The gradual and noisy accumulation of evidence is a fundamental component of decision-making, with noise playing a key role as the source of variability and errors. However, the origins of this noise have never been determined. We developed decision-making tasks in which sensory evidence is delivered in randomly timed pulses, and analyzed the resulting data with models that use the richly detailed information of each trial's pulse timing to distinguish between different decision-making mechanisms. This analysis allowed measurement of the magnitude of noise in the accumulator's memory, separately from noise associated with incoming sensory evidence. In our tasks, the accumulator's memory was noiseless, for both rats and humans. In contrast, the addition of new sensory evidence was the primary source of variability. We suggest our task and modeling approach as a powerful method for revealing internal properties of decision-making processes.
"In some cases, decisions about perfectly stable stimuli appear to involve perfect accumulation, as described by drift-diffusion and related models (Gold and Shadlen, 2000; Roitman and Shadlen, 2002; Brunton et al., 2013; Hanks et al., 2015). Under those conditions, deviations from perfect accumulation in the brain may be considered as inefficient, operating under other constraints "
[Show abstract][Hide abstract] ABSTRACT: In our dynamic world, decisions about noisy stimuli can require temporal accumulation of evidence to identify steady signals; differentiation to detect unpredictable changes in those signals; or both. Normative models can account for learning in these environments but have not yet been applied to faster decision processes. We present a novel, normative formulation of adaptive learning models that forms decisions by acting as a leaky accumulator with non-absorbing bounds. These dynamics, derived for both discrete and continuous cases, depend on the expected rate of change of the statistics of the evidence and balance signal identification and change detection. We found that, for two different tasks, human subjects learned these expectations, albeit imperfectly, then used them to make decisions in accordance with the normative model. The results represent a unified, empirically supported account of decision-making in unpredictable environments that provides new insights into the expectation-driven dynamics of the underlying neural signals.
"All studies above focused on sensory detection for which the transfer function and Bloch's curve are—given the linear systems approach—interchangeable empirical descriptors (once the impulse response of the system is known). Nonetheless, starting perhaps with Ratcliff (1978), drift diffusion became the standard modeling approach to information accumulation over time for both threshold and suprathreshold stimuli and thereby to its relation with response time (e.g., Bogacz, Brown, Moehlis, Holmes, & Cohen, 2006; Brunton, Botvinick, & Brody, 2013; Gold & Shadlen, 2001, 2007; Usher & McClelland, 2001). Drift-diffusion (also referred to as bound diffusion or integration-to-bound) models were and still are meant to account for subjects' decision time and, critically, of its stochastic variability over time in the presence of an ongoing stimulation. "
[Show abstract][Hide abstract] ABSTRACT: In 1885 Adolphe-Moïse Bloch asked the following simple question “Is there a law describing the relationship between the duration of a light and its perceived intensity?” Based on a series of experiments using a Foucault regulator and a candle, Bloch concluded that “when the lighting duration varies from 0.00173 to 0.0518 seconds (…) the [visible] light is markedly in inverse proportion to its duration” – his famous law. As this law pertains to the more general and hotly debated question of accumulation of sensory information over time, it is timely to offer the public a full translation of Bloch’s original paper (from French) and to present it within the context of contemporary research.
i-Perception 08/2015; in press(4). DOI:10.1177/2041669515593043
"In this article, we focus on applications to decision making tasks, where such models have successfully accounted for behavior and neural activity in a wide array of two alternative forced choice tasks (Ratcliff and Rouder, 1998; Bogacz et al., 2006; Ratcliff and McKoon, 2008; Simen et al., 2009; Gold and Shadlen, 2001, 2007; Brunton et al., 2013; Feng, 2009; Shadlen and Newsome, 2001), including phenomena such as the speed-accuracy tradeoff and the dynamics of neural activity during decision making in such tasks. In particular, we will discuss extensions of a specific class of diffusion model referred to as the pure drift diffusion model (DDM; Eq. (1) below), which can be shown to be statistically optimal (Wald, 1945; Wald and Wolfowitz, 1948). "
[Show abstract][Hide abstract] ABSTRACT: In this work, we use Martingale theory to derive formulas for the expected
decision time, error rates, and first passage times associated with a
multistage drift diffusion model, or a Wiener diffusion model with piecewise
constant time-varying drift rates and decision boundaries. The model we study
is a generalization of that considered in Ratcliff (1980). The derivation
relies on using the optional stopping theorem for properly chosen Martingales,
thus obtaining formulae which may be used to compute performance metrics for a
particular stage of the stochastic decision process. We also explicitly solve
the case of a two stage diffusion model, and provide numerical demonstrations
of the computations suggested by our analysis. Finally we present calculations
that allow our techniques to approximate time-varying Ornstein-Uhlenbeck
processes. By presenting these explicit formulae, we aim to foster the
development of refined numerical methods and analytical techniques for studying
diffusion decision processes with time-varying drift rates and thresholds.
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