If you are doing a Bayesian analysis on if a suspect committed a crime at 2:00 AM and they told you they were sleeping then - does this tell you any new information?
I would say without outside evidence it shouldn't update your probability on the subject. If they truly were sleeping they are going to say they were sleeping. If they were committing the act they are going to say they were sleeping.
Saying "the fact the suspect said they were sleeping at 2:00 AM is what they would say if they were committing the act" is not the same as saying "the fact that the suspect said they were sleeping at 2:00 AM is proof they committed the act"
If you are doing a Bayesian analysis on if a suspect committed a crime at 2:00 AM and they told you they were sleeping then - does this tell you any new information?
I would say without outside evidence it shouldn't update your probability on the subject. If they truly were sleeping they are going to say they were sleeping. If they were committing the act they are going to say they were sleeping.
Saying "the fact the suspect said they were sleeping at 2:00 AM is what they would say if they were committing the act" is not the same as saying "the fact that the suspect said they were sleeping at 2:00 AM is proof they committed the act"