Figure 1

Comparison between simple and adapted maximum likelihood estimation. Graph A. The upper panel represents a set of 30 covariate pairs (‚samples‘) which can be described by a linear function. Deviation from this function is due to a simulated technical error. The lower panel comprises 30 samples for which half of the data were shifted for a constant value. Graph B Likelihood distribution for the hypotheses space using the simple maximum likelihood estimator using data from upper and lower panel from graph A. For any given linearity parameter (slope and intercept), the estimated likelihood is increasing from white to cyan, blue, gree, yellow, orange and red. Upper panel: For a single linearity, the global maximum (black circle) matches with the linearity parameters of the simulated function (green circle). Lower panel: The simple maximum likelihood estimator fails to detect and represent the presence of two linear functions. The global maximum is calculated for a single linearity which is depicted in graph A, lower panel. Graph C: Likelihood distribution for the hypotheses space using the simple maximum likelihood estimator using the same data set as in graphs A and B. A single linearity is correctly identified (upper panel). Importantly, data sets comprising more than one linear function are also correctly matched reporting both slope and intercept parameters.