 Consider the result formula_1 of some experiment, with two possible explanations, hypotheses formula_2 and formula_3, and some prior distribution formula_4 representing uncertainty as to which hypothesis is more accurate before taking into account formula_1.Lindley's paradox occurs when

These results can occur at the same time when formula_2 is very specific, formula_3 more diffuse, and the prior distribution does not strongly favor one or the other, as seen below.We can illustrate Lindley's paradox with a numerical example.