ODE Bayesian model not sampling from posterior distribution of parameters

Questions v5
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2

To give more details on the issues encountered during sampling, here is a description of the workflow when the user runs bayes_example.py in the repo.

First, a set of parameters (i.e. absorption constant k and clearance constant Cl) are sampled from a log normal distribution. Let’s refer to them as the true parameters. In my run, these are:

k = [2.81502005, 1.53297557, 4.03010654, 1.12139799, 2.59723459]
CL = [1.63582935, 1.33484215, 3.31452979, 1.91527733, 1.13722572]

For each pair of values, a forward simulation is done using the SBML-defined ODE model and the Roadrunner solver. This results in a xarray.Dataset with 2 dimensions: sim (the amount of simulation i.e. 5) and time (the step size for the Roadrunner solver i.e. 101).

This dataset is the one used for the Bayesian Model to estimate the true parameters. After the MCMC sampler is done, the summary statistics for my run are as follow:

Sampling 3 chains for 2_000 tune and 4_000 draw iterations (6_000 + 12_000 draws total) took 1098 seconds.6000/6000 06:02<00:00 Sampling chain 2, 0 divergences]
We recommend running at least 4 chains for robust computation of convergence diagnostics

      median    mad  eti_3%  eti_97%  mcse_median  ess_median  ess_tail  r_hat
k[0]    1.184  0.350   0.527    2.862        0.006   10802.915    9126.0    1.0
k[1]    1.142  0.347   0.498    2.788        0.007   11948.263    8823.0    1.0
k[2]    1.201  0.349   0.538    2.895        0.006   11661.139    7922.0    1.0
k[3]    1.124  0.346   0.481    2.726        0.007   11963.135    9009.0    1.0
k[4]    1.187  0.351   0.519    2.822        0.005   11831.302    8968.0    1.0
CL[0]   1.001  0.320   0.398    2.522        0.006   11818.290    9040.0    1.0
CL[1]   0.997  0.331   0.387    2.579        0.006   11709.851    8889.0    1.0
CL[2]   0.993  0.328   0.382    2.592        0.006   11906.557    8057.0    1.0
CL[3]   0.994  0.322   0.394    2.486        0.006   11381.412    8591.0    1.0
CL[4]   0.979  0.321   0.390    2.518        0.006   12063.211    9134.0    1.0
sigma   4.949  0.101   4.681    5.249        0.002   12108.402    8454.0    1.0

The median of the MCMC samples for any of the k or CL parameters do not match with the true parameters. That is the issue I am encountering with the model.

Thanks again for any feedback and please let me know if more details are needed.