  We present an updated search for the Higgs boson produced in association with
a vector boson in the final state with missing transverse energy and two jets.
We use the full CDF data set corresponding to an integrated luminosity of 9.45
fb${}^{-1}$ at a proton-antiproton center-of-mass energy of $\sqrt{s}=1.96$
TeV. New to this analysis is the inclusion of a $b$-jet identification
algorithm specifically optimized for $H\to b\bar{b}$ searches. Across the Higgs
boson mass range $90 \le m_H \le 150$ GeV$/c^2$, the expected 95% credibility
level upper limits on the $V H$ production cross section times the $H\to
b\bar{b}$ branching fraction are improved by an average of 14% relative to the
previous analysis. At a Higgs boson mass of 125 GeV$/c^2$, the observed
(expected) limit is 3.06 (3.33) times the standard model prediction,
corresponding to one of the most sensitive searches to date in this final
state.
