The purpose of having priors is to compensate for lack of data, so that at least you are closer to the true model a posterior, and faster training since model averaging would take longer than training a single model. Also it’s not that the true model is within the ensemble of models but that you know before hand that getting a true model is rather difficult, lack of data or just the sheer complexity of the true model and parameter size. If you have enough data, playing around with different prior wouldn’t make any meaningful difference. I think when people talk about true model, what they really mean is how close they are to the true model. There isn’t really a way to know. Take coin flip for example. You only have 50-50 if your flips are perfect and your coin is perfectly uniform, 0 wind, etc. These details are neglected because they aren’t really important theoretically, but the true model isn’t theoretically perfect either since it is supposed to reflect reality.
The purpose of having priors is to compensate for lack of data, so that at least you are closer to the true model a posterior, and faster training since model averaging would take longer than training a single model. Also it’s not that the true model is within the ensemble of models but that you know before hand that getting a true model is rather difficult, lack of data or just the sheer complexity of the true model and parameter size. If you have enough data, playing around with different prior wouldn’t make any meaningful difference. I think when people talk about true model, what they really mean is how close they are to the true model. There isn’t really a way to know. Take coin flip for example. You only have 50-50 if your flips are perfect and your coin is perfectly uniform, 0 wind, etc. These details are neglected because they aren’t really important theoretically, but the true model isn’t theoretically perfect either since it is supposed to reflect reality.