  We extend the model-free Data-Driven computing paradigm to solids and
structures that are stochastic due to intrinsic randomness in the material
behavior. The behavior of such materials is characterized by a likelihood
measure instead of a constitutive relation. We specifically assume that the
material likelihood measure is known only through an empirical point-data set
in material or phase space. The state of the solid or structure is additionally
subject to compatibility and equilibrium constraints. The problem is then to
infer the likelihood of a given structural outcome of interest. In this work,
we present a Data-Driven method of inference that determines likelihoods of
outcomes from the empirical material data and that requires no material or
prior modeling. In particular, the computation of expectations is reduced to
explicit sums over local material data sets and to quadratures over admissible
states, i. e., states satisfying compatibility and equilibrium. The complexity
of the material data-set sums is linear in the number of data points and in the
number of members in the structure. Efficient population annealing procedures
and fast search algorithms for accelerating the calculations are presented. The
scope, cost and convergence properties of the method are assessed with the aid
selected applications and benchmark tests.
