TY - JOUR

T1 - Estimating equations for density dependent markov jump processes

AU - Odubote, Oluseyi

AU - Linder, Daniel F.

N1 - Funding Information:
Funding: The second author would like to acknowledge that part of his effort on this project was funded by the Augusta University early career award.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/2/2

Y1 - 2021/2/2

N2 - Reaction networks are important tools for modeling a variety of biological phenomena across a wide range of scales, for example as models of gene regulation within a cell or infectious disease outbreaks in a population. Hence, calibrating these models to observed data is useful for predicting future system behavior. However, the statistical estimation of the parameters of reaction networks is often challenging due to intractable likelihoods. Here we explore estimating equations to estimate the reaction rate parameters of density dependent Markov jump processes (DDMJP). The variance–covariance weights we propose to use in the estimating equations are obtained from an approximating process, derived from the Fokker–Planck approximation of the chemical master equation for stochastic reaction networks. We investigate the performance of the proposed methodology in a simulation study of the Lotka–Volterra predator–prey model and by fitting a susceptible, infectious, removed (SIR) model to real data from the historical plague outbreak in Eyam, England.

AB - Reaction networks are important tools for modeling a variety of biological phenomena across a wide range of scales, for example as models of gene regulation within a cell or infectious disease outbreaks in a population. Hence, calibrating these models to observed data is useful for predicting future system behavior. However, the statistical estimation of the parameters of reaction networks is often challenging due to intractable likelihoods. Here we explore estimating equations to estimate the reaction rate parameters of density dependent Markov jump processes (DDMJP). The variance–covariance weights we propose to use in the estimating equations are obtained from an approximating process, derived from the Fokker–Planck approximation of the chemical master equation for stochastic reaction networks. We investigate the performance of the proposed methodology in a simulation study of the Lotka–Volterra predator–prey model and by fitting a susceptible, infectious, removed (SIR) model to real data from the historical plague outbreak in Eyam, England.

KW - Chemical master equation

KW - Density dependent Markov jump processes

KW - Generalized estimating equations

UR - http://www.scopus.com/inward/record.url?scp=85101391296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85101391296&partnerID=8YFLogxK

U2 - 10.3390/math9040391

DO - 10.3390/math9040391

M3 - Article

AN - SCOPUS:85101391296

SN - 2227-7390

VL - 9

SP - 1

EP - 16

JO - Mathematics

JF - Mathematics

IS - 4

M1 - 391

ER -