Statistical modelling of neurons

Specialeforsvar ved Mossa Merhi Reimert

Titel: Statistical modelling of neurons

Abstract: In this thesis, a statistical modelling framework based on multiplicative GLM was applied to single neuron modelling. Spike trains with distinct pattern was simulated via Izhikevich dynamics model. A statistical model based on multiplicative history dependent GLM was developed, and penalised regression was employed to attain estimates. Kolmogorov-Smirnov (KS) statistics is used to determine goodness-of-fit of the design. Data-dependent strategies for choosing penalisation was presented, based on KS statistics. For regularly behaved spike trains, the tonic spiking neuron, the specified models performed well, while neurons with deterministic bursting phases, the tonic bursting neuron, the framework could not provide estimates with adequate KS statistics. Based on the indicator basis encoded history models, a filter bank was estimated and used in a neuron type classifier, using the same methodology as in the first part of thesis. Poisson penalised regression was used to attain parameters that equates to filter bank coefficients. In the classification, classifying tonic bursting neurons performed better than classifying tonic spiking neurons. Using the Izhikevich, a spike train that transition from tonic spiking to tonic bursting was explored, with linear transition and logistic transition in Izhikevich parameter space, and an aggregated error analysis showed that linear transition performed worse than logistic transition. Empirical standard errors showed that the predictions in linear transition were wider than comparatively the standard errors for logistic transition.

Vejleder: Jacob Østergaard
Censor: Birger Madsen