We study the comparison of computational simulations of biomolecules to experimental data. We study the convergence of these simulations to equilibrium and determine measures of variance of the data using statistical methods. We run replica-exchange molecular dynamics (REMD) simulations of eight helical peptides and compare the simulation helicity to the experimentally measured helicity of the peptides. We use one-way sensitivity analysis to determine which parameter changes have a large effect on helicity measurements and use Bayesian updating for a parameter of the AMBER potential. We then consider the theoretical convergence behavior of the REMD algorithm itself by evaluating the properties of the isothermal numerical integrators used in the underlying MD. The underlying constant-temperature integrators explored in this thesis represent a majority of the deterministic isothermal methods used with REMD simulations and we show that these methods either fail to be measure-invariant or are not ergodic. For each of the non-ergodic integrators we show that REMD fails to be ergodic when run with the integrator. We give computational results from examples to demonstrate the practical implications of non-ergodicity and describe hybrid Monte Carlo, a method that leads to ergodicity. Finally, we consider the use of stochastic Langevin dynamics to simulate isothermal MD. We show geometric ergodicity of the Langevin diffusion over a simplified system with the eventual goal of determining geometric ergodicity for Langevin dynamics over the full AMBER potential.