Histogram of recovered polynomial order for different inverse signal to noise ratios k. U = 1000 and denotes the sample size. The noise variance σ_n ranges from ≈0 to ≤3. The signal was generated according to Eq. (2)as a 15th order polynomial. We see that the most adequate order selected by the BIC decreases with increasing k. The selected model depends on the specific data realization, therefore we averaged over reconstructed orders with similar k