Stochastic Modelling in the biomedical sciences
Physiological processes at several scales (subcellular, cellular, tissue, organ and even
population) are inherently stochastic, due to a great variety of noisy factors
affecting the phenomenon under investigation.
In
fact, deterministic models (representing the vast majority of formalizations
hitherto employed in biomedicine) are not realistic, unless the random
fluctuations remain small. An incorrect representation, omitting substantial
system noise where this is in fact present, leads to poor model identification,
biased parameter estimations and inconsistent conclusions.
In
recent years there has been an increased emphasis into modeling the randomness
inherent in many physiological phenomena, and tools like Stochastic Differential Equations
(SDE), or Equações Diferenciais Estocásticas , so far mainly utilized in finance, have found initial application.
Connected with the use of these techniques in representing biomedical
processes, are issues such as identifiability, stability or periodicity, which
are typically more complicated to study then their deterministic counterparts.
==
Source: JG. Pires; P Palumbo;
A De Gaetano; C. Manes. ‘Stochastic models in medicine and life
sciences: mathematical analysis, model identification, validation and stability
properties’. Proposal for PhD programme. 2014. Unpublished. ==
Jorge Pires
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