A Bayesian framework for the analysis of systems biology models of the brain
Fig 6
Fig 6a shows data generated from the same test function yi = a x sin(x) + b + ϵ, where a, b are both model parameters and ϵ is random Gaussian noise. x was varied from 0 to 2π, producing data y0, y1 and y2 for the parameter sets Θ0: a = 0, b = 0, Θ1: a = 1, b = 0 and Θ2: a = 0, b = 2.5 respectively. Despite both y1 and y2 being qualitatively very different they are very similar when summarised using only the Euclidean distance, with y1 having a Euclidean distance εeuc,1 = 35.58 and y2 having a Euclidean distance εeuc,2 = 35.44. If we instead look at the scaled baseline-to-peak (SBTP) distance we find that y1 has a SBTP distance SBTP(y1) = 240.5 and y2 has a SBTP distance SBTP(y2) = 0.27, giving εSBTP,1 = 240.2 and εSBTP,2 = 0.11. Fig 6b illustrates how the scaled baseline-to-peak distance is defined using x sin(x) + ϵ as the example signal. The baseline-to-peak distance is the absolute distance from the baseline to max ({|ymax|, |ymin|}). This is then divided by the range of the ‘default’ data, y0, to get the distance as a proportion of the total change seen within the data. In this example, baseline-to-peak distance is 4.82 and the range is 0.02, giving the previously mentioned SBTP distance of 240.5.