  Given a variation of Hodge structure over $\mathbb{P}^1$ with Hodge numbers
$(1,1,\dots,1)$, we show how to compute the degrees of the Deligne extension of
its Hodge bundles, following Eskin-Kontsevich-M\"oller-Zorich, by using the
local exponents of the corresponding Picard-Fuchs equation. This allows us to
compute the Hodge numbers of Zucker's Hodge structure on the corresponding
parabolic cohomology groups. We also apply this to families of elliptic curves,
K3 surfaces and Calabi-Yau threefolds.
