Abstract:
:The paper presents results on the asymptotic properties of the least-squares estimates (LSEs) of the reaction constants in mass-action, stochastic, biochemical network models. LSEs are assumed to be based on the longitudinal data from partially observed trajectories of a stochastic dynamical system, modeled as a continuous-time, pure jump Markov process. Under certain regularity conditions on such a process, it is shown that the vector of LSEs is jointly consistent and asymptotically normal, with the asymptotic covariance structure given in terms of a system of ordinary differential equations (ODE). The derived asymptotic properties hold true as the biochemical network size (the total species number) increases, in which case the stochastic dynamical system converges to the deterministic mass-action ODE. An example is provided, based on synthetic as well as RT-PCR data from the retro-transcription network of the LINE1 gene.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Rempala GAdoi
10.1007/s11538-012-9744-ysubject
Has Abstractpub_date
2012-08-01 00:00:00pages
1938-55issue
8eissn
0092-8240issn
1522-9602journal_volume
74pub_type
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