  We associate the new type of supersymmetric matrix models with any solution
to the quantum master equation of the noncommutative Batalin-Vilkovisky
geometry. The asymptotic expansion of the matrix integrals gives homology
classes in the Kontsevich compactification of the moduli spaces, which we
associated with the solutions to the quantum master equation in our previous
paper. We associate with the queer matrix superalgebra equipped with an odd
differentiation, whose square is nonzero, the family of cohomology classes of
the compactification. This family is the generating function for the products
of the tautological classes. The simplest example of the matrix integrals in
the case of dimension zero is a supersymmetric extenstion of the Kontsevich
model of 2-dimensional gravity.
