Flip Flop tutorial with inaccurate starting values

[Generated automatically as a Tutorial summary]

Model Description

Name:: flip_flop_bad_pop
Title:: Flip Flop tutorial with inaccurate starting values
Author:: PoPy for PK/PD
Abstract:

One compartment model with a depot leading into a central compartment.
Note another interpretation of this is that the model is just over parametrised. Because here
the KE and V parameters act independently unlike the CL/V and V parametrisation.
Here initial values of KE, KA, V are close to the flipped values, so we get a bad fit in the false minima.

Keywords:: one compartment model; flip flop; dep_one_cmp_k; poor start values
Input Script:: flip_flop_bad_tut.pyml
Diagram:

Comparison

True objective value

-275.3301

Final fitted objective value

-194.0807

Compare Main f[X]

Name	Initial	Fitted	True	Abs. Error	Prop. Error
f[KE]	0.4	0.772	0.05	7.22e-01	1443.99%
f[V]	5	1.35	40	3.86e+01	96.62%
f[KA]	0.2	0.021	0.6	5.79e-01	96.50%

Compare Noise f[X]

Name	Initial	Fitted	True	Abs. Error	Prop. Error
f[PNOISE]	0.05	0.00826	0.01	1.74e-03	17.42%
f[ANOISE]	0.1	0.0543	0.05	4.29e-03	8.58%

Compare Variance f[X]

Name	Initial	Fitted	True	Abs. Error	Prop. Error
f[KE_isv]	0.02	0.125	0.05	7.51e-02	150.29%
f[KE_isv;V_isv]	0	-0.302	0	3.02e-01	inf
f[KE_isv;KA_isv]	0	-0.259	0	2.59e-01	inf
f[V_isv;KE_isv]	0	-0.302	0	3.02e-01	inf
f[V_isv]	0.02	0.971	0.05	9.21e-01	1841.36%
f[V_isv;KA_isv]	0	0.875	0	8.75e-01	inf
f[KA_isv;KE_isv]	0	-0.259	0	2.59e-01	inf
f[KA_isv;V_isv]	0	0.875	0	8.75e-01	inf
f[KA_isv]	0.02	0.833	0.05	7.83e-01	1565.44%

Outputs

Fitted f[X] values (after fitting)

f[KE] = 0.7720
f[V] = 1.3534
f[KA] = 0.0210
f[PNOISE] = 0.0083
f[ANOISE] = 0.0543
f[KE_isv,V_isv,KA_isv] = [
    [ 0.1251, -0.3020, -0.2594 ],
    [ -0.3020, 0.9707, 0.8752 ],
    [ -0.2594, 0.8752, 0.8327 ],
]

Generated data .csv file

Synthetic Data:: synthetic_data.csv

Gen and Fit Summaries

Gen: Flip Flop tutorial with inaccurate starting values (gen)
Fit: Flip Flop tutorial with inaccurate starting values (fit)

Inputs

True f[X] values (for simulation)

f[KE] = 0.0500
f[V] = 40.0000
f[KA] = 0.6000
f[PNOISE] = 0.0100
f[ANOISE] = 0.0500
f[KE_isv,V_isv,KA_isv] = [
    [ 0.0500, 0.0000, 0.0000 ],
    [ 0.0000, 0.0500, 0.0000 ],
    [ 0.0000, 0.0000, 0.0500 ],
]

Starting f[X] values (before fitting)

f[KE] = 0.4000
f[V] = 5.0000
f[KA] = 0.2000
f[PNOISE] = 0.0500
f[ANOISE] = 0.1000
f[KE_isv,V_isv,KA_isv] = [
    [ 0.0200, 0.0000, 0.0000 ],
    [ 0.0000, 0.0200, 0.0000 ],
    [ 0.0000, 0.0000, 0.0200 ],
]