Must, may, might, could are used with a perfect infinitive form to show how certain a speaker is that a past situation happened or didn’t happen.
Affirmative → MODAL + HAVE + PAST PARTICIPLE
•Must have + past participle shows a great deal of certainty that something happened. The speaker is 90% sure or even more.
👉 I’ve phoned Jim several times, but he doesn’t answer. He must have gone out.
👉 The students did well on the test. They must have studied hard.
•May / might / could + have + past participle convey the idea that the speaker is not so certain that something happened, maybe 60% sure, or even less.
👉 My wife doesn’t answer the phone. She may (might, could) have gone shopping
👉 What was that noise?’ It might have been an airplane
Negative → MODAL + HAVE + PAST PARTICIPLE
•Can’t have + past participle shows a great deal of certainty that something didn’t happen. The speaker is 90% sure or even more.
👉 She can’t have liked the match. She hates football
👉 They can’t have finished all the exercises on time. There were too many and very little time.
•May / might not have + past participle shows that the speaker is 60% or less certain that something didn’t happen.
👉 She may/might not have been at home yesterday, but I don’t really know.
👉 I might not have given her the money; I’m not sure.