Statistical Models of Spike Trains

Paninski, Liam; Brown, Emery N.; Iyengar, Satish

doi:10.1093/acprof:oso/9780199235070.003.0010

Cited by 18 publications

(28 citation statements)

References 61 publications

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“…Brown, et al (2003); Kass, Ventura and Brown (2005); Paninski, et al (2009); and references therein]. A basic distinction is that of conditional versus marginal intensities: the conditional intensity determines the event rate for a given realization of the process, while the marginal intensity is the expectation of the conditional intensity across realizations.…”

Section: Introductionmentioning

confidence: 99%

Assessment of synchrony in multiple neural spike trains using loglinear point process models

Kelly¹,

Loh²

2011

Ann. Appl. Stat.

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Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity, but contemporary experiments often use time-varying stimuli and produce time-varying neural responses. More recently, many statistical methods have been developed for nonstationary neural point process data. There has also been much interest in identifying synchrony, meaning events across two or more neurons that are nearly simultaneous at the time scale of the recordings. A natural statistical approach is to discretize time, using short time bins, and to introduce loglinear models for dependency among neurons, but previous use of loglinear modeling technology has assumed stationarity. We introduce a succinct yet powerful class of time-varying loglinear models by (a) allowing individual-neuron effects (main effects) to involve time-varying intensities; (b) also allowing the individual-neuron effects to involve autocovariation effects (history effects) due to past spiking, (c) assuming excess synchrony effects (interaction effects) do not depend on history, and (d) assuming all effects vary smoothly across time. Using data from primary visual cortex of an anesthetized

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Section: Introductionmentioning

confidence: 99%

Assessment of synchrony in multiple neural spike trains using loglinear point process models

Kelly¹,

Loh²

2011

Ann. Appl. Stat.

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“…This choice was made assuming that the sensory fiber can be modelled as an integrate-and-fire oscillator with fixed positive threshold driven by a Wiener process with positive drift whose distribution of ISIs is, in fact, inverse Gaussian [11]. …”

Section: Methodsmentioning

confidence: 99%

Point-process analysis of neural spiking activity of muscle spindles recorded from thin-film longitudinal intrafascicular electrodes

Citi

Djilas

Azevedo‐Coste

et al. 2011

2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Recordings from thin-film Longitudinal Intra-Fascicular Electrodes (tfLIFE) together with a wavelet-based de-noising and a correlation-based spike sorting algorithm, give access to firing patterns of muscle spindle afferents. In this study we use a point process probability structure to assess mechanical stimulus-response characteristics of muscle spindle spike trains. We assume that the stimulus intensity is primarily a linear combination of the spontaneous firing rate, the muscle extension, and the stretch velocity. By using the ability of the point process framework to provide an objective goodness of fit analysis, we were able to distinguish two classes of spike clusters with different statistical structure. We found that spike clusters with higher SNR have a temporal structure that can be fitted by an inverse Gaussian distribution while lower SNR clusters follow a Poisson-like distribution. The point process algorithm is further able to provide the instantaneous intensity function associated with the stimulus-response model with the best goodness of fit. This important result is a first step towards a point process decoding algorithm to estimate the muscle length and possibly provide closed loop Functional Electrical Stimulation (FES) systems with natural sensory feedback information.

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“…(First-passage time computations are especially important, for example, in the context of integrate-and-fire-based neural encoding models Paninski et al (2008).) In Smith et al (2004), the authors proposed a hidden state-space model that provides a dynamical description for the learning process of an animal in a task learning experiment (with binary responses), and yields suitable statistical indicators for establishing the occurrence of learning or determining the “learning trial.” In the proposed model, the state variable, x t , evolves according to a Gaussian random walk from trial to trial (labeled by t ), and the probability of a correct response on every trial, q t , is given by a logistic function of the corresponding state variable, x t .…”

Section: Other Applications: Estimation Of Non-marginal Quantititesmentioning

confidence: 99%

Efficient Markov Chain Monte Carlo Methods for Decoding Neural Spike Trains

2011

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Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is log-concave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using efficient optimization algorithms. Unfortunately, the MAP estimate can have a relatively large average error when the posterior is highly non-Gaussian. Here we compare several Markov chain Monte Carlo (MCMC) algorithms that allow for the calculation of general Bayesian estimators involving posterior expectations (conditional on model parameters). An efficient version of the hybrid Monte Carlo (HMC) algorithm was significantly superior to other MCMC methods for Gaussian priors. When the prior distribution has sharp edges and corners, on the other hand, the “hit-and-run” algorithm performed better than other MCMC methods. Using these algorithms we show that for this latter class of priors the posterior mean estimate can have a considerably lower average error than MAP, whereas for Gaussian priors the two estimators have roughly equal efficiency. We also address the application of MCMC methods for extracting non-marginal properties of the posterior distribution. For example, by using MCMC to calculate the mutual information between the stimulus and response, we verify the validity of a computationally efficient Laplace approximation to this quantity for Gaussian priors in a wide range of model parameters; this makes direct model-based computation of the mutual information tractable even in the case of large observed neural populations, where methods based on binning the spike train fail. Finally, we consider the effect of uncertainty in the GLM parameters on the posterior estimators.

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Statistical Models of Spike Trains

Cited by 18 publications

References 61 publications

Assessment of synchrony in multiple neural spike trains using loglinear point process models

Assessment of synchrony in multiple neural spike trains using loglinear point process models

Point-process analysis of neural spiking activity of muscle spindles recorded from thin-film longitudinal intrafascicular electrodes

Efficient Markov Chain Monte Carlo Methods for Decoding Neural Spike Trains

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