Title: Information sensitivity functions to assess parameter information gain and identifiability of dynamical systems,
Abstract: A new class of functions, called the `Information sensitivity functions'
(ISFs), which quantify the information gain about the parameters through the
measurements/observables of a dynamical system are presented. These functions
can be easily computed through classical sensitivity functions alone and are
based on Bayesian and information-theoretic approaches. While marginal
information gain is quantified by decrease in differential entropy,
correlations between arbitrary sets of parameters are assessed through mutual
information. For individual parameters these information gains are also
presented as marginal posterior variances, and, to assess the effect of
correlations, as conditional variances when other parameters are given. The
easy to interpret ISFs can be used to a) identify time-intervals or regions in
dynamical system behaviour where information about the parameters is
concentrated; b) assess the effect of measurement noise on the information gain
for the parameters; c) assess whether sufficient information in an experimental
protocol (input, measurements, and their frequency) is available to identify
the parameters; d) assess correlation in the posterior distribution of the
parameters to identify the sets of parameters that are likely to be
indistinguishable; and e) assess identifiability problems for particular sets
of parameters.