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And in any reasonably large problem I will at some point discard a model and replace it with something new.

It's worth noting that a rigorous Bayesian approach does not license such a model-switch. The strict Bayesian starts with a prior, observes some evidence, and concludes with a new set of probabilities. By using this strategy Gelman is implicitly employing a vague, undefinable meta-model that exists only in his own brain. This isn't terrible, I suppose, if he gets good results, but it does mean that statistics is still as much an art as a science.