Log-Transform Kernel Density Estimation of Income Distribution

Charpentier, Arthur; Flachaire, Emmanuel

doi:10.7202/1036917ar

Cited by 23 publications

(14 citation statements)

References 33 publications

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“…All reported confidence intervals are computed using a non-parametric bootstrap [125] with 10,000 samples. The density curves shown in Fig 2B were computed using a method for logspace density estimation [126] with a Normal kernel, where kernel bandwidths were determined by the Silverman rule [127]. Fig 2C. The percent-streaming (y-axis) is computed for a total of N = 1000 simulation runs of each model (columns) across the three stimuli (colors and line styles) over the first 10 seconds (x-axis).…”

Section: Statistical Analysesmentioning

confidence: 99%

Ensemble modeling of auditory streaming reveals potential sources of bistability across the perceptual hierarchy

2020

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Perceptual bistability-the spontaneous, irregular fluctuation of perception between two interpretations of a stimulus-occurs when observing a large variety of ambiguous stimulus configurations. This phenomenon has the potential to serve as a tool for, among other things, understanding how function varies across individuals due to the large individual differences that manifest during perceptual bistability. Yet it remains difficult to interpret the functional processes at work, without knowing where bistability arises during perception. In this study we explore the hypothesis that bistability originates from multiple sources distributed across the perceptual hierarchy. We develop a hierarchical model of auditory processing comprised of three distinct levels: a Peripheral, tonotopic analysis, a Central analysis computing features found more centrally in the auditory system, and an Object analysis, where sounds are segmented into different streams. We model bistable perception within this system by applying adaptation, inhibition and noise into one or all of the three levels of the hierarchy. We evaluate a large ensemble of variations of this hierarchical model, where each model has a different configuration of adaptation, inhibition and noise. This approach avoids the assumption that a single configuration must be invoked to explain the data. Each model is evaluated based on its ability to replicate two hallmarks of bistability during auditory streaming: the selectivity of bistability to specific stimulus configurations, and the characteristic log-normal pattern of perceptual switches. Consistent with a distributed origin, a broad range of model parameters across this hierarchy lead to a plausible form of perceptual bistability.

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Section: Statistical Analysesmentioning

confidence: 99%

Ensemble modeling of auditory streaming reveals potential sources of bistability across the perceptual hierarchy

2020

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“…All reported confidence intervals are computed using a non-parametric bootstrap [110] with 10,000 samples. The density curves shown in Fig 2B were computed using a method for log-space density estimation [111] with a Normal kernel, where kernel bandwidths were determined by the Silverman rule [112].…”

Section: Statistical Analysesmentioning

confidence: 99%

Ensemble modeling of auditory streaming reveals potential sources of bistability across the perceptual hierarchy

Little

Snyder

Elhilali

2019

Preprint

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AbstractPerceptual bistability—the spontaneous fluctuation of perception between two interpretations of a stimulus—occurs when observing a large variety of ambiguous stimulus configurations. This phenomenon has the potential to serve as a tool for, among other things, understanding how function varies across individuals due to the large individual differences that manifest during perceptual bistability. Yet it remains difficult to interpret the functional processes at work, without knowing where bistability arises during perception. In this study we explore the hypothesis that bistability originates from multiple sources distributed across the perceptual hierarchy. We develop a hierarchical model of auditory processing comprised of three distinct levels: a Peripheral, tonotopic analysis, a Central analysis computing features found more centrally in the auditory system, and an Object analysis, where sounds are segmented into different streams. We model bistable perception within this system by injecting adaptation, inhibition and noise into one or all of the three levels of the hierarchy. We evaluate a large ensemble of variations of this hierarchical model, where each model has a different configuration of adaptation, inhibition and noise. This approach avoids the assumption that a single configuration must be invoked to explain the data. Each model is evaluated based on its ability to replicate two hallmarks of bistability during auditory streaming: the selectivity of bistability to specific stimulus configurations, and the characteristic log-normal pattern of perceptual switches. Consistent with a distributed origin, a broad range of model parameters across this hierarchy lead to a plausible form of perceptual bistability. The ensemble also appears to predict that greater individual variation in adaptation and inhibition occurs in later stages of perceptual processing.Author summaryOur ability to experience the everyday world through our senses requires that we resolve numerous ambiguities present in the physical evidence available. This is accomplished, in part, through a series of hierarchical computations, in which stimulus interpretations grow increasingly abstract. Our ability to resolve ambiguity does not always succeed, such as during optical illusions. In this study, we examine a form of perceptual ambiguity called bistability—cases in which a single individual’s perception spontaneously switches back and forth between two interpretations of a single stimulus. A challenge in understanding bistability is that we don’t know where along the perceptual hierarchy it is generated. Here we test the idea that there are multiple origins by building a simulation of the auditory system. Consistent with a multi-source account of bistability, this simulation accurately predicts perception of a simple auditory stimulus when bistability originates from a number of different sources within the model. The data also indicate that individual differences during ambiguous perception may primarily originate from higher levels of the perceptual hierarchy. This result provides a clue for future work aiming to determine how auditory function differs across individual brains.

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“…It should be noted that the kernel estimation based on transformed data were proposed in several studies. Examples of kernel density based on transformation can be found in [15]- [17].…”

Section: Methodsmentioning

confidence: 99%

An Adaptation of Kernel Density Estimation for Population Abundance using Line Transect Sampling When the Shoulder Condition is Violated

Albadareen*,

Ismail

2019

IJITEE

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Kernel estimation is a commonly used method to estimate the population density in line transect sampling. In general, the classical kernel estimator of (0) X f , which is the probability density function at perpendicular distance x  0 , inclines to be underestimated. In this study, a power transformation of perpendicular distance is proposed for the kernel estimator when the shoulder condition is violated. The mathematical properties of the proposed estimator are derived. A simulation study is also carried out for comparing the proposed estimator with the classical kernel estimators

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Log-Transform Kernel Density Estimation of Income Distribution

Cited by 23 publications

References 33 publications

Ensemble modeling of auditory streaming reveals potential sources of bistability across the perceptual hierarchy

Ensemble modeling of auditory streaming reveals potential sources of bistability across the perceptual hierarchy

Ensemble modeling of auditory streaming reveals potential sources of bistability across the perceptual hierarchy

An Adaptation of Kernel Density Estimation for Population Abundance using Line Transect Sampling When the Shoulder Condition is Violated

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