To express past certainty, the same auxiliariesA helping verb used with main verbs to express mood, voice and tense. E.g.: I can't stand when I am disturbed. ("can", "am") are used as in the case of present and future certainty. However, the infinitives that follow are perfectThe aspect expressing completion. E.g.: He’s finished university. infinitives.

It can't have been David. (= I'm sure it wasn't David.)
It couldn't have been David.
It might have been David. or It could have been David.
It may have been David.
It is likely that it was David.
It must have been David. (= I'm sure it was David.)

Between the two extremes (the first and the last sentence above) the order of the structureThe way in which the parts of a sentence, clause or expression are arranged. E.g.: make somebody + infinitive in "The teacher made me rewrite the composition."s (might, may, could etc.) expresses a growing amount of certainty.

Certainty / uncertainty with modals
Certainty / uncertainty with modals Modals expressing present and future certainty / uncertainty