Microbial_Scaling_Laws.ipynb

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   "source": "# Explaining microbial scaling laws using Bayesian inference\nIn this project, we want to combine methods from _Statistical Physics_ and _Bayesian Data Analysis_ to elucidate the principles behind cellular growth and division. We will study various classes of individual-based growth-division models and infer individual-level processes (model structures and likely ranges of associated parameters) from sigle-cell observations. \n\nIn the _Bayesian framework_, we formalize our process understanding the form of different rate functions, expressing the dependence of growth and division rates on variables characterizing a cell’s state (such as size and protein content), and calculate the Bayesian posteriors for the parameters of these functions.\n\n## Group \n- [Tommaso Amico](https://github.com/tommasoamico)\n- [Andrea Lazzari](https://github.com/AndreaLazzari)\n- [Paolo Zinesi](https://github.com/PaoloZinesi)\n- [Nicola Zomer](https://github.com/NicolaZomer)\n\n## Growth and division processes: general model \nIn our models we consider the evolution of a single non-interacting cell, which undergoes 2 processes:\n- **growth:** the cell size $x(t)$ evolves according to the following equation\n    $$\n    \\dot{x}=g(x(t)) \\quad, \\quad x(0)=x_b\n    $$\n    In some cases this relation can be expressed in vectorial form, where $\\underline{x}$ is the vector of the traits characterizing the cell's state (see model 2). \n- **division:** it is ruled by the _hazard rate function_ $h(x(t))$, which represents the istantaneous probability (or, equivalently, the amount of risk) of the cell to divide. This function is related to the so called _survival function_ $s(t)$, by the relation\n    $$\n    \\frac{\\dot{s}(t)}{s(t)}=-h(t) \\quad , \\quad s(0)=1\n    $$\n    where $s(t)$ gives the probability that the cell will survive (meaning not divide in this case) past a certain time $t$. Once $s(t)$ has been computed for a given model, division times are drawn from this distribution, following the Generalized Gillespie Algorithm. \n\n**While the growth is a deterministic process, division is a stochastic event.** Since the cell does not generally divide into two equal parts, we introduce a parameter $frac$, which is treated as a stochastic variable, such that after the division\n$$\n\\underline{x}_{div} = \\left(frac\\cdot x, (1-frac)\\cdot x\\right)\n$$\n\nFinally, we assume that the division ratios $frac$ are distributed according to a Beta function and that the growth rates $\\omega_1$ follow a Gamma function, hence denoting by $f$ the probability density distribution we obtain\n$$\n\\begin{aligned}\nf(frac|a, b) &= Beta(a, b) \\\\\nf(\\omega_1|c, d) &= Gamma(c, d)\n\\end{aligned}\n$$\n\n### Solution of the differential equations\nFor a given model, first we solve analytically the differential equation for $x(t)$, with the initial condition $x(0)=x_b$. Then, we plug $x(t)$ into $h$ and we use $h(x(t))$ to solve the equation for $s(t)$, with initial condition $s(0)=1$.\n\nOnce $s(t)$ is known, it is possible to generate random division times from their distribution using the **inverse transform method** and the solution can be deterministically propagated to find the simulated time series $x(t)$. To do this, it is also necessary to know or draw the values of $\\omega_1$ and $frac$ at each division cycle. \n\n",
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   "source": "# Models\n\n## Model 0 (Linear)\n**Notebook: [Real data, Model 0](./analysis_real_data/REAL_Model_0.ipynb)**\n\nWe start with a very simple stochastic model, biologically not very realistic, but useful to start familiarizing with the problem. In this first model we define $g(x)$ and $h(x)$ as 2 linear functions\n$$\n\\begin{aligned}\ng(x) &\\equiv \\omega_1(\\mu+x) \\\\\nh(x) &\\equiv \\omega_2(1+x/\\nu)\n\\end{aligned}\n$$\n\nwhere $\\omega_1$ and $\\omega_2$ are frequencies respectively related to the *growth* and *division* phases, while $\\mu$ and $\\nu$ are sizes (tipycally measured in $\\mu m$) that represent the lower and upper limiting trait scales, so they satisfy the relation $ \\mu < \\nu $.\n\nThe ratio between $\\omega_1$ and $\\omega_2$ is the order parameter that triggers the phase transition. The parameters $\\mu$ and $\\nu$ are necessary to cut off the probability distribution (in zero and for large values of $x$), which is important both for physical reasons and for making the distribution normalizable. Introducing these parameters is a mathematical trick, useful for example to prevent the cell from having a too small size, which however is difficult to justify from a biological point of view. We will then see better models, biologically speaking.\n\nThe results of the two differential equations are:\n$$\n\\begin{aligned}\nx(t) &= \\left(x_b+\\mu\\right)e^{\\omega_1 t}-\\mu \\\\\n\\ln(s(t)) &= \\omega_2 t \\left(\\frac{\\mu}{\\nu}-1\\right) + \\frac{\\omega_2}{\\omega_1} \\left(\\frac{\\mu+x_b}{\\nu}\\right) (1-e^{\\omega_1 t}) \\\\\ns(t) &= \\exp\\left\\{ \\omega_2t \\left(\\frac{\\mu}{\\nu}-1\\right) + \\frac{\\omega_2}{\\omega_1}\\left(\\frac{\\mu + x_b}{\\nu}\\right)(1-e^{\\omega_1t})\\right\\}\n\\end{aligned}\n$$\n",
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   "source": "![img](images/s_model0.png)",
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   "source": "## Model 1 (with Plateau)\n**Notebook: [Real data, Model 1](./analysis_real_data/REAL_Model_1.ipynb)**\n\nAs in the previous model, even in this case the cell growth is governed by a single trait, which is the size. However, this model is biologically more realistic, mainly because a lower bound is placed on the size of the cell such that it can divide. \n\nAlso in this case the processes considered are growth and division, governed by $g(x)$ and $h(x)$ respectively. In this model we define $g(x)$ and $h(x)$ as follows\n$$\n\\begin{aligned}\ng(x)&= \\omega_1 x \\\\\nh(x)&=\n\\begin{cases}\n    0  & , \\, x<\\mu \\\\\n    \\omega_2 \\cdot \\frac{x+\\nu}{\\mu+\\nu} & , \\, x\\geq \\mu\n\\end{cases}\n\\end{aligned}\n$$\n\nwhere $g(x)$ again corresponds to an exponential growth, while $h(x)$ is lower bounded by $\\mu$.\n\nThe results of the two differential equations are:\n$$\n\\begin{aligned}\nx(t) &= x_b\\, e^{\\omega_1 t} \\\\\n\\ln(s(t)) &= - \\left[ \\dfrac{x_b}{\\mu+\\nu} \\dfrac{\\omega_2}{\\omega_1} \\left( e^{\\omega_1 t} - e^{\\omega_1 t_0}\\right) + \\dfrac{\\nu}{\\mu+\\nu}\\, \\omega_2 (t-t_0) \\right] \\theta(t-t_0) \\\\\ns(t) &= \\exp\\left\\{ - \\left[ \\dfrac{x_b}{\\mu+\\nu} \\dfrac{\\omega_2}{\\omega_1} \\left( e^{\\omega_1 t} - e^{\\omega_1 t_0}\\right) + \\dfrac{\\nu}{\\mu+\\nu}\\, \\omega_2 (t-t_0) \\right] \\theta(t-t_0) \\right\\}\n\\end{aligned}\n$$\n\nwhere $t_0 \\equiv \\max\\left\\{0,\\dfrac{1}{\\omega_1} \\ln\\left(\\dfrac{\\mu}{x_b}\\right)\\right\\}$ is the minimum time at which the cell can divide and $\\theta(\\tau)$ is the Heaviside function.\n\nNote that this model is different from the linear one only if the new parameter $t_0$ is bigger than zero, i.e., only if $\\mu > x_b$.\n",
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   "source": "![img](images/s_model1.png)\n",
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   "source": "## Model 2 (with Protein)\n**Notebook: [Real data, Model 2](./analysis_real_data/REAL_Model_2.ipynb)**\n\nThe main difference between this model and the previous ones is that here we consider 2 traits: the cell size $m(t)$ and its protein content $p(t)$. We call $\\underline{x}$ the vector\n$$\n\\underline{x} = \\begin{pmatrix} m\\\\ p\\end{pmatrix} \n$$\n\nAs before, the traits evolution and the cell division are governed by $\\underline{g}(m)$ and $h(p)$ respectively, which are defined as \n$$\n\\begin{aligned}\n\\underline{g}(m)&=\\omega_1m\\begin{pmatrix} 1\\\\ c\\end{pmatrix} \\\\\nh(p)&=\n    \\begin{cases}\n    0   & , \\, p<\\mu \\\\\n    \\omega_2 \\, \\frac{p+\\nu}{\\mu+\\nu} & , \\, p\\geq \\mu\n    \\end{cases}\n\\end{aligned}\n$$\nFrom $\\underline{g}(m)$ we can notice that the cell size still grows exponentially and the protein content also follows this evolution, scaled by the factor $c$. As $c$ doesn't have a real meaning, we set it to $1$. \n\nMoreover, in this model the condition under which the cell can divide is that it contains a minimum amount of a specific type of protein, which we call $\\mu$. If $p\\geq \\mu$ the cell can divide, otherwise it cannot. Unlike model 1, we do not have any condition on the size of the cell for the division to take place and $h$ depens only on $p$.\n\nThe initial conditions for $m(t)$ and $p(t)$ are\n$$\n\\begin{aligned}\n    p(t=0) &= 0 \\\\\n    m(t=0) &= m_b\n\\end{aligned}\n$$\n\nand the division process occurs in the following way\n$$\n\\begin{pmatrix} m \\\\ p\\end{pmatrix} \\rightarrow \\begin{pmatrix} frac \\cdot m \\\\ 0\\end{pmatrix} + \\begin{pmatrix} (1-frac) \\cdot m \\\\ 0\\end{pmatrix}\n$$\nwhere $frac$ is the division ratio.\n\nSimilarly to the [Model 1](/analysis_real_data/REAL_Model_1.ipynb), the results of the two differential equations are:\n$$\n\\begin{aligned}\nm(t) &= m_b\\, e^{\\omega_1 t} \\\\\np(t) &= m_b\\, \\left(e^{\\omega_1 t} -1 \\right) \\\\\n\\ln(s(t)) &= - \\left[ \\dfrac{m_b}{\\mu+\\nu} \\dfrac{\\omega_2}{\\omega_1} \\left( e^{\\omega_1 t} - e^{\\omega_1 t_0}\\right) + \\dfrac{\\nu - m_b}{\\mu+\\nu}\\, \\omega_2 (t-t_0) \\right] \\theta   (t-t_0) \\\\\n%s(t) &= \\exp\\left\\{ - \\left[ \\dfrac{m_b}{\\mu+\\nu} \\dfrac{\\omega_2}{\\omega_1} \\left.         %(e^\\omega_1 t} - e^{\\omega_1 t_0}\\right) + \\dfrac{\\nu - m_b}{\\mu+\\nu}\\, \\omega_2 (t-t_0) %\\right] \\theta(t-t_0) \\right\\}\n\\end{aligned}\n$$\n\nwhere $t_0 \\equiv \\dfrac{1}{\\omega_1} \\ln\\left(1 + \\dfrac{\\mu}{m_b}\\right) $ is the minimum time at which the cell can divide and $\\theta(\\tau)$ is the Heaviside function.\n\nNote that in this model $t_0$ is always bigger than zero, because the argument of the logarithm is alway bigger than one. This means that, independently on the choice of parameters, each cell has a time period in which it cannot divide because the protein has not reached yet the threshold value $\\mu$.",
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   "source": "![img](images/s_model2.png)",
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   "source": "# Bayesian Data Analysis\nFor all models, the set of parameters to be inferred is \n$$\n\\underline{\\theta} = \\{\\mu, \\nu, \\omega_2, a, b, c, d\\}\n$$\n\nApplying the Bayes theorem, we can write\n$$\nf(\\underline{\\theta}|\\tau, \\omega_1, frac, M) \\propto f(\\tau, \\omega_1, frac|\\underline{\\theta}, M)\\cdot f(\\underline{\\theta}, M)\n$$\nwhere $M$ is the background information given by the selected model and $\\tau$, $\\omega_1$ and $frac$ are provided by the data. In the following likelihoods $M$ is left implicit.\n\nRegarding the likelihood, $f(\\tau, \\omega_1, frac|\\underline{\\theta})$, applying the chain rule and exploiting the fact that $frac$ and $\\omega_1$ are independent, it can be written as the product of the conditional probability density function of each random variable of interest\n$$\n\\begin{aligned}\nf(\\tau, \\omega_1, frac|\\underline{\\theta}) &=\nf(\\tau|\\omega_1, frac, \\underline{\\theta}) \\cdot f(\\omega_1, frac|\\underline{\\theta}) \\\\\n&=f(\\tau|\\omega_1, frac, \\underline{\\theta}) \\cdot f(\\omega_1|\\underline{\\theta}) \\cdot f(frac|\\underline{\\theta})\n\\end{aligned}\n$$ \nwhere the last 2 are respectively the $Gamma(c, d)$ and $Beta(a, b)$ distributions, while the former is the probability density function of division times, which depends on the selected model and it is minus the derivative of the survival function $s(t)$.\n\n## Workflow \n- **Calibration**  \nPerforming Markov Chain Monte Carlo (MCMC), via the Python implementation [emcee](https://emcee.readthedocs.io/en/stable/), we find the posterior distribution of $\\theta$ and the marginalized posterior of each parameter, of which we calculate the maximum, the median and the 95% credibility interval. Then, we use this results to generate a simulated time series, that can be compared with the real data, to find which model is statistically better.  \n\n- **Validation** \nModel validation and comparison is achieved by \n- making a boxplot of the simulated and real interdivision times\n- computing the overlap of the histograms of the interdivision times\n- calculating the predictive density\n\n\n## Methods\n- **Sampling from the PDF distribution of $\\tau$ with numerical inversion of the CDF**\nFollowing the inverse transform method, to draw a division time $t_d$ from the associated distribution, we draw a random value $K$ from a uniform distribution in the interval $[0, 1]$ (i.e., we draw a \"survival probability”) and solve numerically for $t_d$\n\n$$ \n\\log(s(t_d)) = \\log(K)\n$$\n\nWe use the library [Pyinverse](https://pypi.org/project/pynverse/) to find numerically the inverse of a function.\n\n- **Forward propagation**\nAfter having generated the time series of the survival times, we can forward propagate the evolution of a single cell, according to the following procedure:\n\n1. Start with the initial size $x_b$\n2. Propagate using the equation for $x(t)$ up to the first division time\n3. Divide the cell size according to $frac$ \n4. Repeat the last 2 points for all division times generated, imposing as initial size of the cell the one after division and resetting the time\n\nIn point **3.**, regarding the value of $frac$, three approches can be followed:\n- set $frac=0.5$ in all iterations assuming the cell always divides equally in two parts;\n- draw the values of $frac$ from the associated Beta distribution;\n- use the real values contained in the dataset. \n\nAfter playing with the first approach (see notebooks in folder [analysis_sim_data](./analysis_sim_data)), in order to obtain significant results and consider $frac$ as a stochastic variable, we follow the second one in the generation of the simulated time series. \n\nRegarding $\\omega_1$, as for $frac$, at each iteration we draw a value from the associated Gamma distribution.\n\n- **Predictive density**\nTo compute the predictive density, first we divide the dataset in 2 parts, one used for calibration and the other for validation. This is done randomly and several times, in order to get a more robust estimate of the predictive density. \n\nIn the calibration part, we take the maximum a posteriori (MAP) of the posterior: $\\underline{\\theta}_{MAP}$. Then, at each iteration, we use the inferred values of the parameters and the validation set to calculate the predictive density: \n$$\n    \\mathcal{L}(\\underline{\\tau}^V, \\underline{\\omega}_1^V,\\underline{f}^V | \\underline{\\theta}_{MAP}) =\n    \\prod_{cell \\, cycles} \n    \\mathcal{L}(\\tau_i^V | \\omega_{1, i}^V,f_i^V,\\underline{\\theta}_{MAP}) \n    \\cdot \\mathcal{L}(\\omega_{1, i}^V | \\underline{\\theta}_{MAP}) \n    \\cdot \\mathcal{L}(f_i^V | \\underline{\\theta}_{MAP})\n$$\n\nFinally, we take the average of the values obtained at each iteration for each model. Given the 3 models, the best is the one with the largest value of $\\mathcal{L}(\\underline{\\tau}^V, \\underline{\\omega}_1^V,\\underline{f}^V | \\underline{\\theta}_{MAP})$.\n\n",
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   "source": "# First Simulations\nBefore analyzing the real data, we prefer to carry out simulations for each model. Given a model, we set arbitrary, but meaningful, parameter values ($\\omega_1=1$, $\\omega_2=0.9$, $\\nu=1$, $\\mu=0.1$, $x_b=1$, such that $\\mu \\ll \\nu$ and $\\omega_2<\\omega_1$) and we generate the time series of the cell size. As explained above, this is achieved by sampling the division times inverting $s(t)$ and deterministically propagate the evolution of the cell to find $x(t)$. To keep the simulation simple, we fix $frac=0.5$.\n\nThen we run MCMC to perform inference on the parameters ($\\omega_1, \\omega_2, \\mu, \\nu$). In this case the results can be compared with the true value of the parameters, which are known from the simulation. \n\nThis is mainly done to familiarize with the problem, with the Metropolis algorithm and with the [emcee](https://emcee.readthedocs.io/en/stable/) library. The resulting notebooks can be found in the folder [analysis_sim_data](./analysis_sim_data):\n\n- [Simulated data, Model 0](./analysis_sim_data/model_0.ipynb)\n- [Simulated data, Model 1](./analysis_sim_data/model_1.ipynb)\n- [Simulated data, Model 2](./analysis_sim_data/model_2.ipynb)\n",
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   "source": "# Real Data\n\n",
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    "execution_start": 1655386088356,
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   "source": "import pandas as pd\nimport matplotlib.pyplot as plt\nimport numpy as np\n\nimport sys\nsys.path.insert(0, './analysis_real_data')\n\nfrom Fernando_package import functions\nfrom Fernando_package import plot_funcs",
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   "source": "First, we import the real data and we create the following objects:\n- `size`: length of the time series, i.e., the number of divisions \n- `xb_realdata`: initial size of the cell \n- `df_microbial_growth`: our dataset ",
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   "source": "df_microbial_growth = pd.read_csv('/work/Microbial_Scaling_Laws/data/modified_Susman18_physical_units.csv')\nxb_realdata = df_microbial_growth['length_birth'][0]\n\n# remove first NaN\ndf_microbial_growth  =  df_microbial_growth[~ np.isnan(df_microbial_growth['division_ratio'])]\nsize = len(df_microbial_growth['generationtime'])\n\n# check that there is only one cell in the dataset\nprint('Number of cells in the dataset:', df_microbial_growth['lineage_ID'].nunique()) \n\n# print length of the series and initial size\nprint('Length of the time series:', size)\nprint('Initial size of the cell:', round(xb_realdata, 4))\n\ndisplay(df_microbial_growth)\n\n",
   "execution_count": 2,
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     "text": "Number of cells in the dataset: 1\nLength of the time series: 251\nInitial size of the cell: 1.7914\n",
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      "text/plain": "     div_and_fold  fold_growth  division_ratio  added_length  generationtime  \\\n1        1.009831     0.794984        0.456028      3.198324        0.500000   \n2        0.862482     0.607893        0.469619      2.291172        0.416667   \n3        1.426486     1.037370        0.505526      4.632409        0.833333   \n4        0.729601     0.490156        0.446903      2.028413        0.333333   \n5        0.887982     0.609464        0.482744      2.121432        0.416667   \n..            ...          ...             ...           ...             ...   \n247      0.940427     0.590789        0.520893      2.192641        0.416667   \n248      0.928602     0.604227        0.507478      2.069835        0.500000   \n249      1.568073     1.046815        0.550478      4.644408        0.750000   \n250      0.809727     0.481681        0.500204      2.215210        0.333333   \n251      0.860970     0.711011        0.422863      2.538870        0.500000   \n\n     length_birth  length_final  growth_rate  lineage_ID  generation  \\\n1        2.633655      5.831979     1.589968        15.0         1.0   \n2        2.738808      5.029980     1.458944        15.0         2.0   \n3        2.542786      7.175195     1.244844        15.0         3.0   \n4        3.206619      5.235033     1.470468        15.0         4.0   \n5        2.527183      4.648614     1.462714        15.0         5.0   \n..            ...           ...          ...         ...         ...   \n247      2.722385      4.915026     1.417893        15.0       249.0   \n248      2.494268      4.564104     1.208453        15.0       250.0   \n249      2.512440      7.156848     1.395754        15.0       251.0   \n250      3.579885      5.795095     1.445043        15.0       252.0   \n251      2.450531      4.989402     1.422022        15.0       253.0   \n\n     start_time    end_time  \n1      1.083333    1.583333  \n2      1.666667    2.083333  \n3      2.166667    3.000000  \n4      3.083333    3.416667  \n5      3.500000    3.916667  \n..          ...         ...  \n247  150.583333  151.000000  \n248  151.083333  151.583333  \n249  151.666667  152.416667  \n250  152.500000  152.833333  \n251  152.916667  153.416667  \n\n[251 rows x 12 columns]",
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": "",
   "metadata": {
    "cell_id": "c170c4adda6b4c6cb9a407c5a21a51f2",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 46
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "0eb1ad9dddd04db8ba40d05722ac3be5",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "d5d855a",
    "execution_start": 1655386092493,
    "execution_millis": 895,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 642,
    "deepnote_output_heights": [
     527
    ]
   },
   "source": "fig = plot_funcs.plot_3d_interactive(df_microbial_growth)\nfig.show()",
   "execution_count": 3,
   "outputs": [
    {
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   "source": "|                       |        |\n|:------------------------------------:|:----------------------------------:|\n| ![img](images/fit_beta.png) | ![img](images/fit_gamma.png) |\n",
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   "source": "<table style=\"border-collapse: collapse; border: none; border-spacing: 0px;\">\n\t<tr>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>      a     </b>\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>      b     </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>   </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>   </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>        c       </b>\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>         d         </b>\n\t\t</td>\n\t</tr>\n\t<tr>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t77 ± 6\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t80 ± 6\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t63.8 ± 2.6\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.021 ± 0.001\n\t\t</td>\n\t</tr>\n</table>",
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   "metadata": {
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   "source": "## Data analysis with single models\nFor each model we create a Jupyter notebook, in which we run MCMC, analyze the chains, show the marginalized posterior distributions, simulate the time series using the inferred values of the parameters, compute the overlap and the predictive density. \n\nThese notebooks are collected in the folder [analysis_real_data](./analysis_real_data):\n- [Real data, Model 0](./analysis_real_data/REAL_Model_0.ipynb)\n- [Real data, Model 1](./analysis_real_data/REAL_Model_1.ipynb)\n- [Real data, Model 2](./analysis_real_data/REAL_Model_2.ipynb)\n\nFinally, in the following section we retrieve the results achieved with all models, in order to perform model comparison and validation. ",
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  {
   "cell_type": "markdown",
   "source": "# Final results\n",
   "metadata": {
    "cell_id": "b9a94b17a49e4a2da38b152e1e9fd140",
    "tags": [],
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  {
   "cell_type": "markdown",
   "source": "## Inference results\n### Model 0",
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    "source_hash": "a50e4184",
    "execution_start": 1655386093443,
    "execution_millis": 143,
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    "deepnote_cell_height": 436.265625
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   "source": "df_mod0 = pd.read_csv('./data/model0.csv')\n\ndf_mod0 = df_mod0.round(4).rename({0: 'PosteriorMax',\n                          1: 'LowerBoundCI',\n                          2: 'UpperBoundCI'})\n\ndisplay(df_mod0)",
   "execution_count": 4,
   "outputs": [
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       "rows": [
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       ]
      },
      "text/plain": "              omega_2      mu      nu        a        b        c       d\nPosteriorMax   0.4327  0.4728  1.0452  15.4286  14.6821  30.8215  0.0453\nLowerBoundCI   0.2894  0.1328  0.6895  12.4223  12.3637  26.3462  0.0396\nUpperBoundCI   0.6679  0.7912  1.9139  17.5977  17.5328  35.1631  0.0530",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>omega_2</th>\n      <th>mu</th>\n      <th>nu</th>\n      <th>a</th>\n      <th>b</th>\n      <th>c</th>\n      <th>d</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>PosteriorMax</th>\n      <td>0.4327</td>\n      <td>0.4728</td>\n      <td>1.0452</td>\n      <td>15.4286</td>\n      <td>14.6821</td>\n      <td>30.8215</td>\n      <td>0.0453</td>\n    </tr>\n    <tr>\n      <th>LowerBoundCI</th>\n      <td>0.2894</td>\n      <td>0.1328</td>\n      <td>0.6895</td>\n      <td>12.4223</td>\n      <td>12.3637</td>\n      <td>26.3462</td>\n      <td>0.0396</td>\n    </tr>\n    <tr>\n      <th>UpperBoundCI</th>\n      <td>0.6679</td>\n      <td>0.7912</td>\n      <td>1.9139</td>\n      <td>17.5977</td>\n      <td>17.5328</td>\n      <td>35.1631</td>\n      <td>0.0530</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": "Most probable parameters, expressed in terms of mean and variance of the two distributions.\n<table style=\"border-collapse: collapse; border: none; border-spacing: 0px;\">\n\t<tr>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>      Mean of division factor     </b>\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>      Variance of division factor     </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>   </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>   </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>        Mean of growing factor       </b>\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>         Variance of growing factor         </b>\n\t\t</td>\n\t</tr>\n\t<tr>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.506\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.00805\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t1.38\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.0633\n\t\t</td>\n\t</tr>\n</table>",
   "metadata": {
    "cell_id": "c9983a14b2884ef0b1051a47e40de3b8",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 118.1875
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "8a9cc7f34066400f8ef28faebfee07f6",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "b7d1c0ba",
    "execution_start": 1655386093584,
    "execution_millis": 59,
    "is_code_hidden": true,
    "is_output_hidden": true,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 105.578125
   },
   "source": "print(\"mean division factor = \", df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[0]/(df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[1]))\nprint(\"variance division factor = \", (df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[0]*df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[1])/(((df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[1])**2)*(df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[1]+1)))\n\nprint(\"\\nmean grow factor = \", df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[2]*df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[3])\nprint(\"variance grow factor = \", df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[2]*df_mod0.loc[\"PosteriorMax\",['a','b','c','d']].values[3]**2)",
   "execution_count": 5,
   "outputs": [
    {
     "name": "stdout",
     "text": "mean division factor =  0.5123959257008306\nvariance division factor =  0.008030881369625867\n\nmean grow factor =  1.39621395\nvariance grow factor =  0.063248491935\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": "### Model 1",
   "metadata": {
    "cell_id": "fec3c391364144b58e228077825d6932",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 62
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "30ba76f734de439a8b35bc00b407f300",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "a1cca2e",
    "execution_start": 1655386093652,
    "execution_millis": 728,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 436.265625
   },
   "source": "df_mod1 = pd.read_csv('./data/model1.csv')\n\ndf_mod1 = df_mod1.round(4).rename({0: 'PosteriorMax',\n                          1: 'LowerBoundCI',\n                          2: 'UpperBoundCI'})\n\ndisplay(df_mod1)",
   "execution_count": 6,
   "outputs": [
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      "text/plain": "              omega_2      mu      nu        a        b        c       d\nPosteriorMax   0.5825  0.2002  1.0380  15.1529  14.9653  29.7617  0.0447\nLowerBoundCI   0.3805  0.0537  0.6311  12.5483  12.5305  26.3317  0.0395\nUpperBoundCI   0.8242  0.6599  1.8777  17.6064  17.6249  35.3439  0.0529",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>omega_2</th>\n      <th>mu</th>\n      <th>nu</th>\n      <th>a</th>\n      <th>b</th>\n      <th>c</th>\n      <th>d</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>PosteriorMax</th>\n      <td>0.5825</td>\n      <td>0.2002</td>\n      <td>1.0380</td>\n      <td>15.1529</td>\n      <td>14.9653</td>\n      <td>29.7617</td>\n      <td>0.0447</td>\n    </tr>\n    <tr>\n      <th>LowerBoundCI</th>\n      <td>0.3805</td>\n      <td>0.0537</td>\n      <td>0.6311</td>\n      <td>12.5483</td>\n      <td>12.5305</td>\n      <td>26.3317</td>\n      <td>0.0395</td>\n    </tr>\n    <tr>\n      <th>UpperBoundCI</th>\n      <td>0.8242</td>\n      <td>0.6599</td>\n      <td>1.8777</td>\n      <td>17.6064</td>\n      <td>17.6249</td>\n      <td>35.3439</td>\n      <td>0.0529</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
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   ]
  },
  {
   "cell_type": "markdown",
   "source": "Most probable parameters, expressed in terms of mean and variance of the two distributions.\n<table style=\"border-collapse: collapse; border: none; border-spacing: 0px;\">\n\t<tr>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>      Mean of division factor     </b>\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>      Variance of division factor     </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>   </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>   </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>        Mean of growing factor       </b>\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>         Variance of growing factor         </b>\n\t\t</td>\n\t</tr>\n\t<tr>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.498\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.00811\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t1.38\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.0624\n\t\t</td>\n\t</tr>\n</table>",
   "metadata": {
    "cell_id": "c931d3e72fc648c0981666a6d572853b",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 118.1875
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "4230b8affc8e479783c53bc25bc1684b",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "3b3c8ce5",
    "execution_start": 1655386093753,
    "execution_millis": 660,
    "is_code_hidden": true,
    "is_output_hidden": true,
    "owner_user_id": "7f69bd26-d583-496b-860b-3b60f8ef9538",
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 105.578125
   },
   "source": "print(\"mean division factor = \", df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[0]/(df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[1]))\nprint(\"variance division factor = \", (df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[0]*df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[1])/(((df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[1])**2)*(df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[1]+1)))\n\nprint(\"\\nmean grow factor = \", df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[2]*df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[3])\nprint(\"variance grow factor = \", df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[2]*df_mod1.loc[\"PosteriorMax\",['a','b','c','d']].values[3]**2)",
   "execution_count": 7,
   "outputs": [
    {
     "name": "stdout",
     "text": "mean division factor =  0.5031143959466369\nvariance division factor =  0.008033572010523985\n\nmean grow factor =  1.33034799\nvariance grow factor =  0.05946655515299999\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": "### Model 2",
   "metadata": {
    "cell_id": "66da695d4386460688d9497f777445e8",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 62
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "fafbeb0b917442a1be0a1451bacc22e5",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "11d2e925",
    "execution_start": 1655386093866,
    "execution_millis": 551,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 436.265625
   },
   "source": "df_mod2 = pd.read_csv('./data/model2.csv')\n\ndf_mod2 = df_mod2.round(4).rename({0: 'PosteriorMax',\n                          1: 'LowerBoundCI',\n                          2: 'UpperBoundCI'})\n\ndisplay(df_mod2)",
   "execution_count": 8,
   "outputs": [
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      "text/plain": "              omega_2      mu      nu        a        b        c       d\nPosteriorMax   1.2434  0.5407  0.6052  15.0915  15.3455  31.5883  0.0448\nLowerBoundCI   0.8190  0.1856  0.4447  12.4532  12.4721  26.3999  0.0397\nUpperBoundCI   1.5312  0.5485  0.9821  17.6510  17.6678  35.1114  0.0530",
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   "cell_type": "markdown",
   "source": "Most probable parameters, expressed in terms of mean and variance of the two distributions.\n<table style=\"border-collapse: collapse; border: none; border-spacing: 0px;\">\n\t<tr>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>      Mean of division factor     </b>\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>      Variance of division factor     </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>   </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>   </b>\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>        Mean of growing factor       </b>\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t<b>         Variance of growing factor         </b>\n\t\t</td>\n\t</tr>\n\t<tr>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.508\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.00828\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"padding-right: 3pt; padding-left: 3pt;\">\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t1.40\n\t\t</td>\n\t\t<td style=\"border-width: 1px; border-style: solid; border-color: rgb(0, 0, 0); text-align: center; padding-right: 3pt; padding-left: 3pt;\">\n\t\t\t0.0639\n\t\t</td>\n\t</tr>\n</table>",
   "metadata": {
    "cell_id": "82e41e53becb43d3bc7e407fe2baad03",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 118.1875
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "5cf75d6e9cf040818868d56ca5d2421e",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "49ebb137",
    "execution_start": 1655386093975,
    "execution_millis": 444,
    "is_output_hidden": true,
    "is_code_hidden": true,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 105.578125
   },
   "source": "print(\"mean division factor = \", df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[0]/(df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[1]))\nprint(\"variance division factor = \", (df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[0]*df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[1])/(((df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[1])**2)*(df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[0]+df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[1]+1)))\n\nprint(\"\\nmean grow factor = \", df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[2]*df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[3])\nprint(\"variance grow factor = \", df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[2]*df_mod2.loc[\"PosteriorMax\",['a','b','c','d']].values[3]**2)",
   "execution_count": 9,
   "outputs": [
    {
     "name": "stdout",
     "text": "mean division factor =  0.4958274468574433\nvariance division factor =  0.007951858949653993\n\nmean grow factor =  1.41515584\nvariance grow factor =  0.063398981632\n",
     "output_type": "stream"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": "These three tables show the maximum values of the parameters obtained from the Bayesian Inference of the three different model we analyzed.\nMoreover, the 95% Credibility Interval is reported for each parameter.\n\nThe diversities within the obtained values are the consequence of the structure of the various models, which in fact involve different mechanisms during the phases of cell growth and division. ",
   "metadata": {
    "cell_id": "16ebf4d1af68450aa27c3314ac6394ed",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 133.578125
   }
  },
  {
   "cell_type": "markdown",
   "source": "## Scatter plot of $\\tau, \\omega_1, frac$",
   "metadata": {
    "cell_id": "ade3c0eab4ec4634b92155f34326ce70",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 75.71875
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "12816046ef8a45529ece908e2738350e",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "3fb74c07",
    "execution_start": 1655386094075,
    "execution_millis": 0,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 117
   },
   "source": "df_scatter_start = pd.read_csv('./data/scatter3d_start.csv')\ndf_scatter_mod1 = pd.read_csv('./data/scatter3d_model1.csv')\ndf_scatter_mod2 = pd.read_csv('./data/scatter3d_model2.csv')",
   "execution_count": 10,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "73a4af6f06b54cc48d9fbfeed6620ec9",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "45004075",
    "execution_start": 1655386094131,
    "execution_millis": 298,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 721.625,
    "deepnote_output_heights": [
     606.625
    ]
   },
   "source": "fig = plot_funcs.comparison_3d(df1 = df_microbial_growth, df2= df_scatter_start, df3=df_scatter_mod1, df4=df_scatter_mod2)\nfig.show()",
   "execution_count": 11,
   "outputs": [
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   "cell_type": "markdown",
   "source": "From the 3D Scatter Plots above and the Pairplots below, we can see that in the Real case, apart from some outliers, data are highly concentrated forming a sort of 2-dimensional manifold.\n\nIn the models analyzed, data are more widespread in space, with the exception of the Protein Model, where the parameters have \"less variability\": this can be the first mark that this model better describes what happens in reality. ",
   "metadata": {
    "cell_id": "ae9b0ef62b4f4857bc619ba38bdd1253",
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    "deepnote_cell_type": "markdown",
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   "cell_type": "markdown",
   "source": "## Pairplots\n\n| Real data                            | Model 0: simulation results        |\n|:------------------------------------:|:----------------------------------:|\n| ![img](images/pairplot_realdata.png) | ![img](images/pairplot_model0.png) |\n\n| Model 1: simulation results          | Model 2: simulation results        |\n|:------------------------------------:|:----------------------------------:|\n| ![img](images/pairplot_model1.png)   | ![img](images/pairplot_model2.png) |\n",
   "metadata": {
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    "deepnote_cell_type": "markdown",
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  },
  {
   "cell_type": "markdown",
   "source": "## Boxplot of the inter-division times",
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    "cell_id": "ba7f85467ffc425abf58ad910fa0fe4c",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 70
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    "deepnote_to_be_reexecuted": false,
    "source_hash": "90c8903f",
    "execution_start": 1655386094296,
    "execution_millis": 134,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 618
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   "source": "df_timeseries = pd.read_csv('./data/timeseries.csv')\ndisplay(df_timeseries)",
   "execution_count": 12,
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       ],
       "rows": [
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         "_deepnote_index_column": 9
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       ]
      },
      "text/plain": "     real_data  starting_model   model_1   model_2\n0     0.500000        0.255787  0.236086  0.392268\n1     0.416667        0.064669  0.062620  0.215794\n2     0.833333        0.411319  0.422029  0.656323\n3     0.333333        1.105271  1.373951  0.953599\n4     0.416667        0.622227  0.796732  0.741455\n..         ...             ...       ...       ...\n246   0.416667        0.368738  0.482821  0.407649\n247   0.500000        0.424626  0.546615  0.534430\n248   0.750000        1.030097  1.389950  0.937612\n249   0.333333        0.188717  0.242298  0.377916\n250   0.500000        0.656761  0.842164  0.762865\n\n[251 rows x 4 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>real_data</th>\n      <th>starting_model</th>\n      <th>model_1</th>\n      <th>model_2</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.500000</td>\n      <td>0.255787</td>\n      <td>0.236086</td>\n      <td>0.392268</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.416667</td>\n      <td>0.064669</td>\n      <td>0.062620</td>\n      <td>0.215794</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.833333</td>\n      <td>0.411319</td>\n      <td>0.422029</td>\n      <td>0.656323</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.333333</td>\n      <td>1.105271</td>\n      <td>1.373951</td>\n      <td>0.953599</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.416667</td>\n      <td>0.622227</td>\n      <td>0.796732</td>\n      <td>0.741455</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>246</th>\n      <td>0.416667</td>\n      <td>0.368738</td>\n      <td>0.482821</td>\n      <td>0.407649</td>\n    </tr>\n    <tr>\n      <th>247</th>\n      <td>0.500000</td>\n      <td>0.424626</td>\n      <td>0.546615</td>\n      <td>0.534430</td>\n    </tr>\n    <tr>\n      <th>248</th>\n      <td>0.750000</td>\n      <td>1.030097</td>\n      <td>1.389950</td>\n      <td>0.937612</td>\n    </tr>\n    <tr>\n      <th>249</th>\n      <td>0.333333</td>\n      <td>0.188717</td>\n      <td>0.242298</td>\n      <td>0.377916</td>\n    </tr>\n    <tr>\n      <th>250</th>\n      <td>0.500000</td>\n      <td>0.656761</td>\n      <td>0.842164</td>\n      <td>0.762865</td>\n    </tr>\n  </tbody>\n</table>\n<p>251 rows × 4 columns</p>\n</div>"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "a46060a2f131462ab728221ee1cb0d29",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "4f36818e",
    "execution_start": 1655386094338,
    "execution_millis": 1351,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 1183.3125,
    "deepnote_output_heights": [
     492.328125
    ]
   },
   "source": "res = plot_funcs.boxplot(\n    y=[df_timeseries.iloc[:,0], df_timeseries.iloc[:,1], df_timeseries.iloc[:,2], df_timeseries.iloc[:,3]], \n    colors=['blue', 'C1','green', 'khaki'],  \n    title = 'Inter-division time comparison', \n    ylabel= 'Times', \n    xlabel='', x_font= 30, \n    labels=False \n)\n\nfig, ax, bp = res[0], res[1], res[2]\nax.set_xticklabels(['Real times', 'Starting model', 'Model 1', 'Model 2'], fontdict={'fontsize':15})\n\nfor line in bp['medians']:\n    # get position data for median line\n    x, y = line.get_xydata()[1] #  median line\n    # overlay median value\n    ax.text(x-0.2, y+0.03, '%.2f' % y,\n         horizontalalignment='center', fontsize=12, color='w') # draw above, centered\n\nfor line in bp['caps']:\n    x, y = line.get_xydata()[0] # bottom of left line\n    ax.text(x,y, '%.2f' % y,\n         horizontalalignment='center', # centered\n         verticalalignment='top', fontsize=12)  \n\nfor line in bp['whiskers']:\n    x, y = line.get_xydata()[0] # bottom of left line\n    ax.text(x-0.3,y, '%.2f' % y,\n         horizontalalignment='center', # centered\n         verticalalignment='center', fontsize=12) \n\n\nax.xaxis.set_tick_params(labelsize=12, size=8)\nax.xaxis.set_tick_params(which='minor', size=4)",
   "execution_count": 13,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1080x720 with 1 Axes>",
      "image/png": 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     },
     "metadata": {
      "needs_background": "light",
      "image/png": {
       "width": 906,
       "height": 603
      }
     },
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": "The Boxplot, which compares the inter-division times, again shows that the Model 2 has less variability than the other models; in addition, the median of the yellow distribution is the most similar to the one of the Real Data.",
   "metadata": {
    "cell_id": "7949953400c247d79247f6ff9044db7e",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 74.78125
   }
  },
  {
   "cell_type": "markdown",
   "source": "## Overlap between division time histograms\n\n| Model 0                           |  Model 1                          |\n|:---------------------------------:|:---------------------------------:|\n| ![img](images/overlap_model0.png) | ![img](images/overlap_model1.png) |\n\n| Model 2                           |\n|:---------------------------------:|\n| ![img](images/overlap_model2.png) |\n",
   "metadata": {
    "cell_id": "de7d479f29a445849ef5cffaa11b7645",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 968.203125
   }
  },
  {
   "cell_type": "markdown",
   "source": "These plots show another comparison between the inspected models and the real data.\n\nFrom the values of the overlap, as we expected, the Model 2 (the Protein Model) is the one which mostly reflect the behaviour of real data, also being the most descriptive from the biological point of view. ",
   "metadata": {
    "cell_id": "738a6236655b4484a13b5e3c23981b6e",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 111.1875
   }
  },
  {
   "cell_type": "markdown",
   "source": "## Predictive density",
   "metadata": {
    "cell_id": "4b6596f8c5fc4ee9bf699a9ea9981b59",
    "tags": [],
    "deepnote_cell_type": "markdown",
    "deepnote_cell_height": 70
   }
  },
  {
   "cell_type": "code",
   "metadata": {
    "cell_id": "da39935f32054980ad09469bfbdd2fab",
    "tags": [],
    "deepnote_to_be_reexecuted": false,
    "source_hash": "310b6e88",
    "execution_start": 1655386095697,
    "execution_millis": 111,
    "deepnote_cell_type": "code",
    "deepnote_cell_height": 636
   },
   "source": "df_pd = pd.read_csv('./data/pred_density.csv')\ndisplay(df_pd)\n",
   "execution_count": 14,
   "outputs": [
    {
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    "execution_start": 1655386095800,
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    "deepnote_cell_type": "code",
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   "source": "print('Average Predictive Density over', df_pd.shape[0], 'cycles:')\n\ndf_pd[~np.isinf(df_pd)].mean().to_frame().transpose().rename({0: 'Predictive Density'}).round(3)",
   "execution_count": 15,
   "outputs": [
    {
     "name": "stdout",
     "text": "Average Predictive Density over 10 cycles:\n",
     "output_type": "stream"
    },
    {
     "output_type": "execute_result",
     "execution_count": 15,
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      "text/plain": "                    starting_model  model_1  model_2\nPredictive Density          36.329   27.847   42.316",
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     },
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  },
  {
   "cell_type": "markdown",
   "source": "The predictive density is the last evidence that the Protein Model, within the various model we studied, is the best one. For this reason, it would be valuable to focus future work and analysis on models of this type, where more than a single cell trait is considered.",
   "metadata": {
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  },
  {
   "cell_type": "markdown",
   "source": "# Future developments\n- **Use means and stds as parameters for the Gamma and Beta distributions instead of a,b,c,d** \nThis choice is motivated by the fact that the latter are strongly correlated, so we expect less sharp results using the former. We already implemented this modification, the results can be found in the folder [real_data_alternative_way](./real_data_alternative_way).\n\n- **Removal of outliers**\nFrom the 3-dimensional scatterplot and from the pairplot of the real data it can be seen that most likely our data present outliers. According to [\\[1\\]](https://doi.org/10.1063/1.5141755), their origin may be due to cells in the process of division as well as errors in measurements. These outliers strongly influence the results, as can be seen from the above histograms of the interdivision times, where we observed that the simulated times try to cover also the regions characterized by them, resulting in a less sharp distribution. \n\nIn the future it would be interesting to remove them, to reduce the noise and, hopefully, get results from the models closer to the data. This could be done following the approach presented in [\\[1\\]](https://doi.org/10.1063/1.5141755), aware of the risk that such data processing entails.",
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