SleepingTime.org is a website that will analyze any Twitter account and use that person's tweet times to determine when they are most likely to be sleeping.
I ran my account through the system and it said I am "more likely to be asleep between 1am and 9am." Surprisingly accurate. (Though just between you and me, I'd give myself until at least 9:30, probably 10am on a good day.)
I'm not sure how the site works, but I feel like it could be made even more accurate by searching for certain words.
Example: "Mike is more likely to be asleep between 1am and 9am, unless he has tweeted the words 'beer' or 'motherfuckers' in the past 24 hours, in which case he is more likely to be asleep between 5am and noon."
[NOTE: The site has been having some issues from getting too much traffic. I had to try a number of times before it gave me an accurate assessment.]