Stochastic models are often used to help understand the behavior of
intracellular biochemical processes. The most common such models are continuous
time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of
expectations of model output quantities with respect to model parameters, are
useful in this setting for a variety of applications. In this paper, we
introduce a class of hybrid pathwise differentiation methods for the numerical
estimation of parametric sensitivities. The new hybrid methods combine elements
from the three main classes of procedures for sensitivity estimation, and have
a number of desirable qualities. First, the new methods are unbiased for a
broad class of problems. Second, the methods are applicable to nearly any
physically relevant biochemical CTMC model. Third, and as we demonstrate on
several numerical examples, the new methods are quite efficient, particularly
if one wishes to estimate the full gradient of parametric sensitivities. The
methods are rather intuitive and utilize the multilevel Monte Carlo philosophy
of splitting an expectation into separate parts and handling each in an
efficient manner.Comment: 30 pages. The numerical example section has been extensively
rewritte
