I think what Shalizi means is that a Bayesian model is never “wrong”, in the sense that it is a true description of the current state of the ideal Bayesian agent’s knowledge. I.e., if A says an event X has probability p, and B says X has probability q, then they aren’t lying even if p!=q. And the ideal Bayesian agent updates that knowledge perfectly by Bayes’ rule (where knowledge is defined as probability distributions of states of the world). In this case, if A and B talk with each other then they should probably update, of course.
In frequentist statistics the paradigm is that one searches for the ‘true’ model by looking through a space of ‘false’ models. In this case if A says X has probability p and B says X has probability q != p then at least one of them is wrong.
I think what Shalizi means is that a Bayesian model is never “wrong”, in the sense that it is a true description of the current state of the ideal Bayesian agent’s knowledge. I.e., if A says an event X has probability p, and B says X has probability q, then they aren’t lying even if p!=q. And the ideal Bayesian agent updates that knowledge perfectly by Bayes’ rule (where knowledge is defined as probability distributions of states of the world). In this case, if A and B talk with each other then they should probably update, of course.
In frequentist statistics the paradigm is that one searches for the ‘true’ model by looking through a space of ‘false’ models. In this case if A says X has probability p and B says X has probability q != p then at least one of them is wrong.