Functions to Assess Identifiability

assess_identifiability(ode; funcs_to_check = [], prob_threshold=0.99, loglevel=Logging.Info)

Input:

• ode - the ODE model
• funcs_to_check - list of functions to check identifiability for; if empty, all parameters and states are taken
• known_ic: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).
• prob_threshold - probability of correctness.
• loglevel - the minimal level of log messages to display (Logging.Info by default)

Assesses identifiability of a given ODE model. The result is guaranteed to be correct with the probability at least prob_threshold. The function returns an (ordered) dictionary from the functions to check to their identifiability properties (one of :nonidentifiable, :locally, :globally).

assess_local_identifiability(ode::ODE{P}; funcs_to_check::Array{<: Any, 1}, prob_threshold::Float64=0.99, type=:SE, loglevel=Logging.Info) where P <: MPolyRingElem{Nemo.QQFieldElem}

Checks the local identifiability/observability of the functions in funcs_to_check. The result is correct with probability at least prob_threshold.

Call this function if you have a specific collection of parameters of which you would like to check local identifiability.

type can be either :SE (single-experiment identifiability) or :ME (multi-experiment identifiability). If the type is :ME, states are not allowed to appear in the funcs_to_check.

assess_local_identifiability(dds::DDS{P}; funcs_to_check::Array{<: Any, 1}, known_ic, prob_threshold::Float64=0.99, loglevel=Logging.Info) where P <: MPolyRingElem{Nemo.QQFieldElem}

Checks the local identifiability/observability of the functions in funcs_to_check. The result is correct with probability at least prob_threshold. A list of quantities can be provided as known_ic for which the initial conditions can be assumed to be known and generic.

find_identifiable_functions(ode::ODE; options...)

Finds all functions of parameters/states that are identifiable in the given ODE system.

Options

This functions takes the following optional arguments:

• with_states: When true, also reports the identifiabile functions in the ODE states. Default is false.
• simplify: The extent to which the output functions are simplified. Stronger simplification may require more time. Possible options are:
  • :standard: Default simplification.
  • :weak: Weak simplification. This option is the fastest, but the output functions can be quite complex.
  • :strong: Strong simplification. This option is the slowest, but the output
  functions are nice and simple.
  • :absent: No simplification.
• known_ic: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).
• prob_threshold: A float in the range from 0 to 1, the probability of correctness. Default is 0.99.
• seed: The rng seed. Default value is 42.
• loglevel - the minimal level of log messages to display (Logging.Info by default)

Example

using StructuralIdentifiability

ode = @ODEmodel(
    x0'(t) = -(a01 + a21) * x0(t) + a12 * x1(t),
    x1'(t) = a21 * x0(t) - a12 * x1(t),
    y(t) = x0(t)
)

find_identifiable_functions(ode)

# prints
3-element Vector{AbstractAlgebra.Generic.FracFieldElem{Nemo.QQMPolyRingElem}}:
 a12 + a01 + a21
 a12*a01