[Cry Me A River]

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but I'd rather not be specific,


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The whole point of the previous replies is that you can't generalise here, you need some kind of read on the opponent - ie: a weak/tight opponent, particularly a calling station, is unlikely to try a big river bluff while a LAG is far more likely to be trying to buy the pot. Still, even a huge LAG will sometimes have a hand, and even the biggest rock will try to make a move (or mistake) every once in a while. So there's always going to be some margin of error.

If they've just called all the way then pushed the river, the only information you have is A) reads and B) the calls themselves - ie: Did they call a preflop raise? How many players in the pot before they limped? What about the flop/turn action? Were they calling behind several other callers, possibly giving them pot/implied odds to chase?

Against complete donkeys this kind of info is going to be less valuable if they play the same from any position or will chase regardless of odds. However, this is why the replies have been asking for specific hands, because there may be more information available than you think there is. Particularly if you can get any kind of read on the player with respect to donkey/not donkey, passive/aggressive and loose/tight.