Modeling neural activity with cumulative damage distributions

Leiva, Víctor; Tejo, Mauricio; Guiraud, Pierre; Schmachtenberg, Oliver; Orio, Patricio; Marmolejo‐Ramos, Fernando

doi:10.1007/s00422-015-0651-9

Cited by 28 publications

(21 citation statements)

References 41 publications

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“…2000 spikes was simulated, and the log-likelihoods of the corresponding inter-spike times for each distribution were: -4484,396 for the inverse Gaussian distribution (the exact distribution), -4484.424 for the Birnbaum-Saunders distribution and -4484.738 for the lognormal distribution. As expected, they are close, although Birnbaum-Saunders distribution is closer to the exact distribution than the lognormal distribution, as was anticipated and theoretically explained in Leiva et al (2015) …”

Section: Histogram Of Inter−spike Timessupporting

confidence: 58%

“…This has the advantage that both the inverse Gaussian and the Birnbaum-Saunders distributions appear almost naturally under simple integrate-and-fire neurons. Additionally, they have a close relationship (Leiva et al 2015;Desmond 1986;Balakrishnan et al 2009) where its distributions become closer as PðV 0 VðkÞÞ becomes higher, for any k [ 0, and thus, inverse Gaussian and Birnbaum-Saunders families can be considered as belonging to the family of fatigue life distributions. When such probability decreases the goodness-of-fit of the Birnbaum-Saunders distribution remains high but one of its parameters, the median, losses its interpretation (Leiva et al 2015).…”

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confidence: 99%

“…Additionally, they have a close relationship (Leiva et al 2015;Desmond 1986;Balakrishnan et al 2009) where its distributions become closer as PðV 0 VðkÞÞ becomes higher, for any k [ 0, and thus, inverse Gaussian and Birnbaum-Saunders families can be considered as belonging to the family of fatigue life distributions. When such probability decreases the goodness-of-fit of the Birnbaum-Saunders distribution remains high but one of its parameters, the median, losses its interpretation (Leiva et al 2015). In this situation, the Birnbaum-Saunders distribution can still be used as a predictive tool as in the case of a regression model with high coefficient of determination R 2 where some of its parameters are non-significative.…”

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confidence: 99%

“…The fact that the inverse Gaussian and the lognormal distributions are graphically similar under some specific values of its parameters is just an akin of the pictures of its probability density functions. In Takagi et al (1997) Leiva et al (2015), it is argued that a spike generation is analogous to a material rupture under a cumulative damage process, where such a cumulative damage process will come to represent the injected current in the neuron charging, under a simple integrate-and-fire mechanism. A new distribution was also introduced in this context, the Birnbaum-Saunders distribution (Birnbaum and Saunders 1969), or the fatigue life distribution, which produced a well goodness-of-fit of a real inter-spike time data set.…”

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The membrane potential process of a single neuron seen as a cumulative damage process

Tejo

Niklitschek-Soto

2016

Cogn Neurodyn

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A simple integrate-and-fire mechanism of a single neuron can be compared with a cumulative damage process, where the spiking process is analogous to rupture sequences of a material under cycles of stress. Although in some cases lognormal-like patterns can be recognized in the inter-spike times under a simple integrate-and-fire mechanism, fatigue life models as the inverse Gaussian distribution and the Birnbaum-Saunders distribution (which was recently introduced in the neural activity framework) provide theoretical arguments that make them more suitable for the modeling of the resulting inter-spike times.Keywords Lognormal Á Inverse Gaussian and BirnbaumSaunders distributions Á Integrate-and-fire model Á Interspike distribution In a recent communication, Kish et al. (2015) highlight lognormal-like features in the inter-spike distribution of a single neuron under a simple integrate-and-fire scheme with an additive noise with no long-tail but exponential cutoff. To be more precise, let V(k) be the membrane potential of a typical neuron at discrete time k 2 N. Its dynamics is given by:with initial condition Vð0Þ ¼ V 0 . The injected current is described through the process fnðkÞg k2N , which represents a white noise process (typically normally or uniformly distributed), and the parameters d and D, which represent the drift velocity and the diffusion coefficient, respectively. Here, the condition V 0 VðkÞ is enforced during the whole motion (i.e., V 0 is a reflecting boundary). The process, then, stops at time j ¼ inffk : VðkÞ [ V th g, where V th represents a constant (membrane potential) threshold at which the neuron spikes. Once it occurs, the process resets at V 0 . Although this model is too simple to capture a great part of reality, it is still a reasonable approximation when the input rate is high in comparison with the membrane capacitance. A lognormal-like feature in the inter-spike distribution appears whenActually, this is not a theoretical result but a graphical similarity. Indeed, if we assume that fnðkÞg k2N in (1) is a standard normal process, when no condition on the motion is imposed, it is well-known that the resulting inter-spike times are inverse Gaussian distributed (which is already mentioned in Kish et al. 2015). The fact that the inverse Gaussian and the lognormal distributions are graphically similar under some specific values of its parameters is just an akin of the pictures of its probability density functions.In Takagi et al. (1997)

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Section: Histogram Of Inter−spike Timessupporting

confidence: 58%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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The membrane potential process of a single neuron seen as a cumulative damage process

Tejo

Niklitschek-Soto

2016

Cogn Neurodyn

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“…in cognitive science to model behavioural and neurological data (e.g., Leiva et al 2015). The Beta distribution has been used to model soil data (Haskett et al 1995) and rates and proportions (Ferrari and Cribari-Neto 2004), the Student's t has been used to fit share price changes (Praetz 1972), and the Tukey-λ has been fitted to solar radiation data (Öztürk and Dale 1982).…”

Section: Simulation Studymentioning

confidence: 99%

Automatic detection of discordant outliers via the Ueda’s method

2015

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The importance of identifying outliers in a data set is well known. Although various outlier detection methods have been proposed in order to enable reliable inferences regarding a data set, a simple but less known method has been proposed by Ueda (1996Ueda ( /2009. Since this new method, called Ueda's method, has not been systematically analysed in previous research, a simulation study addressing its performance and robustness is presented. Although the method was derived assuming that the underlying data is normally distributed, its performance was analysed using data from various outlier-prone distributions commonly found in several research fields. The results obtained enable us to define the strengths and weaknesses of the method along with its limits of applicability. Furthermore, an unforeseen field of application of the method, which requires further studies was also identified.

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Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

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Birnbaum and Saunders introduced a two-parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix-variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research. KEYWORDSBayes estimators, EM algorithm, Fisher information matrix, hazard function, length-biased distribution, moments and inverse moments, probability density function, stochastic orderings, TP 2 property 4

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Modeling neural activity with cumulative damage distributions

Cited by 28 publications

References 41 publications

The membrane potential process of a single neuron seen as a cumulative damage process

The membrane potential process of a single neuron seen as a cumulative damage process

Automatic detection of discordant outliers via the Ueda’s method

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

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