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@jessegrabowski
Last active December 22, 2025 19:52
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John Cook Blog Replciation
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{
"cells": [
{
"cell_type": "markdown",
"id": "e6582976",
"metadata": {},
"source": [
"# Logistic Parameter Recovery\n",
"\n",
"This exercise is taken from John Cook's blog here: https://www.johndcook.com/blog/2025/12/20/fit-logistic-curve/\n",
"\n",
"The point is to show that if you only have data from a restricted region of the logistic curve, it is hard to infer information about the function globally."
]
},
{
"cell_type": "markdown",
"id": "3ee4b661",
"metadata": {},
"source": [
"# Setup"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "704fcd7a",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.optimize import curve_fit\n",
"\n",
"import arviz as az\n",
"import xarray as xr\n",
"\n",
"import pymc as pm\n",
"import pytensor.tensor as pt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "24b0475e",
"metadata": {},
"outputs": [],
"source": [
"def f_logistic(a, b, c, t):\n",
" return a / (np.exp(-b * (t - c)) + 1) + c"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "8ce23976",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x136132d50>]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t = np.linspace(-5, 5, 100)\n",
"plt.plot(t, f_logistic(1, 1, 0, t))"
]
},
{
"cell_type": "markdown",
"id": "1d71cfe0",
"metadata": {},
"source": [
"## Recover with scipy\n",
"\n",
"The blog sets the following rules: generate 16 datapoints using random $t$ betweeen `-5` and `-2`, with $a=1$, $b=1$, $c=0$. Add Gaussian noise with $\\sigma = 0.05$. The objective is to recover the value for $a$. I assume we're fixing $b, c, \\sigma$ to their true values."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "a6b090c2",
"metadata": {},
"outputs": [],
"source": [
"def generate_curve(n_obs=16):\n",
" t = np.sort(np.random.uniform(-5, -2, size=n_obs))\n",
" noise = np.random.normal(loc=0, scale=0.05, size=n_obs)\n",
" true_curve = f_logistic(a=1, b=1, c=0, t=t)\n",
" return t, true_curve + noise"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e2fa0f73",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"t = np.linspace(-5, 5, 100)\n",
"ax.plot(t, f_logistic(a=1, b=1, c=0, t=t))\n",
"for _ in range(10):\n",
" ax.scatter(*generate_curve())"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "d0f0bf70",
"metadata": {},
"outputs": [],
"source": [
"def f(t, a):\n",
" return f_logistic(a=a, b=1, c=0, t=t)\n",
"\n",
"a_estimates = np.empty(1000)\n",
"failure = np.empty(1000, dtype=bool)\n",
"for i in range(1000):\n",
" x_data, y_data = generate_curve()\n",
" res = curve_fit(f, xdata=x_data, ydata=y_data, sigma=0.05, full_output=True)\n",
" a_estimates[i] = res[0].item()\n",
" failure[i] = not '0.000000' in res[-2]\n",
" if failure[i]:\n",
" print(res[-2])"
]
},
{
"cell_type": "markdown",
"id": "4b0838a3",
"metadata": {},
"source": [
"I can't reproduce the issue that John mentions in the blog post. All of the fits appear to work fine."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "19d16599",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.float64(0.0)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"failure.mean()"
]
},
{
"cell_type": "markdown",
"id": "bc8d6ec9",
"metadata": {},
"source": [
"Here's the distribution of parameters we recover. The estimates are centered on 1.0, the true value. Seems alright to me!"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "ca1e031f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(a_estimates[~failure]);"
]
},
{
"cell_type": "markdown",
"id": "6d262f91",
"metadata": {},
"source": [
"# Do it again with Bayes"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a47fcd19",
"metadata": {},
"outputs": [],
"source": [
"b = 1.0\n",
"c = 0.0\n",
"sigma = 0.05\n",
"\n",
"with pm.Model() as m:\n",
" t = pm.Data('t', x_data)\n",
" y_obs = pm.Data('y_obs', y_data)\n",
"\n",
" a = pm.Normal('a', mu=0, sigma=3)\n",
"\n",
" mu = pm.Deterministic('mu', a / (pt.exp(-b * (t - c)) + 1) + c)\n",
"\n",
" y_hat = pm.Normal('y_hat', mu=mu, sigma=sigma, observed=y_obs)\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "0c1bb930",
"metadata": {},
"outputs": [],
"source": [
"import logging\n",
"from tqdm.auto import tqdm\n",
"logger = logging.getLogger('pymc')\n",
"logger.setLevel(logging.WARNING)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "14c504fa",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "9c7de75ed3c34c3f902758a5a8cb9892",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
" 0%| | 0/250 [00:00<?, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"idatas = []\n",
"N = 250\n",
"with m:\n",
" for _ in tqdm(range(N)):\n",
" t, obs = generate_curve()\n",
" pm.set_data({'t':t, 'y_obs':obs})\n",
" idatas.append(pm.sample(progressbar=False, ))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "708b8f12",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1400x400 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"idata = xr.concat([idata.posterior.a.expand_dims(model=[i]) \n",
" for i, idata in enumerate(idatas)], \n",
" dim='model',\n",
" join='exact')\n",
"mu = idata.mean(dim=['chain', 'draw'])\n",
"hdi = az.hdi(idata).a\n",
"\n",
"fig, ax = plt.subplots(figsize=(14, 4))\n",
"ax.axhline(1.0, ls='--', c='k')\n",
"ax.scatter(range(N), mu.values)\n",
"ax.vlines(range(N), *hdi.values.T)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "7a0f244c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 2016x576 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 2, figsize=(14, 4), dpi=144)\n",
"az.plot_posterior(a_estimates, ax=ax[0])\n",
"az.plot_posterior(mu.values, ax=ax[1])\n",
"\n",
"ax[0].set(title='Scipy fit_curve')\n",
"ax[1].set(title='PyMC')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d54018bb",
"metadata": {},
"outputs": [],
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}
],
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