Decision Making through Integration of Sensory Evidence at Prolonged Timescales

Abstract

When multiple pieces of information bear on a decision, the best approach is to combine the evidence provided by each one. Evidence integration models formalize the computations underlying this process [1-3], explain human perceptual discrimination behavior [4-9], and correspond to neuronal responses elicited by discrimination tasks [10-14]. These findings suggest that evidence integration is key to understanding the neural basis of decision making [15-18]. But while evidence integration has most often been studied with simple tasks that limit deliberation to relatively brief periods, many natural decisions unfold over much longer durations. Neural network models imply acute limitations on the timescale of evidence integration [19-23], and it is currently unknown whether existing computational insights can generalize beyond rapid judgments. Here, we introduce a new psychophysical task and report model-based analyses of human behavior that demonstrate evidence integration at long timescales. Our task requires probabilistic inference using brief samples of visual evidence that are separated in time by long and unpredictable gaps. We show through several quantitative assays how decision making can approximate a normative integration process that extends over tens of seconds without accruing significant memory leak or noise. These results support the generalization of evidence integration models to a broader class of behaviors while posing new challenges for models of how these computations are implemented in biological networks.

Keywords: computational modeling; decision making; integration time constant; probabilistic inference; psychophysics; sequential sampling; working memory.

Figure 1:. Experimental design.

(A) Subjects viewed brief samples of a contrast pattern while maintaining central fixation. They were cued at the end of the trial to report their decision by making a saccade to one of two targets and received feedback about the accuracy of their choice. (B) Each sample had a different contrast, randomly drawn from one of two overlapping Gaussian distributions in log contrast space. Each trial was generated using samples from the same distribution; the subject’s task was to infer which one. (C) 1–5 samples were shown before cuing a response, determined by drawing from a truncated geometric distribution. (D) Each sample was followed by a gap lasting either 1–4 s (shorter gap sessions) or 2–8 s (longer gap sessions), determined by drawing from one of two truncated exponential distributions.

Figure 2:. Integration of evidence across samples.

(A) Sample mean psychometric function (mPMF), showing the relationship between mean strength of evidence supporting a choice of “high” and the probability of making that choice. (B) Sample count psychometric function (cPMF), showing the relationship between the number of samples in a trial and the probability of making a correct choice. Reverse correlation functions (RCFs) shown separately for trials with different sample counts. In all panels, black points and error bars show means and bootstrap 95% CIs, and blue and gold lines show analytic functions from the best-fitting Linear Integration and Extrema Detection models, respectively. All panels show aggregate data and model fits; see Figure S1 for model predictions and Figure S2 for individual data and fits.

Figure 3:. Integration of graded stimulus evidence.

(A) Data and model cPMFs, showing how the data deviate from a qualitative signature of binarized evidence transformation (Counting model). Black points and error bars show means and bootstrap 95% CIs; purple line shows analytic prediction of the best-fitting Counting model. (B) Estimated subjective weighting of samples with different evidence values. Black points and lines show logistic regression coefficients and 95% CIs for the behavioral data; purple band shows logistic regression coefficients and 95% CIs for simulated data from the Counting model with parameters that best fit the choices. Both panels show aggregate data and model fits; see Figure S1 for model predictions and Figure S3 for individual data and fits.

Figure 4:. Minimal influence of memory leak or noise.

(A) Data and model cPMFs. Black points and error bars show means and bootstrap 95% CIs for the behavioral data, blue line shows analytic function for the best-fitting Linear Integration model, and green band shows simulated performance for the best-fitting Leaky Integration model. (B) Data and model RCFs, aligned to the end of the trial. Element colors are as in panel A; solid lines show functions conditioned on correct choices and dashed lines show functions conditioned on incorrect choices. Note the apparent nonlinearity in the Linear Integration model RCF, an artifact of combing trials with different sample counts (see Methods). (C) Integration model parameter fits. Green elements show parameters for the Leaky Integration model: points show maximum likelihood estimates; thick and thin error bars show bootstrap 68% and 95% CIs, respectively. Blue crosses show σ_ƞ estimated with the Linear Integration model. (D) Data mPMF plotted separately for trials with shorter and longer gaps between samples. All panels show aggregate data and model fits; see Figure S1 for model predictions and Figure S4 for individual data and fits.