  Rigorous statistical methods for estimating thermonuclear reaction rates and
nucleosynthesis are becoming increasingly established in nuclear astrophysics.
The main challenge being faced is that experimental reaction rates are highly
complex quantities derived from a multitude of different measured nuclear
parameters (e.g., astrophysical S-factors, resonance energies and strengths,
particle and gamma-ray partial widths). We discuss the application of the Monte
Carlo method to two distinct, but related, questions. First, given a set of
measured nuclear parameters, how can one best estimate the resulting
thermonuclear reaction rates and associated uncertainties? Second, given a set
of appropriate reaction rates, how can one best estimate the abundances from
nucleosynthesis (i.e., reaction network) calculations? The techniques described
here provide probability density functions that can be used to derive
statistically meaningful reaction rates and final abundances for any desired
coverage probability. Examples are given for applications to s-process neutron
sources, core-collapse supernovae, classical novae, and big bang
nucleosynthesis.
