Modeling across-trial variability in the Wald drift rate parameter

Steingroever, Helen; Wabersich, Dominik; Wagenmakers, Eric–Jan

doi:10.3758/s13428-020-01448-7

Cited by 10 publications

(12 citation statements)

References 40 publications

(71 reference statements)

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“…In our model, we can account for this dependency by allowing the parameters of the baseline dynamic to remain free across fits to choice sequence data. This is a claim for sufficiency of trial-trial variability to capture sequence effects for a specific data-set, however it does not rule out history-dependent variance in sensory integration, as has been reported elsewhere (Urai et al 2019;Steingroever, Wabersich, and Wagenmakers 2021), and suggested by the variance in sensory integration influencing our choice sequence fitting. Nor does it make any claim about what the statistical form of the sequential dependencies may be.…”

Section: Discussionmentioning

confidence: 79%

Choice anticipation as gated accumulation of sensory expectations

Caie,

Endres,

Khan

et al. 2023

Preprint

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Expectations are combined with sensory information when making choices. Some models of the choice process have conceptualized expectations as trial by trial updates to baseline evidence in an accumulator framework. These models have been successful in explaining the influence of choice history across trials on reaction times and choice probabilities, however they do not account for variability in the delay interval within trials. Here, we derive a gated accumulator that models the onset of evidence accumulation as a combination of delayed sensory information and an expectation of sensory timing that changes within trials. To test how the delay intervals interact with trial by trial expectations, we designed a free choice saccade task where participants directed eye movements, as fast as possible, to either of two targets that appeared with variable delays and asynchronies. Despite being instructed to not to anticipate, participants responded prior to target onset on a subset of trials. We reasoned that anticipatory responses may reflect a trade-off between gating the onset of evidence accumulation prior to target onset and releasing this gate as target appearance became more likely. Using a choice history analysis, we found that anticipatory responses were more likely following repeated choices, despite task randomization, suggesting that the balance between anticipatory and sensory responses was driven by an expectation of sensory timing. By fitting the gated accumulator model to reaction time data, we determined that within-trial fluctuations in baseline evidence occurring prior to the onset of the target could explain the joint increase of anticipatory responses and faster sensory-guided responses as the delay period increased. Thus, we conclude that an expectation of sensory timing can shape how the accumulation of choice evidence is gated, allowing us to balance the costs of anticipation with lowering the amount of evidence required to trigger movement.

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Section: Discussionmentioning

confidence: 79%

Choice anticipation as gated accumulation of sensory expectations

Caie,

Endres,

Khan

et al. 2023

Preprint

View full text Add to dashboard Cite

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“…One of the candidate theories for such choice variability involves the noisy accumulation of evidence by competing populations of neurons for and against alternative views about the most significant source of reward (Yang and Shadlen, 2007;Ratcliff et al, 2016;Pisauro et al, 2017;Steingroever, Helen et al, 2018). Indeed, there is growing support for the idea that neurons in these populations regulate their activity in striking accordance with the weight of evidence (Good, 1985;Shadlen, 2002, 2007).…”

Section: Discussionmentioning

confidence: 99%

Fair Odds for Noisy Probabilities

Nash

2018

SSRN Journal

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We suggest that one individual holds multiple degrees of belief about an outcome, given the evidence. We then investigate the implications of such noisy probabilities for a buyer and a seller of binary options and find the odds agreed upon to ensure zero-expectation betting, differ from those consistent with the relative frequency of outcomes. More precisely, the buyer and the seller agree to odds that are higher (lower) than the reciprocal of their averaged unbiased probabilities when this average indicates the outcome is more (less) likely to occur than chance. The favorite-longshot bias thereby emerges to establish the foundation of an equitable market. As corollaries, our work suggests the old-established way of revealing someone's degree of belief through wagers may be more problematic than previously thought, and implies that betting markets cannot generally promise to support rational decisions. JEL-codes: D81, D83, D84, D87. PsycINFO classification: 2340.

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“…In all cases, the model reliably updated parameter estimates in line with the 'true" values. Evidently there is noise in the parameter estimates, and there is some auto-correlation as well (which is known to be the case with Wald parameters, see e.g., Steingroever et al, 2021). However, on the whole the model seems to perform very well, capturing the dynamic properties of both parameters while remaining relatively stable between parameter changes.…”

Section: Time Varying Extension Of the Shifted Wald Modelmentioning

confidence: 95%

An Extension of the Shifted Wald Model of Human Response Times: Capturing the Time Dynamic Properties of Human Cognition

Howard¹,

Fox²,

Evans³

et al. 2022

Preprint

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Despite the ubiquitous nature of Evidence Accumulation Models in cognitive and experimental psychology there has been a comparatively limited uptake of such techniques in the applied literature. While quantifying latent cognitive processing properties has huge potential for applied domains such as adaptive work systems, accumulator models often fall short in practical applications. Two primary reasons for these shortcomings are the complexities and time needed for the application of cognitive models, and the failure of current models to capture systematic trial-to-trial variability in parameters. In this manuscript we develop a novel, trial-varying extension of the Shifted Wald model to address these concerns. By leveraging conjugate properties of the Wald distribution we derive analytic solutions for threshold and drift parameters which can be updated instantaneously with new data. The resulting model allows the quantification systematic variation in latent cognitive parameters across trials and we demonstrate the utility of such analyses through simulations and an exemplar application to an existing data set. The analytic nature of our solutions opens the door for real-world application, significantly extending the reach of computational models of behavioral responses.

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Modeling across-trial variability in the Wald drift rate parameter

Cited by 10 publications

References 40 publications

Choice anticipation as gated accumulation of sensory expectations

Choice anticipation as gated accumulation of sensory expectations

Fair Odds for Noisy Probabilities

An Extension of the Shifted Wald Model of Human Response Times: Capturing the Time Dynamic Properties of Human Cognition

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