Main panel: fit quality as measured by the absolute Bayesian likelihood for the best-fitting template (ℒ_max), versus P, the probability of a given source being of the simulated type, for the  ~18 000 Monte-Carlo-simulated supernovae. The upper panel shows the P distribution and the right panel the ℒ_max distribution. For clarity, large (blue) dots and solid (blue) lines marks the correctly typed SNe (with P > 0.5); small (red) dots and dashed (red) lines the incorrectly typed SNe. The cross and star symbols in the main panel show ℒ_max and P(TN)/P(CC), respectively, for the observed supernovae (see Sect. 5). Three of the thermonuclear SN candidates have ℒ_max < 1 × 10^-14, they are marked by a caret lower limit symbol at ℒ_max < 1 × 10^-14 (note that they have the same P(TN) values, thus the symbols are overlapping) (this figure is available in colour in the electronic version of the article).