of Figure 15 show that the difference of parameter estimates between the first and second runs of the qPR procedure in each session fell within the 95% confidence limits (top and bottom dashed lines). The Bland-Altman plots on probability correct (the bottom row of Figure 15) also show that the estimated iconic memory decay functions from repeated runs of the qPR procedure were quite consistent.

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