id: 05382259
dt: j
an: 05382259
au: Girolami, Mark
ti: Bayesian inference for differential equations.
so: Theor. Comput. Sci. 408, No. 1, 4-16 (2008).
py: 2008
pu: Elsevier Science Publishers, Amsterdam
la: EN
cc:
ut: Bayesian statistics; differential equations; biochemical pathway models;
Markov chain Monte Carlo
ci:
li: doi:10.1016/j.tcs.2008.07.005
ab: Summary: Nonlinear dynamic systems, such as biochemical pathways, can be
represented in abstract form using a number of modelling formalisms. In
particular, differential equations provide a highly expressive
mathematical framework with which to model dynamic systems, and a very
natural way to model the dynamics of a biochemical pathway in a
deterministic manner is through the use of nonlinear ordinary or time
delay differential equations. However if, for example, we consider a
biochemical pathway the constituent chemical species and hence the
pathway structure are seldom fully characterised. In addition it is
often impossible to obtain values of the rates of activation or decay
which form the free parameters of the mathematical model. The system
model in many cases is therefore not fully characterised either in
terms of structure or the values which parameters take. This
uncertainty must be accounted for in a systematic manner when the model
is used in simulation or predictive mode to safeguard against reaching
conclusions about system characteristics that are unwarranted, or in
making predictions that are unjustifiably optimistic given the
uncertainty about the model. The Bayesian inferential methodology
provides a coherent framework with which to characterise and propagate
uncertainty in such mechanistic models and this paper provides an
introduction to Bayesian methodology as applied to system models
represented as differential equations.
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