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.
