  We present an ab initio stochastic method for calculating thermal properties
of a trapped, 1D Bose-gas covering the whole range from weak to strong
interactions. Discretization of the problem results in a Bose-Hubbard-like
Hamiltonian, whose imaginary time evolution is made computationally accessible
by stochastic factorization of the kinetic energy. To achieve convergence for
low enough temperatures such that quantum fluctuations are essential, the
stochastic factorization is generalized to blocks, and ideas from
density-matrix renormalization are employed. We compare our numerical results
for density and first-order correlations with analytic predictions.
