PISAnalysis: Perform identifiability analysis of an ODE system A with the...

In qiuxing/ode.ident: Identifiability Analysis for Linear ODE systems

Description

This function computes three types of practical identifiability scores, the smoothed condition number (SCN), the practical identifiability score (PIS), and Stanhope's kappa statistic.

Usage

PISAnalysis(Y,S,L)

Arguments

Y	An dxn-dimensional matrix of discrete observations. Each row is a dimension and each column is a timepoint.
S	See details.
L	See details.

Details

This function computes three types of identifiability scores, SCN, PIS, and Stanhope's kappa. Y is the matrix of discrete observations, likely with measurement error. S, L are two nxn-dimensional matrices that represents the estimated inner product matrices between the solution curves, and between the derivatives of solution curves and the solution curves. In other words

\hat{Σ}_{\mathbf{x}\mathbf{x}} = Y S Y', \quad \hat{Σ}_{D\mathbf{x}, \mathbf{x}} = Y L Y'.

These two matrices are provided by function twostage2.

Value

SCN	The smoothed condition number (SCN).
PIS	The practical identifiability score (PIS).
kappa	Stanhope's kappa statistic.

Author(s)

Xing Qiu

References

1. Stanhope, S., Rubin, J. E., & Swigon, D. (2014). Identifiability of linear and linear-in-parameters dynamical systems from a single trajectory. SIAM Journal on Applied Dynamical Systems, 13(4), 1792-1815.

2. X. Qiu, T. Xu, B. Soltanalizadeh, and H. Wu. (2020+) Identifiability Analysis of Linear Ordinary Differential Equation Systems with a Single Trajectory. Submitted.

See Also

ICISAnalysis, twostage2

Examples

## load Example 3.1. In this example, yy1 are discrete and noisy
## observations of (A2, x0.A), and yy2 are observations of (A2,x0.B).
## The first case is practically identifiable but the second is not.
data("example3.1")

## To demonstrate that PIS is useful, we will use the functional
## two-stage method to estimate A2
myfit1 <- twostage2(yy1, tt)
S <- myfit1$S; L <- myfit1$L
myfit2 <- twostage2(yy2, tt)

## PISs of the first case are all relatively large
## (good practical identifiability) 
PISs1 <- PISAnalysis(yy1, S, L); PISs1
## PISs of the second case are all relatively small
## (bad practical identifiability) 
PISs2 <- PISAnalysis(yy2, S, L); PISs2

## A2 is the true system matrix
round(A2,2)
## The first case is a good estimate of A2
round(myfit1$Ahat,2); round(sum((myfit1$Ahat - A2)^2),2)
## The second case is a bad estimate of A2 due to
## identifiability issues
round(myfit2$Ahat,2); round(sum((myfit2$Ahat - A2)^2),2)

qiuxing/ode.ident documentation built on Sept. 30, 2020, 11:17 a.m.