- Spike Trains as Event Sequences: Fundamental Implications

doi:10.1201/b14859-6

Cited by 13 publications

(14 citation statements)

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“…This interpretation extends to other approaches (22). That is, the typical situation is that statistical modeling assumptions are not completely explicit but implicitly built in to an estimation or inference procedure (23). In addition to the well-known danger that implicit assumptions lead too easily to misinterpretation, another important concern, particularly with sophisticated smoothing techniques (e.g., crossvalidation, penalized likelihood, and Bayesian models), is that the degree of smoothing may depend on the quantity and quality of the data, and therefore, the same procedure is essentially using different modeling assumptions for different datasets.…”

Section: Implicit Modeling Assumptionsmentioning

confidence: 95%

“…Ambiguous language might also bear some of this blame: many things are called a firing rate in the neurophysiology literature (23). For context, recall the spike count measurements discussed in Trial-to-Trial Variability and Doubly Stochastic Decompositions, Ambiguity of the Firing Rate, where ðλ i , N i Þ forms a doubly stochastic model producing spike counts N 1 , N 2 , .…”

Section: Summary and Discussionmentioning

confidence: 99%

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Ambiguity and nonidentifiability in the statistical analysis of neural codes

Amarasingham

Geman

Harrison

2015

Proc. Natl. Acad. Sci. U.S.A.

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Many experimental studies of neural coding rely on a statistical interpretation of the theoretical notion of the rate at which a neuron fires spikes. For example, neuroscientists often ask, "Does a population of neurons exhibit more synchronous spiking than one would expect from the covariability of their instantaneous firing rates?" For another example, "How much of a neuron's observed spiking variability is caused by the variability of its instantaneous firing rate, and how much is caused by spike timing variability?" However, a neuron's theoretical firing rate is not necessarily well-defined. Consequently, neuroscientific questions involving the theoretical firing rate do not have a meaning in isolation but can only be interpreted in light of additional statistical modeling choices. Ignoring this ambiguity can lead to inconsistent reasoning or wayward conclusions. We illustrate these issues with examples drawn from the neural-coding literature.temporal coding | spike timing | spike count variability | trial-to-trial variability | doubly stochastic A mong the most important open questions in neurophysiology are those regarding the nature of the code that neurons use to transmit information. Experimental approaches to such questions are challenging, because the spike outputs of a neuronal subpopulation, as typically recorded in behaving animals, are influenced by a vast array of factors. Such factors span all levels of description, from the microscopic (e.g., ion fluctuations and states of presynaptic neurons) to the macroscopic (e.g., sensation and attention), but only a small fraction of these is measured, or even understood. As a consequence, it is not clear to what degree variations in unknown and uncontrolled variables alternately reveal or confound the underlying signals that observed spikes are presumed to encode. Another consequence, very much related, is that these uncertainties also disturb our intuitive comfort with common models of statistical repeatability in neurophysiological signal analysis. In this context, there is an increasingly popular strain of thought in the neural-coding literature that "doubly stochastic point processes" (1-8) provide a way to think about and model fundamental questions about the relationship between sources of "trial-to-trial variability" (4, 9) and the observed variability of spike responses.Imagine an experiment consisting of repeated presentations of a sensory stimulus. In a typical probabilistic model of spike responses, the probability that a particular neuron emits (fires) a spike at one time is described by a theoretical firing rate function (a function of time relative to stimulus onset). [Note that theoretical firing rates are distinct from the basic "observed" or "empirical" firing rate, which is a report of how many spikes occur in a window of a specified time length. Here, we discuss the theoretical firing rate. Observed firing rates are used to infer theoretical firing rates or their properties (SI Appendix, section S1)]. For example, in a generic firing r...

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Section: Implicit Modeling Assumptionsmentioning

confidence: 95%

Section: Summary and Discussionmentioning

confidence: 99%

Ambiguity and nonidentifiability in the statistical analysis of neural codes

Amarasingham

Geman

Harrison

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…Hence, hypothesis testing is best used in conjunction with carefully chosen test statistics that are tailored to sensible alternative hypotheses, along with other procedures designed to quantify the experimental relevance of any detected departure from the null hypothesis. In the absence of a complete statistical model for alternative hypotheses, Amarasingham et al (2012) and Harrison et al (2013) suggest choosing test statistics that have physiologically interpretable units (such as the number of synchronous spikes per second), and then quantifying the difference between the observed test statistic and its expected value under the null hypothesis. A negligible difference, regardless of whether the difference is statistically significant or not, may suggest that the detected amounts of precise spiking are of little physiological importance.…”

Section: Statistical and Experimental Interpretationsmentioning

confidence: 99%

Spatiotemporal Conditional Inference and Hypothesis Tests for Neural Ensemble Spiking Precision

2015

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The collective dynamics of neural ensembles create complex spike patterns with many spatial and temporal scales. Understanding the statistical structure of these patterns can help resolve fundamental questions about neural computation and neural dynamics. Spatio-temporal conditional inference (STCI) is introduced here as a semiparametric statistical framework for investigating the nature of precise spiking patterns from collections of neurons that is robust to arbitrarily complex and nonstationary coarse spiking dynamics. The main idea is to focus statistical modeling and inference, not on the full distribution of the data, but rather on families of conditional distributions of precise spiking given different types of coarse spiking. The framework is then used to develop families of hypothesis tests for probing the spatio-temporal precision of spiking patterns. Relationships among different conditional distributions are used to improve multiple hypothesis testing adjustments and to design novel Monte Carlo spike resampling algorithms. Of special note are algorithms that can locally jitter spike times while still preserving the instantaneous peri-stimulus time histogram (PSTH) or the instantaneous total spike count from a group of recorded neurons. The framework can also be used to test whether first-order maximum entropy models with possibly random and time-varying parameters can account for observed patterns of spiking. STCI provides a detailed example of the generic principle of conditional inference, which may be applicable in other areas of neurostatistical analysis.

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“…However, to capture complex behavior of neural networks, many new statistical methods have been recently proposed for analyzing several simultaneously recoded neurons in order to extract information contained in their temporal interactions under different experimental conditions. For more discussion on analysis of spike trains, refer to Harrison et al (2013); Brillinger (1988); Brown et al (2004); Kass et al (2005); West (2007); Reich et al (1998); Barbieri et al (2001); Kass and Ventura (2001); Grün et al (2002); Kass et al (2005); Rigat et al (2006); Patnaik et al (2008); Pillow et al (2008); Jacobs et al (2009); Diekman et al (2009); Sastry and Unnikrishnan (2010); Kottas et al (2012); Kelly and Kass (2012); Shahbaba et al (2014).…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Bayesian Model for Characterizing Cross-Neuronal Interactions During Decision-Making

Zhou

Moorman

Behseta

et al. 2016

Journal of the American Statistical Association

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The goal of this paper is to develop a novel statistical model for studying cross-neuronal spike train interactions during decision making. For an individual to successfully complete the task of decision-making, a number of temporally-organized events must occur: stimuli must be detected, potential outcomes must be evaluated, behaviors must be executed or inhibited, and outcomes (such as reward or no-reward) must be experienced. Due to the complexity of this process, it is likely the case that decision-making is encoded by the temporally-precise interactions between large populations of neurons. Most existing statistical models, however, are inadequate for analyzing such a phenomenon because they provide only an aggregated measure of interactions over time. To address this considerable limitation, we propose a dynamic Bayesian model which captures the time-varying nature of neuronal activity (such as the time-varying strength of the interactions between neurons). The proposed method yielded results that reveal new insight into the dynamic nature of population coding in the prefrontal cortex during decision making. In our analysis, we note that while some neurons in the prefrontal cortex do not synchronize their firing activity until the presence of a reward, a different set of neurons synchronize their activity shortly after stimulus onset. These differentially synchronizing sub-populations of neurons suggests a continuum of population representation of the reward-seeking task. Secondly, our analyses also suggest that the degree of synchronization differs between the rewarded and non-rewarded conditions. Moreover, the proposed model is scalable to handle data on many simultaneously-recorded neurons and is applicable to analyzing other types of multivariate time series data with latent structure. Supplementary materials (including computer codes) for our paper are available online.

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- Spike Trains as Event Sequences: Fundamental Implications

Cited by 13 publications

References 58 publications

Ambiguity and nonidentifiability in the statistical analysis of neural codes

Ambiguity and nonidentifiability in the statistical analysis of neural codes

Spatiotemporal Conditional Inference and Hypothesis Tests for Neural Ensemble Spiking Precision

A Dynamic Bayesian Model for Characterizing Cross-Neuronal Interactions During Decision-Making

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