The statistics of optimal decision making: Exploring the relationship between signal detection theory and sequential analysis

Griffith, Thom; Baker, Sophie-Anne; Lepora, Nathan F.

doi:10.1016/j.jmp.2021.102544

Cited by 21 publications

(15 citation statements)

References 60 publications

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“…7 for a color map of the mean decision time for flat boundaries). In contrast, the 2AFC decision thresholds are points on a line in the space of 2D belief vectors P from (0, 1) to (1,0). Each choice on an extended boundary is a single point with an error and decision time distribution.…”

Section: Mean Error and Decision Time Vary Along The Optimal Decision...mentioning

confidence: 99%

“…Choosing between multiple alternatives is a fundamental aspect of animal behavior in natural environments. Such decisions can depend on a reward-dependent task structure that requires a trade-off between speed and accuracy [1][2][3][4][5][6] . Although significant progress has been made towards understanding the underlying computational principles of binary decision-making, how it transfers to multiple (n > 2) choices remains of significant interest 7 .…”

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confidence: 99%

“…Although significant progress has been made towards understanding the underlying computational principles of binary decision-making, how it transfers to multiple (n > 2) choices remains of significant interest 7 . Several strands point towards integration-to-threshold models of multiple-choice behavior comprised of two key mechanisms: integration of accumulated belief informed by sensory evidence represented as the trajectory of a decision variable and a threshold on the belief that triggers a decision 1,5,[8][9][10][11] . The optimal formulation of these trajectories and boundaries, defined under reward maximization, remains an active topic.…”

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confidence: 99%

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Degenerate boundaries for multiple-alternative decisions

2022

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Integration-to-threshold models of two-choice perceptual decision making have guided our understanding of human and animal behavior and neural processing. Although such models seem to extend naturally to multiple-choice decision making, consensus on a normative framework has yet to emerge, and hence the implications of threshold characteristics for multiple choices have only been partially explored. Here we consider sequential Bayesian inference and a conceptualisation of decision making as a particle diffusing in n-dimensions. We show by simulation that, within a parameterised subset of time-independent boundaries, the optimal decision boundaries comprise a degenerate family of nonlinear structures that jointly depend on the state of multiple accumulators and speed-accuracy trade-offs. This degeneracy is contrary to current 2-choice results where there is a single optimal threshold. Such boundaries support both stationary and collapsing thresholds as optimal strategies for decision-making, both of which result from stationary representations of nonlinear boundaries. Our findings point towards a normative theory of multiple-choice decision making, provide a characterisation of optimal decision thresholds under this framework, and inform the debate between stationary and dynamic decision boundaries for optimal decision making.

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Section: Mean Error and Decision Time Vary Along The Optimal Decision...mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Degenerate boundaries for multiple-alternative decisions

2022

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“…The existence of two separate modeling frameworks is both exciting and disconcerting. Although there are deep links between SDT and sequential sampling (Griffith et al, 2021), the actual models of visual metacognition developed from one framework cannot always be directly translated to the other framework. Yet, currently there is almost no work that directly compares the performance of the two frameworks in explaining metacognitive judgments.…”

Section: Models Of Visual Metacognitionmentioning

confidence: 99%

Visual metacognition: Measures, models, and neural correlates.

Rahnev

2021

American Psychologist

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Visual metacognition is the ability to evaluate one's performance on visual perceptual tasks. The field of visual metacognition unites the long tradition of visual psychophysics with the younger field of metacognition research. This article traces the historical roots of the field and reviews progress in the areas of (a) constructing appropriate measures of metacognitive ability, (b) developing computational models, and (c) revealing the neural correlates of visual metacognition. First, I review the most popular measures of metacognitive ability with an emphasis on their psychophysical properties. Second, I examine the empirical targets for modeling, the dominant modeling frameworks and the assumed computations underlying visual metacognition. Third, I explore the progress on understanding the neural correlates of visual metacognition by focusing on anatomical and functional studies, as well as causal manipulations. What emerges is a picture of substantial progress on constructing measures, developing models, and revealing the neural correlates of metacognition, but very little integration between these three areas of inquiry. I then explore the deep, intrinsic links between the three areas of research and argue that continued progress requires the recognition and exploitation of these links. Throughout, I discuss the implications of progress in visual metacognition for other areas of metacognition research, and pinpoint specific advancements that could be adopted by researchers working in other subfields of metacognition.

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“…Statistical signal detection and the sequential probability ratio test have been two leading theories for binary decisionmaking in dynamic real-time applications such as the radar detection technology [14], where they play the key role when detecting signals in strongly fluctuating background noise [15], [16]. The sequential probability ratio test technique has been also recently established in other areas such as sensing-SNR-based dynamic statistical threshold detection of FBG spectral peaks Gabriel Cibira , Ivan Glesk F based applications [17], [18], communications [19] or biological systems [20]. However, despite the above, there is still lack of real-time denoising algorithms that dynamically could implement multiple noise fluctuations to and lead to reliable noise reduction at different Signal-to-Noise Ratios (SNRs) in optical sensing technologies.…”

Section: Introductionmentioning

confidence: 99%

SNR-based dynamic statistical threshold detection of FBG spectral peaks

Cibira¹,

Glesk²

2022

Preprint

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This paper targets a dynamic statistical threshold detection algorithm of fiber Bragg grating (FBG) spectral peaks at the presence of changing Signal-to-Noise Ratio (<i>SNR</i>) in an optical fiber of a sensing application. The proposed post-demodulation <i>SNR</i>-based detection implements sliding window technique. Its detection threshold is adapted by the targeted probability of false alarms and by background noise statistics. The proposed detection algorithm is independent of FBG spectral peaks shapes and simple enough computationally to implement. It has been demonstrated and validated using sensor network with a deployed group of FBG-based sensors, by implementing simplified sliding window technique. When the adjacent FBG spectral peaks overlap partially, it provides a high degree of certainty in rejecting false FBG detection. The algorithm can be used for „spectral windowing“ or precise measurement of FBG spectral peaks parameters, especially in densely populated FBG sensor networks. This can lead to a significantly higher spectral bandwidth utilization in FBG sensing applications.

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The statistics of optimal decision making: Exploring the relationship between signal detection theory and sequential analysis

Cited by 21 publications

References 60 publications

Degenerate boundaries for multiple-alternative decisions

Degenerate boundaries for multiple-alternative decisions

Visual metacognition: Measures, models, and neural correlates.

SNR-based dynamic statistical threshold detection of FBG spectral peaks

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