2,255 research outputs found
Pathwise Sensitivity Analysis in Transient Regimes
The instantaneous relative entropy (IRE) and the corresponding instanta-
neous Fisher information matrix (IFIM) for transient stochastic processes are
pre- sented in this paper. These novel tools for sensitivity analysis of
stochastic models serve as an extension of the well known relative entropy rate
(RER) and the corre- sponding Fisher information matrix (FIM) that apply to
stationary processes. Three cases are studied here, discrete-time Markov
chains, continuous-time Markov chains and stochastic differential equations. A
biological reaction network is presented as a demonstration numerical example
Hybrid Pathwise Sensitivity Methods for Discrete Stochastic Models of Chemical Reaction Systems
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
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations
In this paper we propose a new class of coupling methods for the sensitivity
analysis of high dimensional stochastic systems and in particular for lattice
Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically
based on approximating continuous derivatives with respect to model parameters
by the mean value of samples from a finite difference scheme. Instead of using
independent samples the proposed algorithm reduces the variance of the
estimator by developing a strongly correlated-"coupled"- stochastic process for
both the perturbed and unperturbed stochastic processes, defined in a common
state space. The novelty of our construction is that the new coupled process
depends on the targeted observables, e.g. coverage, Hamiltonian, spatial
correlations, surface roughness, etc., hence we refer to the proposed method as
em goal-oriented sensitivity analysis. In particular, the rates of the coupled
Continuous Time Markov Chain are obtained as solutions to a goal-oriented
optimization problem, depending on the observable of interest, by considering
the minimization functional of the corresponding variance. We show that this
functional can be used as a diagnostic tool for the design and evaluation of
different classes of couplings. Furthermore the resulting KMC sensitivity
algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz
algorithm's philosophy, where here events are divided in classes depending on
level sets of the observable of interest. Finally, we demonstrate in several
examples including adsorption, desorption and diffusion Kinetic Monte Carlo
that for the same confidence interval and observable, the proposed
goal-oriented algorithm can be two orders of magnitude faster than existing
coupling algorithms for spatial KMC such as the Common Random Number approach
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