{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Pseudobatch transformation with uncertainties\n", "\n", "This notebook describes how to use the Pseudobatch transformation with error propagation of the measurement uncertainties. This utilizes a Bayesian model which is provided as a precompiled model implemented in the programming language [Stan](https://mc-stan.org/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/s143838/.virtualenvs/pseudobatch-dev/lib/python3.10/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", " from .autonotebook import tqdm as notebook_tqdm\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "{'stan_version_major': '2', 'stan_version_minor': '29', 'stan_version_patch': '2', 'STAN_THREADS': 'false', 'STAN_MPI': 'false', 'STAN_OPENCL': 'false', 'STAN_NO_RANGE_CHECKS': 'false', 'STAN_CPP_OPTIMS': 'false'}\n" ] } ], "source": [ "import logging\n", "\n", "from itertools import islice\n", "\n", "import arviz as az\n", "import cmdstanpy\n", "import numpy as np\n", "import pandas as pd\n", "import xarray as xr\n", "\n", "from matplotlib import pyplot as plt\n", "from matplotlib.collections import PolyCollection\n", "from scipy.special import logit\n", "\n", "from pseudobatch.data_correction import pseudobatch_transform\n", "from pseudobatch.datasets import load_standard_fedbatch\n", "from pseudobatch.error_propagation import run_error_propagation\n", "\n", "cmdstanpy_logger = logging.getLogger(\"cmdstanpy\")\n", "cmdstanpy_logger.disabled = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading data\n", "\n", "This cell uses the function `load_standard_fedbatch` from pseudobatch's `datasets` module to load a standard dataset. It then adds some columns that will be useful later." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", " | Kc_s | \n", "mu_max | \n", "Yxs | \n", "Yxp | \n", "Yxco2 | \n", "F0 | \n", "mu0 | \n", "s_f | \n", "sample_volume | \n", "timestamp | \n", "... | \n", "m_CO2_gas | \n", "c_Glucose | \n", "c_Biomass | \n", "c_Product | \n", "c_CO2 | \n", "mu_true | \n", "v_Feed_interval | \n", "c_Biomass_pseudobatch | \n", "c_Glucose_pseudobatch | \n", "c_Product_pseudobatch | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | \n", "0.15 | \n", "0.3 | \n", "1.85 | \n", "0.82151 | \n", "0.045193 | \n", "0.062881 | \n", "0.1 | \n", "100.0 | \n", "170.0 | \n", "10.000000 | \n", "... | \n", "38.827037 | \n", "0.075016 | \n", "1.337852 | \n", "0.694735 | \n", "0.0 | \n", "0.100014 | \n", "15.906036 | \n", "1.337852 | \n", "0.075016 | \n", "0.694735 | \n", "
1 | \n", "0.15 | \n", "0.3 | \n", "1.85 | \n", "0.82151 | \n", "0.045193 | \n", "0.062881 | \n", "0.1 | \n", "100.0 | \n", "170.0 | \n", "17.142857 | \n", "... | \n", "92.155995 | \n", "0.075103 | \n", "2.664023 | \n", "1.794378 | \n", "0.0 | \n", "0.100091 | \n", "21.847477 | \n", "2.732828 | \n", "-2.505689 | \n", "1.840722 | \n", "
2 | \n", "0.15 | \n", "0.3 | \n", "1.85 | \n", "0.82151 | \n", "0.045193 | \n", "0.062881 | \n", "0.1 | \n", "100.0 | \n", "170.0 | \n", "24.285714 | \n", "... | \n", "179.754779 | \n", "0.075053 | \n", "5.175767 | \n", "3.877080 | \n", "0.0 | \n", "0.100047 | \n", "35.885358 | \n", "5.582507 | \n", "-7.777595 | \n", "4.181762 | \n", "
3 | \n", "0.15 | \n", "0.3 | \n", "1.85 | \n", "0.82151 | \n", "0.045193 | \n", "0.062881 | \n", "0.1 | \n", "100.0 | \n", "170.0 | \n", "31.428571 | \n", "... | \n", "317.230058 | \n", "0.075015 | \n", "9.612284 | \n", "7.555778 | \n", "0.0 | \n", "0.100013 | \n", "56.317871 | \n", "11.403591 | \n", "-18.546600 | \n", "8.963843 | \n", "
4 | \n", "0.15 | \n", "0.3 | \n", "1.85 | \n", "0.82151 | \n", "0.045193 | \n", "0.062881 | \n", "0.1 | \n", "100.0 | \n", "170.0 | \n", "38.571429 | \n", "... | \n", "521.048177 | \n", "0.075011 | \n", "16.561967 | \n", "13.318358 | \n", "0.0 | \n", "0.100010 | \n", "83.496054 | \n", "23.294434 | \n", "-40.544661 | \n", "18.732292 | \n", "
5 | \n", "0.15 | \n", "0.3 | \n", "1.85 | \n", "0.82151 | \n", "0.045193 | \n", "0.062881 | \n", "0.1 | \n", "100.0 | \n", "170.0 | \n", "45.714286 | \n", "... | \n", "804.712744 | \n", "0.075009 | \n", "25.635276 | \n", "20.841818 | \n", "0.0 | \n", "0.100008 | \n", "116.205937 | \n", "47.584179 | \n", "-85.480689 | \n", "38.686567 | \n", "
6 | \n", "0.15 | \n", "0.3 | \n", "1.85 | \n", "0.82151 | \n", "0.045193 | \n", "0.062881 | \n", "0.1 | \n", "100.0 | \n", "170.0 | \n", "52.857143 | \n", "... | \n", "1178.794116 | \n", "0.075033 | \n", "35.029969 | \n", "28.631766 | \n", "0.0 | \n", "0.100029 | \n", "153.246173 | \n", "97.201461 | \n", "-177.272659 | \n", "79.447672 | \n", "
7 | \n", "0.15 | \n", "0.3 | \n", "1.85 | \n", "0.82151 | \n", "0.045193 | \n", "0.062881 | \n", "0.1 | \n", "100.0 | \n", "170.0 | \n", "60.000000 | \n", "... | \n", "1662.311084 | \n", "0.075012 | \n", "42.688520 | \n", "34.982129 | \n", "0.0 | \n", "0.100011 | \n", "198.077362 | \n", "198.556125 | \n", "-364.778789 | \n", "162.711567 | \n", "
8 rows × 26 columns
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\n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
---|---|---|---|---|---|---|---|---|---|
lp | \n", "-116.613 | \n", "4.641 | \n", "-125.567 | \n", "-108.514 | \n", "0.108 | \n", "0.076 | \n", "1875.0 | \n", "2489.0 | \n", "1.00 | \n", "
acceptance_rate | \n", "0.860 | \n", "0.129 | \n", "0.624 | \n", "1.000 | \n", "0.002 | \n", "0.001 | \n", "4825.0 | \n", "4000.0 | \n", "1.00 | \n", "
step_size | \n", "0.391 | \n", "0.013 | \n", "0.375 | \n", "0.406 | \n", "0.006 | \n", "0.005 | \n", "4.0 | \n", "4.0 | \n", "inf | \n", "
tree_depth | \n", "3.466 | \n", "0.506 | \n", "3.000 | \n", "4.000 | \n", "0.096 | \n", "0.068 | \n", "28.0 | \n", "28.0 | \n", "1.10 | \n", "
n_steps | \n", "12.572 | \n", "5.231 | \n", "7.000 | \n", "15.000 | \n", "0.722 | \n", "0.514 | \n", "45.0 | \n", "56.0 | \n", "1.06 | \n", "
diverging | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "4000.0 | \n", "4000.0 | \n", "NaN | \n", "
energy | \n", "138.084 | \n", "6.558 | \n", "126.165 | \n", "150.635 | \n", "0.166 | \n", "0.118 | \n", "1582.0 | \n", "2067.0 | \n", "1.00 | \n", "
\n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
---|---|---|---|---|---|---|---|---|---|
v0 | \n", "1.014967e+03 | \n", "6.274000e+00 | \n", "1003.020 | \n", "1026.440 | \n", "5.800000e-02 | \n", "4.100000e-02 | \n", "11762.0 | \n", "2675.0 | \n", "1.0 | \n", "
c[5, Product] | \n", "2.525166e+09 | \n", "1.596903e+11 | \n", "0.000 | \n", "382.677 | \n", "2.519860e+09 | \n", "1.781939e+09 | \n", "6104.0 | \n", "3090.0 | \n", "1.0 | \n", "
c[5, Glucose] | \n", "2.220015e+10 | \n", "1.403833e+12 | \n", "0.000 | \n", "346.289 | \n", "2.215507e+10 | \n", "1.566714e+10 | \n", "6059.0 | \n", "3041.0 | \n", "1.0 | \n", "
c[5, Biomass] | \n", "2.521762e+06 | \n", "1.333038e+08 | \n", "0.000 | \n", "556.668 | \n", "2.103310e+06 | \n", "1.487494e+06 | \n", "7532.0 | \n", "3018.0 | \n", "1.0 | \n", "
c[4, Product] | \n", "7.300870e+08 | \n", "3.772254e+10 | \n", "0.000 | \n", "1022.640 | \n", "5.951675e+08 | \n", "4.209284e+08 | \n", "6743.0 | \n", "2939.0 | \n", "1.0 | \n", "
... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
apump | \n", "-6.000000e-03 | \n", "4.400000e-02 | \n", "-0.092 | \n", "0.070 | \n", "1.000000e-03 | \n", "1.000000e-03 | \n", "7492.0 | \n", "2746.0 | \n", "1.0 | \n", "
pseudobatch_c[7, Product] | \n", "6.206539e+09 | \n", "3.906427e+11 | \n", "0.000 | \n", "2727.340 | \n", "6.164198e+09 | \n", "4.359074e+09 | \n", "8877.0 | \n", "2982.0 | \n", "1.0 | \n", "
pump_bias | \n", "NaN | \n", "NaN | \n", "-11.833 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "
cfeed[Biomass] | \n", "0.000000e+00 | \n", "0.000000e+00 | \n", "0.000 | \n", "0.000 | \n", "0.000000e+00 | \n", "0.000000e+00 | \n", "4000.0 | \n", "4000.0 | \n", "NaN | \n", "
cfeed[Product] | \n", "0.000000e+00 | \n", "0.000000e+00 | \n", "0.000 | \n", "0.000 | \n", "0.000000e+00 | \n", "0.000000e+00 | \n", "4000.0 | \n", "4000.0 | \n", "NaN | \n", "
119 rows × 9 columns
\n", "\n", " | mean | \n", "sd | \n", "hdi_3% | \n", "hdi_97% | \n", "mcse_mean | \n", "mcse_sd | \n", "ess_bulk | \n", "ess_tail | \n", "r_hat | \n", "
---|---|---|---|---|---|---|---|---|---|
v0 | \n", "1013.674 | \n", "6.047 | \n", "1002.120 | \n", "1024.430 | \n", "0.085 | \n", "0.060 | \n", "5069.0 | \n", "3144.0 | \n", "1.0 | \n", "
c[5, Product] | \n", "20.841 | \n", "1.030 | \n", "18.947 | \n", "22.801 | \n", "0.014 | \n", "0.010 | \n", "5480.0 | \n", "3012.0 | \n", "1.0 | \n", "
c[5, Glucose] | \n", "0.075 | \n", "0.004 | \n", "0.068 | \n", "0.082 | \n", "0.000 | \n", "0.000 | \n", "5702.0 | \n", "3056.0 | \n", "1.0 | \n", "
c[5, Biomass] | \n", "25.649 | \n", "1.276 | \n", "23.197 | \n", "27.988 | \n", "0.016 | \n", "0.011 | \n", "6228.0 | \n", "3694.0 | \n", "1.0 | \n", "
c[4, Product] | \n", "13.328 | \n", "0.676 | \n", "12.090 | \n", "14.615 | \n", "0.009 | \n", "0.006 | \n", "5446.0 | \n", "3471.0 | \n", "1.0 | \n", "
... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
apump | \n", "0.009 | \n", "0.033 | \n", "-0.054 | \n", "0.070 | \n", "0.001 | \n", "0.001 | \n", "2136.0 | \n", "2454.0 | \n", "1.0 | \n", "
pseudobatch_c[7, Product] | \n", "155.983 | \n", "12.100 | \n", "133.595 | \n", "178.295 | \n", "0.230 | \n", "0.163 | \n", "2737.0 | \n", "3220.0 | \n", "1.0 | \n", "
pump_bias | \n", "NaN | \n", "NaN | \n", "-11.956 | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "NaN | \n", "
cfeed[Biomass] | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "4000.0 | \n", "4000.0 | \n", "NaN | \n", "
cfeed[Product] | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "0.000 | \n", "4000.0 | \n", "4000.0 | \n", "NaN | \n", "
119 rows × 9 columns
\n", "draw | \n", "0 | \n", "1 | \n", "2 | \n", "3 | \n", "4 | \n", "5 | \n", "6 | \n", "7 | \n", "8 | \n", "9 | \n", "... | \n", "3990 | \n", "3991 | \n", "3992 | \n", "3993 | \n", "3994 | \n", "3995 | \n", "3996 | \n", "3997 | \n", "3998 | \n", "3999 | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
slope | \n", "0.102516 | \n", "0.096615 | \n", "0.101327 | \n", "0.096538 | \n", "0.101856 | \n", "0.100044 | \n", "0.099655 | \n", "0.097026 | \n", "0.099064 | \n", "0.097570 | \n", "... | \n", "0.101227 | \n", "0.100904 | \n", "0.099847 | \n", "0.099308 | \n", "0.099897 | \n", "0.098900 | \n", "0.099894 | \n", "0.099580 | \n", "0.10023 | \n", "0.099364 | \n", "
intercept | \n", "-0.807900 | \n", "-0.614030 | \n", "-0.776267 | \n", "-0.619113 | \n", "-0.797399 | \n", "-0.721281 | \n", "-0.691591 | \n", "-0.667151 | \n", "-0.676970 | \n", "-0.619378 | \n", "... | \n", "-0.724136 | \n", "-0.735155 | \n", "-0.708653 | \n", "-0.679298 | \n", "-0.656992 | \n", "-0.661648 | \n", "-0.707765 | \n", "-0.695189 | \n", "-0.70449 | \n", "-0.685411 | \n", "
2 rows × 4000 columns
\n", "\n", " | 0 | \n", "1 | \n", "2 | \n", "3 | \n", "4 | \n", "5 | \n", "6 | \n", "7 | \n", "8 | \n", "9 | \n", "... | \n", "3990 | \n", "3991 | \n", "3992 | \n", "3993 | \n", "3994 | \n", "3995 | \n", "3996 | \n", "3997 | \n", "3998 | \n", "3999 | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
slope | \n", "-1.744210 | \n", "-1.757008 | \n", "-1.741915 | \n", "-1.723624 | \n", "-1.871941 | \n", "-1.838772 | \n", "-1.823377 | \n", "-1.836021 | \n", "-1.699397 | \n", "-2.036570 | \n", "... | \n", "-1.845025 | \n", "-1.872864 | \n", "-1.875026 | \n", "-1.919493 | \n", "-1.854989 | \n", "-1.886462 | \n", "-1.896649 | \n", "-1.864343 | \n", "-1.842283 | \n", "-1.924881 | \n", "
intercept | \n", "-2.587623 | \n", "1.628419 | \n", "-0.189456 | \n", "-0.116613 | \n", "2.007992 | \n", "2.594703 | \n", "2.372684 | \n", "0.084090 | \n", "0.129974 | \n", "4.094919 | \n", "... | \n", "-1.764112 | \n", "-1.661884 | \n", "3.475286 | \n", "4.223898 | \n", "-0.092433 | \n", "-1.238829 | \n", "1.127363 | \n", "1.162724 | \n", "-0.245896 | \n", "3.203416 | \n", "
2 rows × 4000 columns
\n", "\n", " | 0 | \n", "1 | \n", "2 | \n", "3 | \n", "4 | \n", "5 | \n", "6 | \n", "7 | \n", "8 | \n", "9 | \n", "... | \n", "3990 | \n", "3991 | \n", "3992 | \n", "3993 | \n", "3994 | \n", "3995 | \n", "3996 | \n", "3997 | \n", "3998 | \n", "3999 | \n", "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
slope | \n", "0.717567 | \n", "0.830149 | \n", "0.799137 | \n", "0.811471 | \n", "0.820391 | \n", "0.820898 | \n", "0.781038 | \n", "0.815743 | \n", "0.803372 | \n", "0.897239 | \n", "... | \n", "0.833248 | \n", "0.790404 | \n", "0.889563 | \n", "0.877858 | \n", "0.808814 | \n", "0.822912 | \n", "0.862858 | \n", "0.836267 | \n", "0.825557 | \n", "0.881137 | \n", "
intercept | \n", "2.035210 | \n", "-0.845795 | \n", "-0.920503 | \n", "0.366229 | \n", "-1.117119 | \n", "-1.476975 | \n", "-0.584068 | \n", "0.767538 | \n", "-0.163943 | \n", "-1.097187 | \n", "... | \n", "0.044753 | \n", "1.346261 | \n", "-2.497430 | \n", "-2.395350 | \n", "0.753787 | \n", "0.738677 | \n", "-0.983234 | \n", "-1.065378 | \n", "-0.643284 | \n", "-1.157595 | \n", "
2 rows × 4000 columns
\n", "