Fig. 1: Trial history-dependent initial states give rise to apparent lapses.
From: Trial-history biases in evidence accumulation can give rise to apparent lapses in decision-making
a Schematic of two common suboptimalities: history biases (top) and lapses (bottom). (Left): Rat making one of two decisions (left, right) based on accumulated sensory evidence (clicks on either side). (Top left): History biases i.e. an inappropriate influence of the previous trial (n-1) on the current decision (n) in addition to sensory evidence. (Top right): Typically assumed effect of history bias on the psychometric curve, shifting it horizontally around the inflection point. (Bottom left): Lapses i.e. a tendency to make seemingly random choices irrespective of sensory evidence. (Bottom right): Typically assumed effect of lapses on the psychometric curve, vertically scaling its asymptotes (Figure adapted with permission from Bingni W. Brunton et al., Rats and Humans Can Optimally Accumulate Evidence for Decision Making. Science 340,95-98(2013). DOI:10.1126/science.1233912) b Normative model of within-trial processing. (Top) Optimal decision rule that chooses when the summed log-ratios of priors and likelihoods exceeds one of two decision bounds, corresponding to a drift-diffusion process. (Bottom left): Generative model, where one of two hypotheses (H1, H2) produce noisy evidence over time (ϵt). (Bottom right): A sample trajectory based on noisy evidence (bold line), and alternate trajectories (thin lines) based on noisy instantiations of the same drift rate (black arrow). c Model of across-trial processing that accommodates prior updates. Past choices and outcomes can affect the initial state with different magnitudes (η) and timescales (β) depending on whether they were wins/losses (top left/right). (Bottom): Example trial sequence ans corresponding initial states following previous wins (triangles) or losses (circles) on right (R) or left (L) choices. Colors denote initial state biases, towards positive (blue) or negative (pink) bounds. d Effect of initial state values on psychometric curves. Colors same as c. Small deviations in initial state (grey) lead to largely horizontal biases whereas larger deviations (saturated colors) additionally reduce its effective slope (dotted black lines) or “sensitivity" to stimulus. e Pooling psychometric function (black) across trials with different initial state biases gives rise to apparent lapses (purple arrow). Conditioning the curve on previous rightward (blue) or leftward (pink) wins reveals a modulation of apparent lapses by trial history.
