which results in that formula_105. It is also clear from the equation above that there might be a huge difference between formula_77 and formula_97 if the condition is not satisfied, as can be demonstrated by toy examples. Crucially, it was shown that sufficiency for formula_75 or formula_76 alone, or for both models, does not guarantee sufficiency for ranking the models. However, it was also shown that any sufficient summary statistic for a model formula_23 in which both formula_75 and formula_76 are nested is valid for ranking the nested models.