Modals can be used to show a degree of certainty.
Must have been, may have been, might have been, and could have been are used to show a degree of certainty in the past.
To show degrees of certainty in the past we use modal + present perfect.
Since the verb that follows a modal is in simple form the structure is: modal + have + verb in past participle.
If you are very confident then use the simple past.
If you are not completely certain then use must + present perfect.
If you are around 50% certain use may + present perfect.
If you are not very sure at all use might or could + present perfect . These show that you doubt it.