7,651 research outputs found
Lie algebra solution of population models based on time-inhomogeneous Markov chains
Many natural populations are well modelled through time-inhomogeneous
stochastic processes. Such processes have been analysed in the physical
sciences using a method based on Lie algebras, but this methodology is not
widely used for models with ecological, medical and social applications. This
paper presents the Lie algebraic method, and applies it to three biologically
well motivated examples. The result of this is a solution form that is often
highly computationally advantageous.Comment: 10 pages; 1 figure; 2 tables. To appear in Applied Probabilit
TIPPtool: Compositional Specification and Analysis of Markovian Performance Models
In this short paper we briefly describe a tool which is based on a Markovian stochastic process algebra. The tool offers both model specification and quantitative model analysis in a compositional fashion, wrapped in a userfriendly graphical front-end
Parameter Estimation via Conditional Expectation --- A Bayesian Inversion
When a mathematical or computational model is used to analyse some system, it
is usual that some parameters resp.\ functions or fields in the model are not
known, and hence uncertain. These parametric quantities are then identified by
actual observations of the response of the real system. In a probabilistic
setting, Bayes's theory is the proper mathematical background for this
identification process. The possibility of being able to compute a conditional
expectation turns out to be crucial for this purpose. We show how this
theoretical background can be used in an actual numerical procedure, and
shortly discuss various numerical approximations
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