Maximum Likelihood Analysis of Neuronal Spike Trains

Emhemmed, Yousef Mohammed (1995) Maximum Likelihood Analysis of Neuronal Spike Trains. PhD thesis, University of Glasgow.

Abstract

The main aim of this thesis is to introduce and develop a very powerful statistical technique, maximum likelihood estimation, to show how best this approach can be used in analysing neuronal spike train data. We then compare some of the likelihood results with those obtained via stochastic point processes techniques which will highlight the advantages of using the likelihood approach. Chapter 1 is aimed to give the physiological background and to provide a brief description of some aspects of neurophysiology which are relevant to the discussions that follow throughout this thesis. A brief description of the neuromuscular control system is followed by a more detailed one of the structure and operation of one of its components, the muscle spindle. Some basic statistics and a brief summary of a real data set obtained from a mammalian muscle spindle are also presented. The last part of this introductory chapter describes the simulation procedure used to generate the data sets for this thesis. Chapter 2 presents some brief historical notes of point process theory, followed by a definition of point process and some of the standard assumptions. The final part of this chapter is a review of the stochastic point processes techniques in both time and frequency domains followed by a demonstration of the uses of the square root of the cross intensity function, the ordinary coherence and the phase function with two simple examples from simulated neuronal spike train data. In chapter 3 we introduce the maximum likelihood estimation procedure as an alternative technique to the point process techniques used in the analysis of neuronal spike train data followed by a definition of the likelihood function and the maximum likelihood estimator (m.l.e.). An analytic likelihood model is introduced. The model is based on two underlying processes, the linear summation of the effects of the input spike train on the membrane potential and a recovery process, which, among other things, represents intrinsic properties of the neurone. The link function, the log likelihood for binomial data and a computational procedure are also discussed. The analysis of deviance, which highlights the difficulty in the goodness of fit assessment for models used to analyse binary data, is discussed. A linearisation technique for estimating non-linear parameters, which is used to estimate the non-linear parameters in the case of an exponentially decaying threshold, is introduced. In the final part of this chapter the summation, recovery and threshold functions are estimated using the same two sets of data considered in chapter 2, where a comparison of the summation function with the corresponding cross intensity function in each example indicates that the cross intensity function is underestimating the underlying excitatory effects of a synaptic input and may be misleading. We start chapter 4 with a discussion of certain issues concerning the likelihood approach, in particular an assessment of goodness of fit. We introduce a method of checking the validity of the model based on a graphical comparison between estimated and corresponding theoretical probabilities. We follow this with a discussion of the choice of link function. The second part of this chapter then applies the likelihood procedure to some simulated data sets. We start the analysis with a spontaneous discharge data set using three different link functions. This is a case where only threshold and recovery functions can be estimated, and also where the traditional stochastic point process techniques do not provide an analogous measure for the spontaneous behaviour of the cell. This gives the likelihood approach a further advantage over time and frequency domain analyses. Also we consider the case of a single input and single output neuronal spike train data set, where we introduce the idea of a carry-over effect of the synaptic inputs on the firing of a neurone. The likelihood approach is able, to some extent, to separate aspects of the relationship between spike trains through the threshold, recovery, summation and carry over effect functions and such ability and flexibility are not provided by other techniques. The demonstrations again suggest that the cross intensity function is difficult to interpret and may be misleading and underestimate the underlying excitatory and inhibitory effects of a synaptic input. In each case the improvement of the model is assessed at each stage of complexity by constructing a table of deviances. A sufficient reduction in deviance when proceeding to higher levels of complexity reflects a significant improvement in the model. In chapter 5 we extend the application of the likelihood procedure by taking advantage of its flexibility in the cases of one and two observed inputs and a single observed output of neuronal spike train data both in the absence and presence of "unobservable" inputs. This is to show that the approach is sufficiently flexible, and it may further be extended in principle to the case of an arbitrary number of neurone inputs. (Abstract shortened by ProQuest.).

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: Peter Breeze
• Keywords: Statistics, Neurosciences
• Date of Award: 1995
• Depositing User: Enlighten Team
• Unique ID: glathesis:1995-75740
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Dec 2019 09:15
• Last Modified: 19 Dec 2019 09:15
• URI: https://theses.gla.ac.uk/id/eprint/75740