Goodness-of-fit tests for neural population models: the multivariate time-rescaling theorem
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We study the problem of parametric model-fitting in a finite alphabet setting. We characterize the weak convergence of the goodness-of-fit statistic with respect to an exponential family when the observations are drawn from some alternate distribution. We ...
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Schizophrenia is a devastating psychiatric illness characterized by deterioration of cognitive and emotional processing. It has been hypothesized that aberrant cortical connectivity is implicated in the disease (Friston, 1998), yet previous studies of func ...
Generalized Linear Models (GLMs) are an increasingly popular framework for modeling neural spike trains. They have been linked to the theory of stochastic point processes and researchers have used this relation to assess goodness-of-fit using methods from ...
The ability of simple mathematical models to predict the activity of single neurons is important for computational neuroscience. In neurons, stimulated by a time-dependent current or conductance, we want to predict precisely the timing of spikes and the su ...
The notions of Poisson Lie group and Poisson homogeneous space are extended to the Dirac category. The theorem of Drinfeld on the one-to-one correspondence between Poisson homogeneous spaces of a Poisson Lie group and a special class of Lagrangian subalgeb ...
Multiple types of measures have been developed to measure the similarity between two spike trains. These were extensively used to classify neuron responses according to stimuli and to validate mathematical models that predict the spike times. Here we analy ...
Micro-electrode array (MEA) technology has been exploited as a powerful tool for providing distributed information on learning, memory and information processing in cultured neuronal tissue, enabling an experimental perspective from the single cell level u ...
Measures of surprise have been recently studied in statistics. This new concept can be used as the first exploratory tool to verify if a model under the null hypothesis fits appropriately. As no alternative models are necessary, the use of the measures of ...
Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically det ...
The coordinated, collective spiking activity of neuronal populations encodes and processes information. One approach towards understanding such population based computation is to fit statistical models to simultaneously recorded spike trains and use these ...