Created
December 19, 2025 09:13
-
-
Save emilyhunt/f656ac05e42e32efa723df7e741b006f to your computer and use it in GitHub Desktop.
Making histograms is a common way to estimate the true density distribution of a sample. But how can we choose the number of histogram bins? And if we get fancy and use kernel density estimation (KDE), how do we choose a KDE bandwidth?
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "id": "60636b7b", | |
| "metadata": {}, | |
| "source": [ | |
| "# How should I choose a number of histogram bins?\n", | |
| "\n", | |
| "Making histograms is a common way to estimate the true density distribution of a sample. But how can we choose the number of histogram bins? And if we get fancy and use kernel density estimation (KDE), how do we choose a KDE bandwidth?" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "id": "033ad88f", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "from scipy.stats import beta, gaussian_kde\n", | |
| "from matplotlib import pyplot as plt" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "fd96d8c5", | |
| "metadata": {}, | |
| "source": [ | |
| "## Test data\n", | |
| "\n", | |
| "Firstly, let's make some test data: a skewed distribution (made from a beta distribution.)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "id": "0eacecff", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "[<matplotlib.lines.Line2D at 0x76d687396150>]" | |
| ] | |
| }, | |
| "execution_count": 2, | |
| "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": [ | |
| "true_distribution = beta(1.5, 3.5, scale=2000)\n", | |
| "\n", | |
| "x_true = np.linspace(0, 2000, num=1000)\n", | |
| "y_true = true_distribution.pdf(x_true)\n", | |
| "\n", | |
| "plt.plot(x_true, y_true)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "55ffa23b", | |
| "metadata": {}, | |
| "source": [ | |
| "## Try histogram binning\n", | |
| "\n", | |
| "Estimating the true distribution from a **large** number of samples is easy! For instance, let's say this is something like a **distance distribution of galaxies**, and we have 100,000 galaxies in our sample.\n", | |
| "\n", | |
| "Let's pick 100 histogram bins for no reason other than that it's a nice round number." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "id": "ba518aa8", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "samples = true_distribution.rvs(100000, random_state=42)\n", | |
| "\n", | |
| "plt.plot(x_true, y_true, \"k-\", label=\"True distribution\")\n", | |
| "plt.hist(\n", | |
| " samples, bins=100, histtype=\"step\", density=True, label=\"100 bins\", linewidth=2\n", | |
| ")\n", | |
| "_ = plt.legend()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "196b7db3", | |
| "metadata": {}, | |
| "source": [ | |
| "In this case, our **inferred** distribution fits the **true** distribution well.\n", | |
| "\n", | |
| "But this quickly breaks down if we have a **smaller number of samples** - let's say, 500:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "id": "f4b0ad7f", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "samples = true_distribution.rvs(500, random_state=42)\n", | |
| "\n", | |
| "plt.plot(x_true, y_true, \"k-\", label=\"True distribution\")\n", | |
| "plt.hist(\n", | |
| " samples, bins=100, histtype=\"step\", density=True, label=\"100 bins\", linewidth=2\n", | |
| ")\n", | |
| "_ = plt.legend()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "a7c1c5cf", | |
| "metadata": {}, | |
| "source": [ | |
| "It could be tempting to say that our data do not follow the distribution, as they're very peaky - but it may also be a function of our chosen number of bins.\n", | |
| "\n", | |
| "Thankfully, there are good ways to estimate the number of bins when making a histogram. Behind the scenes, matplotlib uses `numpy.histogram_bin_edges` [(link to docs)](https://numpy.org/doc/stable/reference/generated/numpy.histogram_bin_edges.html), which accepts strings for various different estimators. Each of them returns a slightly different estimate for our data." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "id": "e41fd01c", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "fd: 15 bins\n", | |
| "doane: 13 bins\n", | |
| "scott: 12 bins\n", | |
| "stone: 11 bins\n", | |
| "rice: 16 bins\n", | |
| "sturges: 10 bins\n", | |
| "sqrt: 23 bins\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "for method in (\"fd\", \"doane\", \"scott\", \"stone\", \"rice\", \"sturges\", \"sqrt\"):\n", | |
| " n_bins = len(np.histogram_bin_edges(samples, bins=method)) - 1\n", | |
| " print(f\"{method}: {n_bins} bins\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "3b2b8e3b", | |
| "metadata": {}, | |
| "source": [ | |
| "**Which estimator should we use?** You can read up [here on the numpy docs](https://numpy.org/doc/stable/reference/generated/numpy.histogram_bin_edges.html), but in practice, it's usually fine to use \"auto\", which uses the maximum of the 'Sturges' and 'fd' (Freedman Diaconis) estimators:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "id": "ff271154", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "auto mode: 15 bins\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "n_bins = len(np.histogram_bin_edges(samples, bins=\"auto\")) - 1\n", | |
| "print(f\"auto mode: {n_bins} bins\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "0f659807", | |
| "metadata": {}, | |
| "source": [ | |
| "We can use this directly in matplotlib by setting `bins='auto'`:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "id": "aba90b74", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.plot(x_true, y_true, \"k-\", label=\"True distribution\")\n", | |
| "plt.hist(\n", | |
| " samples,\n", | |
| " bins=\"auto\",\n", | |
| " histtype=\"step\",\n", | |
| " density=True,\n", | |
| " label=f\"{n_bins} bins\",\n", | |
| " linewidth=2,\n", | |
| ")\n", | |
| "_ = plt.legend()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "8068194c", | |
| "metadata": {}, | |
| "source": [ | |
| "This histogram is now no longer 'peaky', and follows our true distribution much better even with a much smaller number of samples. \n", | |
| "\n", | |
| "In practice, I think you should **never** choose a number of histogram bins manually, unless you have a **very good reason**. Even though they aren't perfect, using an automatic estimator will almost always be less biased. As humans, we often have a desire to try and see patterns where they aren't, especially if one way or another would support a conclusion we're interested in. Using something automated is always a good way to remove this bias." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "3344d21d", | |
| "metadata": {}, | |
| "source": [ | |
| "## Kernel density estimation\n", | |
| "\n", | |
| "Kernel density estimation is also a common way to estimate the true underlying distribution of a sample. I won't get into all the gory details here, but will just show that it has the same caveat - estimating **bandwidth** by hand is a great way to make a mistake, and it's usually better to just use an automatic option. ('scott' is the default in [scipy's Gaussian KDE](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html), and you'll notice that it outperforms almost everything else.)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "id": "f65a19d6", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "<matplotlib.legend.Legend at 0x76d687217b60>" | |
| ] | |
| }, | |
| "execution_count": 8, | |
| "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": [ | |
| "\n", | |
| "plt.plot(x_true, y_true, 'k-', label=\"True\", lw=2)\n", | |
| "\n", | |
| "bandwidth_modes = 0.05, 0.1, 0.25, 0.5, 1.0, \"scott\"\n", | |
| "for i, bandwidth in enumerate(bandwidth_modes):\n", | |
| " kde = gaussian_kde(samples, bw_method=bandwidth)\n", | |
| " color, alpha = plt.get_cmap(\"viridis\")(i / (len(bandwidth_modes) - 2)), 0.25\n", | |
| " if bandwidth == \"scott\":\n", | |
| " color, alpha = \"red\", 1.0\n", | |
| " plt.plot(x_true, kde(x_true), label=bandwidth, color=color, alpha=alpha, lw=2)\n", | |
| "\n", | |
| "plt.legend(title=\"Bandwidth\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "bf60c799", | |
| "metadata": {}, | |
| "source": [ | |
| "Notice how awfully a lot of the KDE estimates match up with the true distribution. The automatically estimated one (in red) is probably the best." | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "notebooks", | |
| "language": "python", | |
| "name": "python3" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.12.9" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment