I don’t think Greaves’ example suffers the same problem actually—if we truly don’t know anything about what the possible colours are (just that each book has one colour), then there’s no reason to prefer {red, yellow, blue, other} over {red, yellow, blue, green, other}.
In the case of truly having no information, I think it makes sense to use Jeffreys prior in the box factory case because that’s invariant to reparametrisation, so it doesn’t matter whether the problem is framed in terms of length, area, volume, or some other parameterisation. I’m not sure what that actually looks like in this case though
Hm, but if we don’t know anything about the possible colours, the natural prior to assume seems to me to give all colors the same likelihood. It seems arbitrary to decide to group a subsection of colors under the label “other”, and pretend like it should be treated like a hypothesis on equal footing with the others in your given set, which are single colors.
I don’t think Greaves’ example suffers the same problem actually—if we truly don’t know anything about what the possible colours are (just that each book has one colour), then there’s no reason to prefer {red, yellow, blue, other} over {red, yellow, blue, green, other}.
In the case of truly having no information, I think it makes sense to use Jeffreys prior in the box factory case because that’s invariant to reparametrisation, so it doesn’t matter whether the problem is framed in terms of length, area, volume, or some other parameterisation. I’m not sure what that actually looks like in this case though
Hm, but if we don’t know anything about the possible colours, the natural prior to assume seems to me to give all colors the same likelihood. It seems arbitrary to decide to group a subsection of colors under the label “other”, and pretend like it should be treated like a hypothesis on equal footing with the others in your given set, which are single colors.
Yeah, Jeffreys prior seems to make sense here.