The present paper provides a Bayesian analysis of two-parameter disper
sion models under noninformative priors. The focus is on first-and sec
ond-order probability matching priors. Other noninformative priors, in
cluding Jeffreys' and reference priors, are examined in the light of t
hese criteria. For certain models some unique second-order probability
matching priors are found which are different from either Jeffreys' o
r reference priors.