Accumulation of evidence during sequential decision making: the importance of top-down factors

Abstract

In the last decade, great progress has been made in characterizing the accumulation of neural information during simple unitary perceptual decisions. However, much less is known about how sequentially presented evidence is integrated over time for successful decision making. The aim of this study was to study the mechanisms of sequential decision making in humans. In a magnetoencephalography (MEG) study, we presented healthy volunteers with sequences of centrally presented arrows. Sequence length varied between one and five arrows, and the accumulated directions of the arrows informed the subject about which hand to use for a button press at the end of the sequence (e.g., LRLRR should result in a right-hand press). Mathematical modeling suggested that nonlinear accumulation was the rational strategy for performing this task in the presence of no or little noise, whereas quasilinear accumulation was optimal in the presence of substantial noise. MEG recordings showed a correlate of evidence integration over parietal and central cortex that was inversely related to the amount of accumulated evidence (i.e., when more evidence was accumulated, neural activity for new stimuli was attenuated). This modulation of activity likely reflects a top-down influence on sensory processing, effectively constraining the influence of sensory information on the decision variable over time. The results indicate that, when making decisions on the basis of sequential information, the human nervous system integrates evidence in a nonlinear manner, using the amount of previously accumulated information to constrain the accumulation of additional evidence.

Figure 1.

Task setup and diagram. A, Subjects were shown sequences of one to five arrows. Each arrow was shown for 100 ms followed by a 200 ms blank screen, leading to a stimulus onset asynchrony between two arrows of 300 ms. At the end of each arrow sequence, the fixation square turned green, and subjects had to decide as fast as possible whether the predominant direction of the arrow stimuli was left or right, by pressing a button with their left or right hand. B, The cumulative number arrows favoring one or the other direction, which is used here as a proxy for accumulated evidence (see mathematical model), is plotted as a function of time. Subjects start with no evidence for either direction (0, in black). Each incoming arrow moves the sum up or down in the diagram. The transitions of the example sequence of A are shown in solid lines in the diagram. States at which no decision can be made yet are shaded light gray, whereas states at which enough information has been accrued for a decision are shaded dark gray.

Figure 2.

Predictions from mathematical model. The LLR is plotted as a function of the amount of accumulated evidence and three scenarios of perceptual uncertainty: complete perceptual certainty (p = 1) (A), high amount of perceptual certainty (p = 0.95) (B), and low amount of perceptual certainty (p = 0.6) (C).

Figure 3.

Behavioral results suggesting that subjects accumulate incoming evidence. A, RTs as a function of accumulated evidence and sequence length. B, Subject's responses as a function of accumulated evidence for a rightward response. C, Influence of the position of the arrow in the sequence on RT. The later arrows (fourth and fifth in the sequence) showed a larger contribution to subject's RT than arrows presented early in the sequence. Error bars indicate SEM.

Figure 4.

Amount of previous evidence determines neural activity at stimulus onset. A, Grand average of the topography of the influence of previously accumulated evidence (evidence) on brain activity at the onset of the incoming stimulus (0–50 ms). The markers indicate clusters of significant regression weights (p < 0.05, corrected for multiple comparisons). The right parietal cluster is denoted by “+,” and the central cluster is denoted by “o.” B, Time course of sensors showing a significant influence of evidence on activity at stimulus onset. For illustration purposes, as well as to be able to dissociate between the effects of evidence and change (see below), we only plot trials in which there was no stimulus change. It can be seen that both at the onset of the third stimulus (600 ms), the fourth stimulus (900 ms) and the fifth stimulus (1200 ms) there is overall lower activity when more evidence has been accumulated.

Figure 5.

Amount of accumulated evidence changes processing of new stimuli. A, Grand average of the topography of the influence of accumulated evidence (evidence) on brain activity changes induced by the new stimulus, at two time intervals (150–225 and 225–300 ms after stimulus onset). The dots indicate clusters of significant regression weights (p < 0.05, corrected for multiple comparisons). B, Time course of the sensors showing a significant influence of evidence on activity changes. More evidence leads to attenuated activity changes for the third stimulus (750–900 ms), the fourth stimulus (1050–1200 ms), and the fifth stimulus (1350–1500 ms). Other conventions are as in Figure 4.

Figure 6.

Change in evidence leads to increased activity. A, B, Grand average of the topography of the influence of a change in arrow direction (change) on brain activity change, at two time intervals [150–225 ms (A) and 225–300 ms (B) after stimulus onset]. The dots indicate clusters of significant regression weights (p < 0.05, corrected for multiple comparisons). C, D, Time course of posterior sensors showing a significant influence of change after 150–225 ms (C), and of frontal sensors showing a significant influence of change after 225–300 ms (D). For illustration purposes, as well as to be able to dissociate between evidence and change (see below), we present one level of evidence for each time window.

Figure 7.

Occipital activity attenuates and frontal activity increases over time. A, B, Grand average of the topography of the influence of time on changes in brain activity induced by the stimulus, at two time intervals [150–225 ms (A) and 225–300 ms (B) after stimulus onset]. The dots indicate clusters of significant regression weights (p < 0.05, corrected for multiple comparisons). C, Time course of occipital sensors showing a significant negative relationship with time after 150–225 ms. D, Time course of frontal sensors showing a significant positive relationship with time both after 150–225 ms and after 225–300 ms. Other conventions are as in Figure 4.