Higher Order Probabilities
  A number of writers have supposed that for the full specification of belief,
higher order probabilities are required. Some have even supposed that there may
be an unending sequence of higher order probabilities of probabilities of
probabilities.... In the present paper we show that higher order probabilities
can always be replaced by the marginal distributions of joint probability
distributions. We consider both the case in which higher order probabilities
are of the same sort as lower order probabilities and that in which higher
order probabilities are distinct in character, as when lower order
probabilities are construed as frequencies and higher order probabilities are
construed as subjective degrees of belief. In neither case do higher order
probabilities appear to offer any advantages, either conceptually or
computationally.
