I am building some new metrics to better understand the Bitcoin economy and one that seems to be useful is a probabilistic notion that a Bitcoin has been lost. I'm aware of the bitcoin days destroyed, but has anyone done any modeling to gain a sense if a Bitcoin has been destroyed as a result of a lost key or a transaction to a bad address?
There is no way to determine (that I can imagine) the number of lost private keys, you would have to make a guess that after x years without movement the private key is lost but that would just be a guess.
A digital currency with user-defined anonymity will cause any estimates to simply be guesstimates.
There are other areas where studies have attempted to quantify something and simply have concluded there is no reliable way to come up with the number so rather than provide misinformation there simply is no estimate made.
Essentially you could give a rough guesstimate of the upper bound. Any coin that hasn't moved in the past year, for instance, might go under the possibly lost for a year or more. That data is available and reportable. But who knows if the real level of coins that haven't moved for over a year is because they were lost or simply are being saved and not spent. Maybe it is 98% saved and 2% lost. Or not. Who knows.