At least the way I think about it, the main role of Bayesian model testing is to compare gears-level models. A prior belief like “this phenomenon is going to be quite complex” doesn’t have any gears in it, so it doesn’t really make sense to think about in this context at all. I could sort-of replace “it’s complex” with a “totally ignorant” uniform-prior model (the trivial case of a gears-level model with no gears), but I’m not sure that captures quite the same thing.
Anyway, I recommend reading the second post on Wolf’s Dice. That should give a better intuition for why we’re privileging the unbiased coin hypothesis here. The prior is not arbitrary—I chose it because I actually do believe that most coins are (approximately) unbiased. The prior is where the (hypothesized) gears are: in this case, the hypothesis that most coins are approximately unbiased is a gear.
At least the way I think about it, the main role of Bayesian model testing is to compare gears-level models. A prior belief like “this phenomenon is going to be quite complex” doesn’t have any gears in it, so it doesn’t really make sense to think about in this context at all. I could sort-of replace “it’s complex” with a “totally ignorant” uniform-prior model (the trivial case of a gears-level model with no gears), but I’m not sure that captures quite the same thing.
Anyway, I recommend reading the second post on Wolf’s Dice. That should give a better intuition for why we’re privileging the unbiased coin hypothesis here. The prior is not arbitrary—I chose it because I actually do believe that most coins are (approximately) unbiased. The prior is where the (hypothesized) gears are: in this case, the hypothesis that most coins are approximately unbiased is a gear.