10,641 research outputs found
A unified approach to linking experimental, statistical and computational analysis of spike train data
A fundamental issue in neuroscience is how to identify the multiple biophysical mechanisms through which neurons generate observed patterns of spiking activity. In previous work, we proposed a method for linking observed patterns of spiking activity to specific biophysical mechanisms based on a state space modeling framework and a sequential Monte Carlo, or particle filter, estimation algorithm. We have shown, in simulation, that this approach is able to identify a space of simple biophysical models that were consistent with observed spiking data (and included the model that generated the data), but have yet to demonstrate the application of the method to identify realistic currents from real spike train data. Here, we apply the particle filter to spiking data recorded from rat layer V cortical neurons, and correctly identify the dynamics of an slow, intrinsic current. The underlying intrinsic current is successfully identified in four distinct neurons, even though the cells exhibit two distinct classes of spiking activity: regular spiking and bursting. This approach β linking statistical, computational, and experimental neuroscience β provides an effective technique to constrain detailed biophysical models to specific mechanisms consistent with observed spike train data.Published versio
Bounded Influence Approaches to Constrained Mixed Vector Autoregressive Models
The proliferation of many clinical studies obtaining multiple biophysical signals from several individuals repeatedly in time is increasingly recognized, a recognition generating growth in statistical models that analyze cross-sectional time series data. In general, these statistical models try to answer two questions: (i) intra-individual dynamics of the response and its relation to some covariates; and, (ii) how this dynamics can be aggregated consistently in a group. In response to the first question, we propose a covariate-adjusted constrained Vector Autoregressive model, a technique similar to the STARMAX model (Stoffer, JASA 81, 762-772), to describe serial dependence of observations. In this way, the number of parameters to be estimated is kept minimal while offering flexibility for the model to explore higher order dependence. In response to (ii), we use mixed effects analysis that accommodates modelling of heterogeneity among cross-sections arising from covariate effects that vary from one cross-section to another. Although estimation of the model can proceed using standard maximum likelihood techniques, we believed it is advantageous to use bounded influence procedures in the modelling (such as choosing constraints) and parameter estimation so that the effects of outliers can be controlled. In particular, we use M-estimation with a redescending bounding function because its influence function is always bounded. Furthermore, assuming consistency, this influence function is useful to obtain the limiting distribution of the estimates. However, this distribution may not necessarily yield accurate inference in the presence of contamination as the actual asymptotic distribution might have wider tails. This led us to investigate bootstrap approximation techniques. A sampling scheme based on IID innovations is modified to accommodate the cross-sectional structure of the data. Then the M-estimation is applied to each bootstrap sample naively to obtain the asymptotic distribution of the estimates.We apply these strategies to the extracted BOLD activation from several regions of the brain from a group of individuals to describe joint dynamic behavior between these locations. We used simulated data with both innovation and additive outliers to test whether the estimation procedure is accurate despite contamination
The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction
Stimulus dimensionality-reduction methods in neuroscience seek to identify a
low-dimensional space of stimulus features that affect a neuron's probability
of spiking. One popular method, known as maximally informative dimensions
(MID), uses an information-theoretic quantity known as "single-spike
information" to identify this space. Here we examine MID from a model-based
perspective. We show that MID is a maximum-likelihood estimator for the
parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical
single-spike information corresponds to the normalized log-likelihood under a
Poisson model. This equivalence implies that MID does not necessarily find
maximally informative stimulus dimensions when spiking is not well described as
Poisson. We provide several examples to illustrate this shortcoming, and derive
a lower bound on the information lost when spiking is Bernoulli in discrete
time bins. To overcome this limitation, we introduce model-based dimensionality
reduction methods for neurons with non-Poisson firing statistics, and show that
they can be framed equivalently in likelihood-based or information-theoretic
terms. Finally, we show how to overcome practical limitations on the number of
stimulus dimensions that MID can estimate by constraining the form of the
non-parametric nonlinearity in an LNP model. We illustrate these methods with
simulations and data from primate visual cortex
False discovery rate regression: an application to neural synchrony detection in primary visual cortex
Many approaches for multiple testing begin with the assumption that all tests
in a given study should be combined into a global false-discovery-rate
analysis. But this may be inappropriate for many of today's large-scale
screening problems, where auxiliary information about each test is often
available, and where a combined analysis can lead to poorly calibrated error
rates within different subsets of the experiment. To address this issue, we
introduce an approach called false-discovery-rate regression that directly uses
this auxiliary information to inform the outcome of each test. The method can
be motivated by a two-groups model in which covariates are allowed to influence
the local false discovery rate, or equivalently, the posterior probability that
a given observation is a signal. This poses many subtle issues at the interface
between inference and computation, and we investigate several variations of the
overall approach. Simulation evidence suggests that: (1) when covariate effects
are present, FDR regression improves power for a fixed false-discovery rate;
and (2) when covariate effects are absent, the method is robust, in the sense
that it does not lead to inflated error rates. We apply the method to neural
recordings from primary visual cortex. The goal is to detect pairs of neurons
that exhibit fine-time-scale interactions, in the sense that they fire together
more often than expected due to chance. Our method detects roughly 50% more
synchronous pairs versus a standard FDR-controlling analysis. The companion R
package FDRreg implements all methods described in the paper
Statistical Analysis of fMRI Time-Series: A Critical Review of the GLM Approach.
Functional magnetic resonance imaging (fMRI) is one of the most widely used tools to study the neural underpinnings of human cognition. Standard analysis of fMRI data relies on a general linear model (GLM) approach to separate stimulus induced signals from noise. Crucially, this approach relies on a number of assumptions about the data which, for inferences to be valid, must be met. The current paper reviews the GLM approach to analysis of fMRI time-series, focusing in particular on the degree to which such data abides by the assumptions of the GLM framework, and on the methods that have been developed to correct for any violation of those assumptions. Rather than biasing estimates of effect size, the major consequence of non-conformity to the assumptions is to introduce bias into estimates of the variance, thus affecting test statistics, power, and false positive rates. Furthermore, this bias can have pervasive effects on both individual subject and group-level statistics, potentially yielding qualitatively different results across replications, especially after the thresholding procedures commonly used for inference-making
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