This package contains two examples (in Matlab) of how to compute the log likelihood using Gaussian quadrature. The first example (RenewalExample.m) corresponds to a Renewal Process (with inverse Gaussian ISI-distribution). Using a simulated Renewal Process we give the approximation of the true log likelihood using the four approximations used in the article (DR1, DR2, CT and GL) The second example (ExampleGLM.m) is a simple refractory GLM model with 1-dimensional covariate and 2 parameters to be estimated, gain and log baseline firing rate. First, a spike train is simulated, and then estimation is done using Newton Method with backtracking linesearches, both for DR1 and GL approximations. For the GL method, there are several ways of computing the log likelihood evaluation nodes and weights. For example, the nodes can be obtained by finding the roots of the derivatives of the Legendre polynomials, and the weights through evaluations of some function of the polynomials and their derivatives at the corresponding roots. See lglnodes.m for computational details.