  Models of biological systems often have many unknown parameters that must be
determined in order for model behavior to match experimental observations.
Commonly-used methods for parameter estimation that return point estimates of
the best-fit parameters are insufficient when models are high dimensional and
under-constrained. As a result, Bayesian methods, which treat model parameters
as random variables and attempt to estimate their probability distributions
given data, have become popular in systems biology. Bayesian parameter
estimation often relies on Markov Chain Monte Carlo (MCMC) methods to sample
model parameter distributions, but the slow convergence of MCMC sampling can be
a major bottleneck. One approach to improving performance is parallel tempering
(PT), a physics-based method that uses swapping between multiple Markov chains
run in parallel at different temperatures to accelerate sampling. The
temperature of a Markov chain determines the probability of accepting an
unfavorable move, so swapping with higher temperatures chains enables the
sampling chain to escape from local minima. In this work we compared the MCMC
performance of PT and the commonly-used Metropolis-Hastings (MH) algorithm on
six biological models of varying complexity. We found that for simpler models
PT accelerated convergence and sampling, and that for more complex models, PT
often converged in cases MH became trapped in non-optimal local minima. We also
developed a freely-available MATLAB package for Bayesian parameter estimation
called PTempEst (http://github.com/RuleWorld/ptempest), which is closely
integrated with the popular BioNetGen software for rule-based modeling of
biological systems.
