  Quantum Monte Carlo (QMC) methods can very accurately compute ground state
properties of quantum systems. We applied these methods to a system of boson
hard spheres to get exact, infinite system size results for the ground state at
several densities.
  Variational Monte Carlo (VMC) requires optimizing a parameterized wave
function to find the minimum energy. We examine several techniques for
optimizing VMC wave functions, focusing on the ability to optimize parameters
appearing in the Slater determinant.
  The kinds of problems that can be simulated with Monte Carlo methods are
expanded through the development of new algorithms for combining a QMC
simulation of the electrons with a classical Monte Carlo simulation for the
nuclei, which we call Coupled Electronic-Ionic Monte Carlo (CEIMC). The new
CEIMC method is applied to a system of molecular hydrogen at temperatures
ranging from 2800K to 4500K and densities from 0.25 to 0.46 g/cm**3.
  The challenges in constructing an efficient CEIMC simulation center mostly
around the noisy results generated from the QMC computations of the electronic
energy. The penalty method is a modification of the Metropolis method that can
tolerate noise. An improved correlated sampling method, the two-sided energy
difference method, is also presented as a method for reducing the noise.
