Posterior probability ratios of models including a different a number of background functions, ζ, in the analysis of the time series in Additional file 1, Figure S1. The first two ratios favour the more complex model (ratio below 1). The ratio between models with two and three background functions, H2ζ/H3ζ, is above 1 thus favouring the simpler model. The analysis would then normally automatically stop at two background functions, but for demonstration we include more functions here. The ratio stays above 1 thereby building a chain of decisions that always prefer the simpler model.