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Update docs/src/inverse_problems/structural_identifiability.md
Co-authored-by: Sam Isaacson <[email protected]>
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docs/src/inverse_problems/structural_identifiability.md

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@@ -7,7 +7,7 @@ Structural identifiability (which is what this tutorial considers) can be illust
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${dx \over dt} = p1*p2*x(t)$
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where, however much data is collected on $x$, it is impossible to determine the distinct values of $p1$ and $p2$. Hence, these parameters are non-identifiable (however, their product, $p1*p2$, *is* identifiable).
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Catalyst contains a special extension for carrying out structural identifiability analysis using the [StructuralIdentifiability.jl](https://github.com/SciML/StructuralIdentifiability.jl) package. This enables StructuralIdentifiability's `assess_identifiability`, `assess_local_identifiability`, and `find_identifiable_functions` functions to be called directly on Catalyst `ReactionSystem`s. It also implements specialised routines to make these more efficient when applied to reaction network models. How to use these functions is described in the following tutorial, with [StructuralIdentifiability providing a more extensive documentation](https://docs.sciml.ai/StructuralIdentifiability/stable/).
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Catalyst contains a special extension for carrying out structural identifiability analysis of generated reaction rate equation ODE models using the [StructuralIdentifiability.jl](https://github.com/SciML/StructuralIdentifiability.jl) package. This enables StructuralIdentifiability's `assess_identifiability`, `assess_local_identifiability`, and `find_identifiable_functions` functions to be called directly on Catalyst `ReactionSystem`s. This bypasses the need for users to convert `ReactionSystem`s to `ODESystem`s, provides a cleaner interface for calculating identifiability of reaction rate equation models, and implements specialised routines to speed up the identifiability calculations for the generated ODE models. How to use these functions is described in the following tutorial, with [StructuralIdentifiability providing a more extensive documentation](https://docs.sciml.ai/StructuralIdentifiability/stable/).
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Structural identifiability can be divided into *local* and *global* identifiability. If a model quantity is locally identifiable, it means that its true value can be determined down to a finite-number of possible options. This also means that there is some limited region around the quantity's true value where this true value is the only possible value (and hence, within this region, the quantity is fully identifiable). Globally identifiable quantities' values, on the other hand, can be uniquely determined. Again, while identifiability can be confirmed structurally for a quantity, it does not necessarily mean that it is practically identifiable for some given data.
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