Characterising the neuron spike train firing as a function of external stimulus applied in an experiment and intrinsic dynamics of neurons such as absolute and relative refractory periods, history effects are important in neuroscience. Such a characterisation is very complex and the broad class of models to capture such details are required consistently. One of the useful method which characterising neuron spike trains activity is a point process model. For instance, they have successfully characterised spiking activity of rat hippocampal place cells and sea hare nerve cells.

In general there are two approaches estimating the point process. One is the parametric modelling and there are many parametric point process models based on likelihood analysis. The self exiting process is carried out with history dependence which were selected by decaying function of effect of history. A simulation study is performed by Thinning method to check the self exciting process with selected history dependence reflects well neuron firings. Another is non-parametric method, point process based on B-spline basis function is carried out to characterise the single neuron firing rate and the FPCA (Functional Principal Component Analysis) is also performed to consider the dominant mode of variation of the functional data from the same session. In addition, the mFPCA (Multivariate Functional Principal Component Analysis) is applied to take into account the variation of a different session as well. The comparison of these methods with the same data set is performed in Chapter 6.