On the convergence of time interval moments: caveat sciscitator

Harris, Christopher M.; Waddington, Jonathan

doi:10.1016/j.jneumeth.2012.01.017

Cited by 8 publications

(16 citation statements)

References 31 publications

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“…For easy tasks where RTs are low, the probability of rate reaching zero (i.e., RT approaching infinity) is negligible and the problem might be dismissed as a mathematical nuance. However, for difficult tasks, the probability becomes significant, as we have shown (Harris and Waddington, 2012). A departure from the reciprocal Normal has been reported for saccade latency to very dim targets, but this has been modeled instead as an inverse Gaussian based on a diffusion process (Carpenter et al, 2009).…”

Section: Introductionmentioning

confidence: 53%

“…Right column: equivalent pdf's in the rate (reciprocal RT) domain. See Harris and Waddington (2012) for the mathematical relationship between the two domains.…”

Section: Introductionmentioning

confidence: 99%

“…In the time-domain this would imply very large negative RTs, which would require the response to occur long before the stimulus onset and violate causality. Therefore, we need to consider the reciprocal truncated Normal distribution ( rectrN ), (where the Normal rate distribution is left truncated at or near zero; see Harris and Waddington, 2012). The question is what happens at or near zero rate?…”

Section: Introductionmentioning

confidence: 99%

“…It is difficult to distinguish among highly skewed distributions in the time-domain. The method of moments is infeasible due to poor convergence (the reciprocal Normal has no finite moments; Harris and Waddington, 2012). Maximum likelihood estimation of parameters requires vast amounts of data to distinguish between models (Waddington and Harris, 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Maximum likelihood estimation of parameters requires vast amounts of data to distinguish between models (Waddington and Harris, 2012). There is also the problem of under-sampling at extreme values (Harris and Waddington, 2012) which is further exacerbated by the tendency of many investigators to discard “outliers.” It is easier in the rate-domain, although large data sets are still needed. Distributions that are less skewed than the reciprocal Normal (such as the inverse Gaussian) remain positively skewed in the rate-domain, whereas the reciprocal Normal does not.…”

Section: Introductionmentioning

confidence: 99%

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Manual choice reaction times in the rate-domain

Harris

Waddington

Biscione

et al. 2014

Front. Hum. Neurosci.

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Over the last 150 years, human manual reaction times (RTs) have been recorded countless times. Yet, our understanding of them remains remarkably poor. RTs are highly variable with positively skewed frequency distributions, often modeled as an inverse Gaussian distribution reflecting a stochastic rise to threshold (diffusion process). However, latency distributions of saccades are very close to the reciprocal Normal, suggesting that “rate” (reciprocal RT) may be the more fundamental variable. We explored whether this phenomenon extends to choice manual RTs. We recorded two-alternative choice RTs from 24 subjects, each with 4 blocks of 200 trials with two task difficulties (easy vs. difficult discrimination) and two instruction sets (urgent vs. accurate). We found that rate distributions were, indeed, very close to Normal, shifting to lower rates with increasing difficulty and accuracy, and for some blocks they appeared to become left-truncated, but still close to Normal. Using autoregressive techniques, we found temporal sequential dependencies for lags of at least 3. We identified a transient and steady-state component in each block. Because rates were Normal, we were able to estimate autoregressive weights using the Box-Jenkins technique, and convert to a moving average model using z-transforms to show explicit dependence on stimulus input. We also found a spatial sequential dependence for the previous 3 lags depending on whether the laterality of previous trials was repeated or alternated. This was partially dissociated from temporal dependency as it only occurred in the easy tasks. We conclude that 2-alternative choice manual RT distributions are close to reciprocal Normal and not the inverse Gaussian. This is not consistent with stochastic rise to threshold models, and we propose a simple optimality model in which reward is maximized to yield to an optimal rate, and hence an optimal time to respond. We discuss how it might be implemented.

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Section: Introductionmentioning

confidence: 53%

“…Right column: equivalent pdf's in the rate (reciprocal RT) domain. See Harris and Waddington (2012) for the mathematical relationship between the two domains.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Manual choice reaction times in the rate-domain

Harris

Waddington

Biscione

et al. 2014

Front. Hum. Neurosci.

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Biomimetics of Choice Behaviour for Autonomous Agents

Harris¹,

Waddington²

2012

Advances in Autonomous Robotics

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The distribution of quick phase interval durations in human optokinetic nystagmus

Waddington

Harris

2012

Exp Brain Res

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There is an interesting dichotomy between models that predict the quick phase interval durations (QPIDs) of human optokinetic nystagmus (OKN). Accumulator models describe a stochastic signal in a neural network that triggers a response once the signal reaches a fixed threshold value. However, it is also possible that quick phases are triggered after eye position reaches a variable amplitude threshold. In this study, we fitted a range of probability density functions previously predicted by stochastic models of OKN (including those of the reciprocal truncated Normal, inverse Gaussian, gamma, lognormal and the mixture of two reciprocal truncated Normal distributions) to individual QPID histograms. We compared the goodness of fit between these models, and a model where the distribution of QPIDs is determined by the ratio of two correlated and truncated Normal random variables. The ratio distribution gave the best fit to the data, and we propose this is due to the approximately linear trajectory of slow phases (SPs) and that QPIDs are given by the ratio of a variable SP amplitude threshold and variable SP velocity.

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On the convergence of time interval moments: caveat sciscitator

Cited by 8 publications

References 31 publications

Manual choice reaction times in the rate-domain

Manual choice reaction times in the rate-domain

Biomimetics of Choice Behaviour for Autonomous Agents

The distribution of quick phase interval durations in human optokinetic nystagmus

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