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Fig. 1 | BMC Systems Biology

Fig. 1

From: Clustering reveals limits of parameter identifiability in multi-parameter models of biochemical dynamics

Fig. 1

Canonical correlations and identifiability. a Illustrative view of the sensitivity vectors S i . b Conceptual illustration of the canonical correlations. Two subsets of sensitivity vectors represented as linear subspaces (planes Ω A and Ω B ). Canonical vectors on the planes are found to yield maximum cosine. In a two-dimensional subspace case, the second canonical vectors u 2,v 2 are required to be perpendicular to the first ones. c The introduced δ-condition requires that each parameter θ i is correlated less than δ with the remaining parameters θ i =(θ 1,..,θ i−1,θ i+1,…,θ l ). It can be interpreted in terms of how variance of the estimates changes when a single parameter and all model parameters are estimated. Parameter θ 0 denotes the linear combination of θ i maximally correlated with θ i , i.e. θ 0=lin{θ i }. d Mutual information as a measure of similarity between two parameter sets θ A ,θ B , which span linear subspaces Ω A ,Ω B interpreted in terms of the asymptotic posterior \(P(\hat {\theta }|\theta)\)

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