And that's exactly the wrong reasoning in this case. Because you want to predict the future from the past, over a really long time span and with the adverse eve

And that's exactly the wrong reasoning in this case. Because you want to predict the future from the past, over a really long time span and with the adverse events being extremely catastrophic. Just read up on how the Fukushima cleanup is going and how the cost estimates have risen... Bayesian reasoning would require you to argue about priors. You want to take priors from the past. Fine and dandy, when trying to predict the weather or even where the stock market is going. But when talking about how likely it is that something blows up and contaminates a huge area, maybe there are higher standards. And philosophizing about the average is all nice and well, until you happen to live near the site of an accident. And in Ukraine the assumption "nobody is going to shoot around a nuclear plant", which most assurance of nuclear safety depend upon, doesn't hold anymore.