2 research outputs found
Identifiability results for several classes of linear compartment models
Identifiability concerns finding which unknown parameters of a model can be
estimated from given input-output data. If some subset of the parameters of a
model cannot be determined given input-output data, then we say the model is
unidentifiable. In past work we identified a class of models, that we call
identifiable cycle models, which are not identifiable but have the simplest
possible identifiable functions (so-called monomial cycles). Here we show how
to modify identifiable cycle models by adding inputs, adding outputs, or
removing leaks, in such a way that we obtain an identifiable model. We also
prove a constructive result on how to combine identifiable models, each
corresponding to strongly connected graphs, into a larger identifiable model.
We apply these theoretical results to several real-world biological models from
physiology, cell biology, and ecology.Comment: 7 figure
Identifiability of linear compartmental tree models
A foundational question in the theory of linear compartmental models is how
to assess whether a model is identifiable -- that is, whether parameter values
can be inferred from noiseless data -- directly from the combinatorics of the
model. We completely answer this question for those models (with one input and
one output) in which the underlying graph is a bidirectional tree. Such models
include two families of models appearing often in biological applications:
catenary and mammillary models. Our proofs are enabled by two supporting
results, which are interesting in their own right. First, we give the first
general formula for the coefficients of input-output equations (certain
equations that can be used to determine identifiability). Second, we prove that
identifiability is preserved when a model is enlarged in specific ways
involving adding a new compartment with a bidirected edge to an existing
compartment.Comment: 32 page