Fig 1.
A stimulus trial starts with a blank screen with a fixation circle.
After 500ms the stimulus appears for 750ms: a circular spot with random black and white pixels, darker than the random black and white background. Then, the blank screen returns and remains until the observer reports whether or not a spot was detected. The input level is the probability of a black pixel in the circular spot (here 0.6), whereas the background has probability 0.5. The spot, appearing at a random angle at a distance 150 pixels from the center, is marked here with an arrow for illustration.
Fig 2.
Temporal structure of stimuli.
Examples of input levels in their temporal order (top panels), and their corresponding power spectral densities (PSD, bottom panels), for the three types of stimuli used in the experiments. In the “White” stimulus (left; grey lines), consecutive input levels are independent and the PSD is flat. In the “Pink” stimulus (center; pink lines), consecutive input levels are correlated and the PSD decreases with frequency. The “Brown” session (right; brown lines) varies extremely slowly, consecutive input levels are highly correlated and the PSD decreases sharply.
Fig 3.
Experimental protocol.
Fig 4.
Psychometric curve parameters.
The input level at which detection probability is 0.5 defines the threshold θ. The steepness of the curve at threshold is represented by the slope k, see Eq 1.
Fig 5.
Instantaneous model observers were simulated to separate effects of the input structure from internal biases.
Instantaneous model observers receive a stream of input signals (xi; left) which goes through a local sigmoid input-output relation f(xi) to define a probability of detection for each input (middle). The response is then determined by a coin-toss according to this probability resulting in a binary detection (right).
Fig 6.
Slope of psychometric curve depends on input temporal structure.
a) Example of psychometric curve for a single observer, IR_F_23. Symbols: binned detection probability, lines: fitted sigmoid. Color code marked in legend. b) Estimated slopes of psychometric curves for all observers (each colored dot is an individual). On average, the slope increases for more slowly varying input signals: 29.3 ± 2.5 32.8 ± 4.2 36.5 ± 2.7 for White, Pink and Brown respectively. Errorbars mark the standard deviation (STD) across observers. c) Individual slopes relative to White session: Slope estimated for White signal is subtracted from slopes of the other signals for each observer individually. Statistical T-test performed, significant changes were found with p-values 0.02 and 0.0003 respectively.
Fig 7.
Repetitive bias quantified by Probability of Alternations (POA).
a) POA computed for human observers (filled circles) and for 15 instantaneous model observers (Black +’s). Means are [0.43,0.28,0.21] for the model and [0.49,0.35,0.27] for the data, for White, Pink and Brown inputs respectively. Errorbars: Standard Deviation. Two sided T-test was performed between the groups of values showed strong significant difference (p-values: 0.0007,<0.0001,0.01). b) POA strongly depends on response time in all stimulus regimes. Trials were separated to shorter and longer than median for each observer, and POA computed for each group separately. The slow trials (marked Δ’s) exhibit a POA similar to the bias-less observer (marked black +’s), while the fast trials (marked O’s) show a much stronger repetitive bias and are largely responsible for the average effect seen in a.
Fig 8.
a) An example b) Psychometric curves are formed by estimating the detection probability as a function of the previous input from experimental data. The curve becomes sharper for colored inputs partly due to the correlation between current and previous input. c) Comparison to unbiased instantaneous model observers exposed to the same inputs, reveals the effect of recency bias inherent to the observers, in white and pink inputs. In brown there is much larger variability between individual data values.
Fig 9.
Dependence of response on previous response.
Detection probability of current signal conditioned on previous positive detections for White stimulus. +”: DP of current input. ‘++’: DP conditioned on detection of previous input, etc. DP increases significantly (p-value: 0.009) when the last input was detected, but does not continue to increase significantly for detection events further into the past.
Fig 10.
Positive and negative hysteresis in conditioned psychometric curves.
a) Example of Up (Δ′s) and Down (O’s) psychometric curves, conditioned on whether the current stimulus is higher or lower than the previous one, in a White stimulus experiment for one observer. Data points: markers, sigmoid fits: lines. Inset: value of hysteresis, defined as the difference between thresholds, for all observers in the three stimulus regimes (White, Pink, Brown from left to right). b) The same analysis as in A, where Up and Down are determined by comparing the current input level to its trend over τ = 32 previous trials. Hysteresis is negative here: Up has lower threshold than Down. Example data is taken from Brown stimulus of the same observer. Inset: Hysteresis value for all observers in the three stimulus regimes with τ = 32. c) Hysteresis value of all observers in the three stimulus regimes, as a function of the timescale defining the past trend (τ).
Fig 11.
Model of perception with two biases.
The backbone structure of the model (black arrows) is composed of a fixed input-output relation (sensory process) determining the probability of detection, and a coin flip decision based on this probability. Two biases modulate this backbone (red arrows): an Adaptation Bias varies the threshold based on the input history; and a Recency Bias modifies the final response based on previous one.
Fig 12.
Empirical psychometric curve parameters for model observers.
Model observers were presented with the three stimulus types, and their responses analysed to estimate empirical psychometric curves. Relative slopes a) and thresholds b) were computed by subtracting the corresponding parameters of the White stimulus from those of the Pink and Brown. Compare to experimental results in Fig 6.
Fig 13.
Probability of alternation (POA) in the response of humans observers (filled circles) and of model observers (Black).
Fig 14.
Hysteresis in model psychometric curves conditioned on stimulus trend.
Hysteresis in model shows qualitatively the same behavior as a function of τ, the timescale used to define the stimulus trend as Up or Down, as human observers, for all stimulus regimes.