diff --git a/doc/notebooks/weighted_histograms.ipynb b/doc/notebooks/weighted_histograms.ipynb new file mode 100644 index 00000000..4be26d73 --- /dev/null +++ b/doc/notebooks/weighted_histograms.ipynb @@ -0,0 +1,1921 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fitting weighted histograms\n", + "\n", + "If histograms are filled with weighted data, we need to construct cost functions that handle this case correctly. Particularly troublesome is when bins contain a negative sum of weights, which can occur randomly if weights are partially negative, like sweights.\n", + "\n", + "Bohm and Zech showed a way to fit weighted histograms, but their approach formally only works if the sum of weights is non-negative. Here, we discuss the ideas behind the cost functions that iminuit uses for weighted histograms, and how to generalize the Bohm-Zech approach to bin entries that are negative. This work is based and references the following papers:\n", + "\n", + "- [1] Baker & Cousins, NIM 221 (1984) 437-442\n", + "- [2] Bohm and Zech, NIMA 748 (2014) 1-6\n", + "- [3] H. Dembinski, M. Schmelling, R. Waldi, NIMA 940 (2019) 135-141.\n", + "\n", + "## Baker-Cousins transform\n", + "\n", + "The maximum-likelihood method is widely very successful, and its qualities shine in particular in the application to Poisson-distributed data, because maximizing the likelihood yields an unbiased estimate of models fitted to this data [3], while naive least-squares does not unless one uses a special iterative scheme.\n", + "\n", + "In constrast to least-squares methods, maximizing the likelihood does not yield a chi-square distributed minimum value, that can be used as a goodness-of-fit test statistic. Baker and Cousins [1] showed that the log-likelihood for Poisson distributed data can be replaced by a delta-log-likelihood, which has this property and is otherwise equivalent. One essentially adds a constant to the log-likelihood, which does not change the location of the minimum. For a single bin in a histogram, one can derive the following statistic, which is also known as the Cash statistic:\n", + "\n", + "$$\n", + "\\ell_\\text{poisson}(n; \\mu) = 2 [n (\\ln(n) - \\ln(\\mu)) - \\mu + n]\n", + "$$\n", + "\n", + "It can be minimized to obtain an unbiased estimate for $\\mu$, and the minimum value is asymptotically chi-square distributed and serves as a goodness-of-fit test statistic. The case $n = 0$ is handled by formally extending the integer realm to the real realm, and realizing that $x \\ln x \\to 0$ for $x\\to 0$. In other words, in case of $n = 0$, $n \\ln n$ has to be replaced by 0.\n", + "\n", + "Furthermore, this form is beneficial for numerical computation on a computer, because near the minimum we have $\\mu \\approx n$ and $\\ell_\\text{poisson}(n;\\mu) \\approx 0$. This means that the sum $\\sum_k \\ell_\\text{poisson}(n_k;\\mu_k)$ over $k$ bins grows slowly and adds terms of similar size, which is ideal from the point of view of accuracy in floating point arithmetic.\n", + "\n", + "As shown by Baker & Cousins, a similar statistic with the same nice properties can be derived from the log-likelihood for multinomially-distributed data:\n", + "\n", + "$$\n", + "\\ell_\\text{multinomial}(n; \\mu) = 2 [n (\\ln(n) - \\ln(\\mu))]\n", + "$$\n", + "\n", + "We further note that $\\ell_\\text{multinomial}$ and $\\ell_\\text{poisson}$ are equivalent for multinomially-distributed data. Because $\\sum_k \\mu_k = \\sum_k n_k$ is always guaranteed, if the sum goes over all $k$ bins, the terms $n_k - \\mu_k$ always sum up to zero, so they can be removed altogether.\n", + "\n", + "## Bohm-Zech transform\n", + "\n", + "Bohm and Zech proposed the scaled Poisson distribution (SPD) as an approximate way to handle sums of weights instead of Poisson counts. This approach also works for multinomially distributed data, as we will see later. The idea of the Bohm and Zech is to use the likelihood for Poisson distributed data also for weighted data. They match the first and second moment of the compound Poisson distribution for weighted data with a single Poisson distribution through a scaling factor $s$, that is multiplied with the prediction and the observation.\n", + "\n", + "The scaling factor is computed as $s = \\sum_i w_i / \\sum_i w_i^2$, where $w_i$ are the weights in the current bin. Instead of the Baker & Cousins transformed log-likelihood $\\ell(n; \\mu)$ for Poisson-distributed data, where $n$ is the observed count and $\\mu$ is the expectation, we now compute $\\ell(s w; s \\mu)$ with $w = \\sum_i w_i$. This can be further simplified:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\ell_\\text{poisson}(s w; s \\mu) &= 2 [(s w) (\\ln(s w) - \\ln(s \\mu)) - s \\mu + s w] \\\\\n", + "&= 2 s [w (ln(w) - ln(\\mu)) - \\mu + w] \\\\\n", + "&= s \\, \\ell_\\text{poisson}(w; \\mu)\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Eventually, we find that the normal delta-log-likelihood gets scaled by the factor $s$. Note that we did transformations here that are only allowed for $s > 0$ and $w > 0$, otherwise the logarithms are not defined. The case $w = 0$ can be included in the same way as $n = 0$ by replacing $w \\ln w$ with 0.\n", + "\n", + "### Handling $s=0$\n", + "\n", + "Often, $w = 0$ also implies $\\sum w_i^2 = 0$. In that case $s$ becomes undefined. There is no elegant solution for this, because we need to know the true value of $s$ to perform a correct scaling, but we cannot get it empirically, as there is no data.\n", + "\n", + "One might consider setting $s$ to 0 or 1, but these choices lead to problems. Using $s=0$ implies that empty bins cannot pull the prediction $\\mu$ down, which would result in $\\mu$ values that are overestimated. Similarly, $s=1$ may introduce a too strong pull if the average value of $s$ for the other bins is much smaller than 1, or too little if that average is way larger than 1. We cannot simply use the average value of $s$ either, because $s$ may vary systematically from bin-to-bin. This variation may not even be predictable.\n", + "\n", + "In iminuit, we use the median of $s$ values from bins with entries, which will reduce the bias in at least some scenarios, but in general, practitioners should avoid empty bins in weighted histograms altogether.\n", + "\n", + "### Multinomially-distributed weighted data\n", + "\n", + "While it is irrelvant whether we use $\\ell_\\text{multinomial}$ or $\\ell_\\text{poisson}$ for ordinary multinomially-distributed data, the situation becomes different when weights are involved. If we consider weighted data and apply the Bohm-Zech transform, we find that $\\ell_\\text{multinomial}(s w; s \\mu) \\neq \\ell_\\text{poisson}(s w; s \\mu)$. This is because $\\sum_k s_k (w_k - \\mu_k) \\neq 0$ in general, even if $\\sum_k (w_k - \\mu_k) = 0$ holds. Numerical experiments confirm that $\\ell_\\text{multinomial}(s w; s \\mu)$ yields biased results, the correct cost function for weighted multinomial data is therefore $\\ell_\\text{poisson}(s w; s \\mu)$.\n", + "\n", + "### Extension to datasets with negative sums of weights\n", + "\n", + "The Bohm-Zech formula is only applicable if $w = \\sum_i w_i \\ge 0$ (with the extra condition that we\n", + "discussed), but formally fails if $w < 0$. Since $\\sum_i w_i^2$ is always non-negative, $w < 0$ implies $s < 0$.\n", + "\n", + "Our extension of $\\ell_\\text{poisson}(s w; s \\mu)$ to this case is to use $s = |\\sum_i w_i| / \\sum_i w_i^2$ and replace $w \\ln (w)$ with 0 for $w \\le 0$.\n", + "\n", + "This solution works, because it has the same gradient as a sum of squared studentized residuals $\\sum_k s_k (w_k - \\mu_k)^2/\\mu'_k$, where $\\mu'_k$ approaches $\\mu_k$ in successive iterations, but is fixed during the gradient computation [3]. We know from the Gauss-Markov-Aitken theorem that the minimum of this quadratic function yields an unbiased estimate of $\\mu_k$, if there are no additional constraints on $\\mu_k$. Here, we have the constraint $\\mu_k > 0$, so this won't be perfectly unbiased for very small $\\mu_k$, but otherwise. Since the quadratic function and the original function have the same gradient, the minima of both functions are the same, and the original function also yields an unbiased or a low-bias estimate for very small $\\mu_k$.\n", + "\n", + "We mention the sum of squared studentized residuals, because it provides better intuitive insight. For example, it is clear that $s$ should be positive, since it acts as a modifier of the variance, effectively replacing $\\mu'$ with $\\mu'/s$. A negative $s$ cannot fulfill this purpose. Also, a negative $s_k$ would allow us to reduce the sum by making the disagreement between $w_k$ and $\\mu_k$ larger, which is contradictory.\n", + "\n", + "The gradient is not affected by the particular choice of replacing $w \\ln(w)$ with 0 for $w < 0$, any other constant would also do, since this term drops out in the computation of the gradient. Our choice is motivated by the goal to keep the function minimum approximately chi-square distributed, although that property generally dissolves when negative weights are involved. The delta-log-likelihood compares the expectation from the model with the expectation from the so-called saturated model, but the definition of the latter breaks down for $w < 0$. Our ad hoc choices cannot fix that. The function minimum value can even become negative.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's visualize variations of $\\ell_\\text{poisson}$ for a signle bin and a couple of $w$ values, with $w^2 = 1$.\n", + "\n", + "* `l1`: This is the chosen extension of $\\ell_\\text{poisson}$ as discussed above, with $s = |\\sum_i w_i| / \\sum_i w_i^2$, and $w \\ln w$ replaced by 0 for $w < 0$.\n", + "* `l2`: Like `l1`, but we replace $w \\ln w$ with $w \\ln|w|$.\n", + "* `l3`: Like `l2`, but we use $s = \\sum_i w_i / \\sum_i w_i^2$." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def log_or_zero(x):\n", + " x = np.atleast_1d(x).copy()\n", + " ma = x > 0\n", + " x[ma] = np.log(x[ma])\n", + " x[~ma] = 0\n", + " return x\n", + "\n", + "def l1(w, w2, mu):\n", + " s = np.abs(w) / w2\n", + " return 2 * s * (w * (log_or_zero(w) - log_or_zero(mu)) + mu - w)\n", + "\n", + "def l2(w, w2, mu):\n", + " s = np.abs(w) / w2\n", + " return 2 * s * (w * log_or_zero(np.abs(w)) - w * log_or_zero(mu) + mu - w)\n", + "\n", + "def l3(w, w2, mu):\n", + " s = w / w2\n", + " return 2 * s * (w * (log_or_zero(np.abs(w)) - log_or_zero(mu)) + mu - w)\n", + "\n", + "w2 = 1\n", + "fig, ax = plt.subplots(1, 3, figsize=(10, 4))\n", + "for i, (axi, w) in enumerate(zip(ax, (-10, -5, 5))):\n", + " mu = np.geomspace(1e-3, 10, 100)\n", + " color = f\"C{i}\"\n", + " plt.sca(axi)\n", + " plt.plot(mu, l1(w, w2, mu), color=color, label=f\"l1 w={w}\")\n", + " plt.plot(mu, l2(w, w2, mu), color=color, ls=\":\", label=f\"l2 w={w}\")\n", + " plt.plot(mu, l3(w, w2, mu), color=color, ls=\"--\", label=f\"l3 w={w}\")\n", + " plt.ylim(-1000, 1000)\n", + " plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All cost functions only differ for $w < 0$. `l3` is contradictory, since it prefers an infinite value of $\\mu$ for $w < 0$. Both `l1` and `l2` prefer $\\mu = 0$, which is correct. The vertical offset between `l1` and `l2` grows as $w$ becomes more negative. For both `l1` and `l2`, the function value at the minimum can become arbitrarily negative, something that never happens for $w > 0$ and should not happen for a chi-square-distributed variable. For $w < 0$, we cannot ensure this property, and hence function minimum value is no longer chi-square distributed. It can still qualitatively used as a GoF test statistic, as we will see below." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Toy experiments\n", + "\n", + "We illustrate these ideas with toy experiments. We generate data from an exponential distribution whose samples are weighted with a normal distribution. To make the toy more interesting, the width of the normal distribution is a function of the value realised by the exponential distribution. We then form weighted histograms from these data. The average weight per bin is constant, but the variance of the weights increases." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from iminuit.cost import BinnedNLL, ExtendedBinnedNLL\n", + "from iminuit import Minuit\n", + "from scipy.stats import expon, norm, chi2\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import boost_histogram as bh\n", + "from joblib import Parallel, delayed\n", + "\n", + "rng = np.random.default_rng(1)\n", + "\n", + "npoints = 100000\n", + "bins = 20\n", + "\n", + "x = expon.rvs(size=npoints, random_state=rng)\n", + "w = norm.rvs(0.1, x, size=len(x), random_state=rng)\n", + "\n", + "h = bh.Histogram(bh.axis.Regular(bins, np.min(x), np.max(x)), storage=bh.storage.Weight())\n", + "h.fill(x, weight=w)\n", + "\n", + "plt.stairs(h.values(), h.axes[0].edges)\n", + "ma = h.values() > 0\n", + "plt.errorbar(h.axes[0].centers[ma], h.values()[ma], h.variances()[ma] ** 0.5, fmt=\"o\", color=\"C0\")\n", + "plt.errorbar(h.axes[0].centers[~ma], h.values()[~ma], h.variances()[~ma] ** 0.5, fmt=\"s\", color=\"C3\")\n", + "plt.axhline(0, ls=\":\", color=\"0.5\", zorder=0)\n", + "xm = np.linspace(0, h.axes[0].edges[-1])\n", + "plt.plot(xm, expon.pdf(xm) * npoints * np.mean(w) * h.axes[0].widths[0]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The line shows the true density, and the data points show the outcome of the sample. Error bars indicate the statistical uncertainty. Bins with negative sums of weights use square markers." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We fit this histogram with iminuit's builtin cost functions, which use the ideas discussed above, to obtain an estimate of the slope $\\lambda$ of the exponential." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "xe = h.axes[0].edges\n", + "n = h.values()\n", + "vn = h.variances()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
Migrad
FCN = 22.93 (χ²/ndof = 1.3) Nfcn = 40
EDM = 4.77e-05 (Goal: 0.0002) time = 0.2 sec
Valid Minimum Below EDM threshold (goal x 10)
No parameters at limit Below call limit
Hesse ok Covariance accurate
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Name Value Hesse Error Minos Error- Minos Error+ Limit- Limit+ Fixed
0 n 10.9e3 0.4e3 0
1 lambd 1.16 0.06 0
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n lambd
n 2.01e+05 26.722 (0.927)
lambd 26.722 (0.927) 0.00413
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Migrad
FCN = 32.6 (χ²/ndof = 1.7) Nfcn = 13
EDM = 1.18e-06 (Goal: 0.0002)
Valid Minimum Below EDM threshold (goal x 10)
No parameters at limit Below call limit
Hesse ok Covariance accurate
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Name Value Hesse Error Minos Error- Minos Error+ Limit- Limit+ Fixed
0 lambd 0.996 0.021 0
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lambd
lambd 0.000457
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The estimates obtained with `ExtendedBinnedNLL` and `BinnedNLL` differ, and we note that the uncertainty of $\\lambda$ is smaller for `BinnedNLL`. That is a consequence of fitting weighted data. For ordinary data the estimates are equal.\n", + "\n", + "To see whether these estimates are biased, we repeat the toy experiment many times with independent data." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "def run(seed):\n", + " rng = np.random.default_rng(seed)\n", + " # we also randomize the sample size\n", + " x = expon.rvs(size=rng.poisson(npoints), random_state=rng)\n", + " w = norm.rvs(0.1, x, size=len(x), random_state=rng)\n", + "\n", + " h = bh.Histogram(bh.axis.Regular(bins, np.min(x), np.max(x)), storage=bh.storage.Weight())\n", + " h.fill(x, weight=w)\n", + " xe = h.axes[0].edges\n", + " n = h.values()\n", + " vn = h.variances()\n", + " data = np.transpose((n, vn))\n", + " ntot = np.sum(n)\n", + "\n", + " m1 = Minuit(ExtendedBinnedNLL(data, xe, model1), ntot, 0.6)\n", + " m1.limits[0] = (0, None)\n", + " m1.limits[1] = (0, None)\n", + " m1.migrad()\n", + "\n", + " m2 = Minuit(BinnedNLL(data, xe, model2), 0.6)\n", + " m2.limits = (0, None)\n", + " m2.migrad()\n", + "\n", + " return ntot, m1.valid, m1.values[0], m1.values[1], m1.fval, m2.valid, m2.values[0], m2.fval\n", + "\n", + "result = Parallel(n_jobs=8)(delayed(run)(seed) for seed in range(1000))\n", + "ntot, valid1, ntot1, lambd1, minval1, valid2, lambd2, minval2 = np.transpose(result)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.title(\"$\\\\lambda$ estimate\")\n", + "plt.hist(lambd1, bins=20, alpha=0.5, label=f\"ExtendedBinnedNLL\\nvalid={np.mean(valid1)*100:.0f}%\\nmean = {np.mean(lambd1):.2f}\\nstd.dev. = {np.std(lambd1):.2f}\")\n", + "plt.hist(lambd2, bins=20, alpha=0.5, label=f\"BinnedNLL\\nvalid={np.mean(valid2)*100:.0f}%\\nmean = {np.mean(lambd2):.2f}\\nstd.dev. = {np.std(lambd2):.2f}\")\n", + "plt.legend()\n", + "\n", + "plt.figure()\n", + "plt.hist(ntot1 / ntot - 1)\n", + "plt.title(f\"ExtendedBinnedNLL: $n_\\\\mathrm{{tot}}$ estimate\\n(mean-truth)/truth = {np.mean(ntot1) / np.mean(ntot) - 1:.3f}\")\n", + "plt.xlabel(\"(estimate - truth) / truth\")\n", + "plt.xlim(-0.2, 0.2);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, we find that the estimates of $\\lambda$ have low bias, although they are not perfectly unbiased.\n", + "\n", + "The variance of $\\lambda$ is smaller for `BinnedNLL`. If you are not interested in the amplitude of the distribution, it is therefore better to use `BinnedNLL` for weighted histograms. Note that `BinnedNLL` and `ExtendedBinnedNLL` internally use the same cost function for weighted data, so the difference in precision originates from the additional information used in `BinnedNLL`, that the sample is complete, there are no further events in other bins.\n", + "\n", + "The second plot shows the estimate of the total sum of weights with `ExtendedBinnedNLL`, which is distributed around the true value. We observe a small upward bias of 2%.\n", + "\n", + "We claim above that estimates for our chosen cost function are unbiased, while these results show small bias. There are two reasons for that. i) The cost Bohm-Zech approach does not guarantee unbiasedness anymore, since we must estimate $s$ from the information in the bin, and the empirical estimate for $s$ that we use is not an unbiased estimate of the true value, because it is a non-linear function of the weights. ii) The unbiasedness was claimed for the bin expectations and linear functions thereof. The model parameter $\\lambda$ is not a linear function of the bin expectations, therefore it is also not guaranteed to be unbiased. We will come back to this point below.\n", + "\n", + "We further said that the minimum value is no longer chi-square distributed when bins with negative sums of weights are fitted, so let's look at the actual distribution of the minimum value of the cost function." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n", + "\n", + "plt.sca(ax[0])\n", + "plt.hist(minval1, bins=50, density=True)\n", + "x = np.linspace(0, 100)\n", + "plt.plot(x, chi2(bins-2).pdf(x))\n", + "plt.title(f\"ExtendedBinnedNLL minimum value\\nndf = {bins-2} mean = {np.mean(minval1):.2f} median = {np.median(minval1):.2f}\")\n", + "\n", + "plt.sca(ax[1])\n", + "plt.hist(minval2, bins=50, density=True)\n", + "x = np.linspace(0, 100)\n", + "plt.plot(x, chi2(bins-2).pdf(x))\n", + "plt.title(f\"BinnedNLL minimum value\\nndf = {bins-2} mean = {np.mean(minval2):.2f} median = {np.median(minval2):.2f}\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We find that these distributions are broader than the asymptotical chi-square distribution and contain negative values, as expected. One can qualitatively still use very large values compared ot the expected mean as evidence for a bad fit, however, since bins with $w < 0$ only reduce the function minimum value." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For reference, it is interesting to run the toy experiment again with a very narrow weight distribution. We expect that the bias largely disappears, as our original toy experiment with its broad weight distribution was designed to be challenging. For this run, we draw the weights from a narrow normal distribution with constant width of 0.01." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [], + "source": [ + "def run(seed):\n", + " rng = np.random.default_rng(seed)\n", + " # we also randomize the sample size\n", + " x = expon.rvs(size=rng.poisson(npoints), random_state=rng)\n", + " w = rng.normal(0.1, 0.01, size=len(x))\n", + "\n", + " h = bh.Histogram(bh.axis.Regular(bins, np.min(x), np.max(x)), storage=bh.storage.Weight())\n", + " h.fill(x, weight=w)\n", + " xe = h.axes[0].edges\n", + " n = h.values()\n", + " vn = h.variances()\n", + " data = np.transpose((n, vn))\n", + " ntot = np.sum(n)\n", + "\n", + " m1 = Minuit(ExtendedBinnedNLL(data, xe, model1), ntot, 0.6)\n", + " m1.limits[0] = (0, None)\n", + " m1.limits[1] = (0, None)\n", + " m1.migrad()\n", + "\n", + " m2 = Minuit(BinnedNLL(data, xe, model2), 0.6)\n", + " m2.limits = (0, None)\n", + " m2.migrad()\n", + "\n", + " return ntot, m1.valid, m1.values[0], m1.values[1], m1.fval, m2.valid, m2.values[0], m2.fval\n", + "\n", + "result = Parallel(n_jobs=8)(delayed(run)(seed) for seed in range(1000))\n", + "ntot, valid1, ntot1, lambd1, minval1, valid2, lambd2, minval2 = np.transpose(result)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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lFwEId7XU1FRNnjxZo0ePlrv73ft2v3z5ssaPH3/TxzncjuPHj2v8+PHasWPHLbdRp04dde3aVa+99lq+dXbt2iU3Nzf98MMPpWJMd0rOfYPKlSunwMBADRw4sEjPv/r888/VpEkTeXt7q3Llyho3bpz9gbrXu3DhgoYOHarg4GCVLVtW7du31/bt22+rTaCkunu/EQD99hyozMzMIj9zqbS5fPmyJkyY4NKwMGHChNsOC88++6yWLl2qxMTEPNcvX75cISEhuu+++0rNmFzt119/VZs2bXTw4EFNmjRJL774opYvX66HHnpI165dK3D7L7/8Uj169FBAQICmTZumHj166PXXX9eIESMc6mVnZ6tr166aP3++hg8frilTpujUqVNq166dDhw4cEttAiUZD0PFXW3OnDnq3r27vL29i7srJcqlS5fsT96+kzp27Kjy5cvrww8/1MSJE3OtX7FihTp37iw3N7cit11cY3K1SZMm6dKlS9q2bZsqV64sSWrevLkeeughzZ07V0OHDr3p9i+++KIaNGigr7/+Wp6ev/2T7+fnp0mTJulPf/qTatWqJUlavHixNm7cqEWLFqlXr16SpD59+qhGjRoaN26cw00aC9smUKIV76PIANc5dOiQkWTmzp3rUJ6UlGQkmalTp5p3333XREVFGR8fH/PQQw+ZI0eOmOzsbDNx4kRTsWJF4+3tbbp3727Onj2bq/0VK1aYVq1amTJlyphy5cqZLl265HpY5k8//WRiY2NNVFSUsdlsJjQ01AwePNicOXPGoV7OwyYPHDhgYmNjjb+/v/Hz8zODBg0yly5duuk4c8Zz4zJu3DhjzH8fWHnw4EHTuXNnU65cOfPII48YY0yeD6M05reHWeY8IHTt2rX5PsQ2p27dunXNnj17TLt27YyPj4+JiIgwkydPzrO/jz76qGnQoEGu8vPnzxsPDw/zr3/9q9SNyZVCQkJM7969c5XXqFHDdOjQ4abb7tmzx0gy06dPdyg/duyYkWT+8pe/2Mt69+5tQkNDTVZWlkPdoUOHmjJlypirV68WuU2gJOMIEO5aGzdulCQ1adIkz/Xz5s3TtWvXNGLECJ07d05TpkxRnz599OCDD2rdunUaPXq0Dh48qGnTpunFF1/U7Nmz7dt+/PHHio2NVUxMjCZPnqzLly9rxowZatWqlX788UdVrVpVkrRq1SodOnRIgwcPVlhYmPbs2aOZM2dqz549+v7773Md6ejTp4+ioqIUHx+v7du36x//+IdCQkI0efLkfMcZHBysGTNm6I9//KMeffRRPfbYY5KkBg0a2OtkZmYqJiZGrVq10htvvKEyZcoUeh5r166tiRMn6rXXXtPQoUPVunVrSb890DPH+fPn1alTJz322GPq06ePFi9erNGjR6t+/frq3LmzQ3tNmzbVZ599ptTUVPn5+dnLv/rqK7m5uenhhx+Wp6dnqRrTjVJSUpSRkVFgP7y9vVWuXLl81x87dkynTp1Ss2bNcq1r3ry5VqxYcdP2f/zxR0nKtX1ERIQqVapkX59Tt0mTJrnOlWvevLlmzpypn3/+WfXr1y9Sm0CJVtwJDHCVsWPHGknm4sWLDuU5RxeCg4PNhQsX7OVxcXFGkmnYsKHJyMiwl/fr1894eXnZ/wv44sWLJiAgwDz99NMO7SYnJxt/f3+H8suXL+fq14IFC4wks379entZzhGgJ5980qHuo48+aoKCggoc6+nTpx2OkFwvNjbWSDJjxozJta4wR0uMMWbLli0OR0hurCvJfPTRR/ay9PR0ExYWZnr27Jmr/vz5840ks3nzZofygQMHOuyzNI0pv+0LWvLq5/Vy+nh9P3K89NJLRpL9fZmXqVOnGknmyJEjudbdd9995v7777e/Llu2bK73nzHGLF++3EgyK1euLHKbQEnGESDctc6ePStPT898/wu7d+/e8vf3t7/OeWr3gAED7Oc15JQvWLBAx44dU7Vq1bRq1SpduHBB/fr105kzZ+z1PDw8FB0drbVr19rLfHx87H9fvXpVaWlpuv/++yVJ27dvtx95yPHss886vG7durWWLl2a62jJrfjjH/94W9vfTLly5TRgwAD7ay8vLzVv3lyHDh3KVTfnIaDXz112drZWrlypl156qUj7LSljutGbb76p8+fPF1gvIiLipuuvXLkiSbLZbLnW5ZzXduXKlTzXF2b71NRUh7oF7aeobQIlGQEIlpVzQmmOnDAUGRmZZ3nOF1rOFTEPPvhgnu1eH1TOnTunCRMmaOHChTp16pRDvZSUlAL7lBMWzp8/Lz8/P507d87hyh8fHx+HEJcfT09PVapUqcB6t6pSpUq5fs4rX768du7cmauu+b/nL19ff8uWLTp9+rS6du1a6H2WpDHdqGnTpk7pQ06ATk9Pz7Xu6tWrDnVuZfvrt/Xx8SnUforSJlCSEYBw1woKClJmZqYuXrwoX1/fXOs9PDzy3C6/8pwv7pwbKn788ccKCwvLVe/6o0d9+vTRxo0b9dJLL6lRo0YqV66csrOz1alTpzxvzFjQvh977DF9++239vLY2FjNnTs3z22uZ7PZ8rwPUn5XW2VlZeXbl7wU1O/r5QTJChUq2MtWrFihqlWrqk6dOoXeZ0ka041uDKr5KSjAhoeHS5JOnDiRa92JEycUGBiY79GfG7e/MdifOHFCzZs3d6ib336k/x6tKkqbQElGAMJdK+dS3KSkJIeTZ29X9erVJUkhISHq2LFjvvXOnz+vNWvWaMKECQ43/7vxnipFceNPKzlfSrdy2bj02xGNCxcu5Cr/5ZdfVK1aNfvrW20/L0lJSXJ3d1eNGjXsZcuXL1eXLl0c6pWmMd3oxqCan4ICbMWKFRUcHKytW7fmWvfDDz+oUaNGN20/Z/3WrVsdgsnx48f166+/OlxC36hRI3333XfKzs52CJabN29WmTJl7P9/FaVNoCQjAOGu1aJFC0m//UPtzAAUExNjv+dJ+/btdc899zisP336tIKDg+1HEG48YvD222/f8r7z+2kl5wqovL74b6Z69er67rvvdO3aNXl5eUmSvvjiCx09etQhLOTcX6eo7edl27Ztqlu3rv3Ix8mTJ7V9+/Zc9wUqTWO6kbPOAZKknj176sMPP9TRo0ftR1zWrFmjn3/+WSNHjrTXy8jIUGJiovz9/e1HaerWratatWpp5syZeuaZZ+zvyRkzZsjNzc1+vx9J6tWrlxYvXqwlS5bYy8+cOaNFixapW7du9iNNRWkTKMkIQLhrVatWTfXq1dPq1av15JNPOq1dPz8/zZgxQwMHDlSTJk3Ut29fBQcH68iRI1q+fLlatmypd999V35+fmrTpo2mTJmijIwMVaxYUV9//bWSkpKc1pccPj4+qlOnjv7nf/5HNWrUUGBgoOrVq1fg86yeeuopLV68WJ06dVKfPn2UmJioTz75xH6UK0f16tUVEBCg999/X76+vipbtqyio6MVFRVVpH5mZGTo22+/1XPPPWcvW7Fihby9vdW+fftSOaa8OOscIEl6+eWXtWjRIrVv315/+tOflJaWpqlTp6p+/foaPHiwvd6xY8dUu3btXEeVpk6dqu7du+vhhx9W3759tXv3br377rt66qmnVLt2bXu9Xr166f7779fgwYO1d+9eVahQQe+9956ysrI0YcIEhz4Vtk2gRCvOS9AAV3vrrbdMuXLlHC5Hv/5GiNfLuTneokWLHMrnzJljJJktW7bkqh8TE2P8/f2Nt7e3qV69uhk0aJDZunWrvc6vv/5qHn30URMQEGD8/f1N7969zfHjx3Nd3p1zGfzp06fz3HdSUlKBY924caNp2rSp8fLyyvOmgfl58803TcWKFY3NZjMtW7Y0W7duzXXJuDHGfPbZZ6ZOnTrG09Mzz5sG3ig2NtZUqVLFoezLL7+03/AxR69evUyXLl1K7ZjuhN27d5uHH37YlClTxgQEBJj+/fub5ORkhzo57+u8Lq1funSpadSokbHZbKZSpUpm7Nix5tq1a7nqnTt3zgwZMsQEBQWZMmXKmLZt2+Z63xe1TaCkcjOmEGf0AaVUSkqKqlWrpilTpmjIkCHF3R3L69Gjh9zc3LR06VJJv93MMCgoSPHx8Q5HhQDA1QhAuOtNnjxZc+bM0d69e+/qJ8KXdPv27VP9+vW1Y8cO+89Yp06d0nvvvadnnnnGft4KANwJBCAAAGA5/OcwAACwHAIQAACwHAIQAACwHAIQAACwnFJ5I8Ts7GwdP35cvr6+Lr2dPQAAcB5jjC5evKiIiIhivyq3VAag48eP53oIHwAAKB2OHj2qSpUqFWsfSmUAynmy99GjR+Xn51fMvQEAAIWRmpqqyMhI+/d4cSqVASjnZy8/Pz8CEAAApUxJOH2Fk6ABAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDlEIAAAIDleBZ3B2BdVccsd0m7hxO6uqRdAMDdgyNAAADAcghAAADAcghAAADAcghAAADAcoocgNavX69u3bopIiJCbm5uWrZsmcN6Nze3PJepU6fa61StWjXX+oSEhNseDAAAQGEUOQBdunRJDRs21PTp0/Ncf+LECYdl9uzZcnNzU8+ePR3qTZw40aHeiBEjbm0EAAAARVTky+A7d+6szp0757s+LCzM4fVnn32m9u3bq1q1ag7lvr6+ueoCAADcCS49B+jkyZNavny5hgwZkmtdQkKCgoKC1LhxY02dOlWZmZmu7AoAAICdS2+E+OGHH8rX11ePPfaYQ/nzzz+vJk2aKDAwUBs3blRcXJxOnDiht956K8920tPTlZ6ebn+dmprqym4DAIC7nEsD0OzZs9W/f395e3s7lI8aNcr+d4MGDeTl5aVnnnlG8fHxstlsudqJj4/XhAkTXNlVAABgIS77Cey7777T/v379dRTTxVYNzo6WpmZmTp8+HCe6+Pi4pSSkmJfjh496uTeAgAAK3HZEaB//vOfatq0qRo2bFhg3R07dsjd3V0hISF5rrfZbHkeGQIAALgVRQ5AaWlpOnjwoP11UlKSduzYocDAQFWuXFnSb+foLFq0SG+++Wau7Tdt2qTNmzerffv28vX11aZNmzRy5EgNGDBA5cuXv42hAAAAFE6RA9DWrVvVvn17++uc83liY2M1d+5cSdLChQtljFG/fv1ybW+z2bRw4UKNHz9e6enpioqK0siRIx3OCwIAAHAlN2OMKe5OFFVqaqr8/f2VkpIiPz+/4u4OblHVMctd0u7hhK4uaRcAcHtK0vc3zwIDAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACWQwACAACW41ncHQCcreqY5S5r+3BCV5e1DQC4czgCBAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALIcABAAALKfIAWj9+vXq1q2bIiIi5ObmpmXLljmsHzRokNzc3ByWTp06OdQ5d+6c+vfvLz8/PwUEBGjIkCFKS0u7rYEAAAAUVpED0KVLl9SwYUNNnz493zqdOnXSiRMn7MuCBQsc1vfv31979uzRqlWr9MUXX2j9+vUaOnRo0XsPAABwCzyLukHnzp3VuXPnm9ax2WwKCwvLc92+ffu0cuVKbdmyRc2aNZMkTZs2TV26dNEbb7yhiIiIonYJAACgSFxyDtC6desUEhKimjVr6o9//KPOnj1rX7dp0yYFBATYw48kdezYUe7u7tq8eXOe7aWnpys1NdVhAQAAuFVOD0CdOnXSRx99pDVr1mjy5Mn69ttv1blzZ2VlZUmSkpOTFRIS4rCNp6enAgMDlZycnGeb8fHx8vf3ty+RkZHO7jYAALCQIv8EVpC+ffva/65fv74aNGig6tWra926derQocMttRkXF6dRo0bZX6emphKCAADALXP5ZfDVqlVThQoVdPDgQUlSWFiYTp065VAnMzNT586dy/e8IZvNJj8/P4cFAADgVrk8AP366686e/aswsPDJUktWrTQhQsXtG3bNnudb775RtnZ2YqOjnZ1dwAAAIr+E1haWpr9aI4kJSUlaceOHQoMDFRgYKAmTJignj17KiwsTImJifrzn/+se++9VzExMZKk2rVrq1OnTnr66af1/vvvKyMjQ8OHD1ffvn25AgwAANwRRT4CtHXrVjVu3FiNGzeWJI0aNUqNGzfWa6+9Jg8PD+3cuVPdu3dXjRo1NGTIEDVt2lTfffedbDabvY158+apVq1a6tChg7p06aJWrVpp5syZzhsVAADATRT5CFC7du1kjMl3/VdffVVgG4GBgZo/f35Rdw0AAOAUPAsMAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYjmdxdwAlW9Uxy4u7CwAAOB1HgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUQgAAAgOUUOQCtX79e3bp1U0REhNzc3LRs2TL7uoyMDI0ePVr169dX2bJlFRERoT/84Q86fvy4QxtVq1aVm5ubw5KQkHDbgwEAACiMIgegS5cuqWHDhpo+fXqudZcvX9b27dv16quvavv27VqyZIn279+v7t2756o7ceJEnThxwr6MGDHi1kYAAABQRJ5F3aBz587q3Llznuv8/f21atUqh7J3331XzZs315EjR1S5cmV7ua+vr8LCwoq6ewAAgNvm8nOAUlJS5ObmpoCAAIfyhIQEBQUFqXHjxpo6daoyMzPzbSM9PV2pqakOCwAAwK0q8hGgorh69apGjx6tfv36yc/Pz17+/PPPq0mTJgoMDNTGjRsVFxenEydO6K233sqznfj4eE2YMMGVXQUAABbisgCUkZGhPn36yBijGTNmOKwbNWqU/e8GDRrIy8tLzzzzjOLj42Wz2XK1FRcX57BNamqqIiMjXdV1AABwl3NJAMoJP7/88ou++eYbh6M/eYmOjlZmZqYOHz6smjVr5lpvs9nyDEYAAAC3wukBKCf8HDhwQGvXrlVQUFCB2+zYsUPu7u4KCQlxdncAAAByKXIASktL08GDB+2vk5KStGPHDgUGBio8PFy9evXS9u3b9cUXXygrK0vJycmSpMDAQHl5eWnTpk3avHmz2rdvL19fX23atEkjR47UgAEDVL58eeeNDHCBqmOWu6TdwwldXdIuACBvRQ5AW7duVfv27e2vc87NiY2N1fjx4/X5559Lkho1auSw3dq1a9WuXTvZbDYtXLhQ48ePV3p6uqKiojRy5EiHc3wAAABcqcgBqF27djLG5Lv+ZuskqUmTJvr++++LulsAAACn4VlgAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcoocgNavX69u3bopIiJCbm5uWrZsmcN6Y4xee+01hYeHy8fHRx07dtSBAwcc6pw7d079+/eXn5+fAgICNGTIEKWlpd3WQAAAAAqryAHo0qVLatiwoaZPn57n+ilTpuidd97R+++/r82bN6ts2bKKiYnR1atX7XX69++vPXv2aNWqVfriiy+0fv16DR069NZHAQAAUASeRd2gc+fO6ty5c57rjDF6++23NXbsWD3yyCOSpI8++kihoaFatmyZ+vbtq3379mnlypXasmWLmjVrJkmaNm2aunTpojfeeEMRERG3MRwAAICCOfUcoKSkJCUnJ6tjx472Mn9/f0VHR2vTpk2SpE2bNikgIMAefiSpY8eOcnd31+bNm/NsNz09XampqQ4LAADArSryEaCbSU5OliSFhoY6lIeGhtrXJScnKyQkxLETnp4KDAy017lRfHy8JkyY4MyuAiVK1THLXdb24YSuLmsbAEqrUnEVWFxcnFJSUuzL0aNHi7tLAACgFHNqAAoLC5MknTx50qH85MmT9nVhYWE6deqUw/rMzEydO3fOXudGNptNfn5+DgsAAMCtcmoAioqKUlhYmNasWWMvS01N1ebNm9WiRQtJUosWLXThwgVt27bNXuebb75Rdna2oqOjndkdAACAPBX5HKC0tDQdPHjQ/jopKUk7duxQYGCgKleurBdeeEGvv/66fve73ykqKkqvvvqqIiIi1KNHD0lS7dq11alTJz399NN6//33lZGRoeHDh6tv375cAQYAAO6IIgegrVu3qn379vbXo0aNkiTFxsZq7ty5+vOf/6xLly5p6NChunDhglq1aqWVK1fK29vbvs28efM0fPhwdejQQe7u7urZs6feeecdJwwHAACgYG7GGFPcnSiq1NRU+fv7KyUlhfOBXMyVVyfhzuAqMAAlRUn6/i4VV4EBAAA4EwEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYDgEIAABYjtMDUNWqVeXm5pZrGTZsmCSpXbt2udY9++yzzu4GAABAvjyd3eCWLVuUlZVlf71792499NBD6t27t73s6aef1sSJE+2vy5Qp4+xuAAAA5MvpASg4ONjhdUJCgqpXr662bdvay8qUKaOwsDBn7xoAAKBQXHoO0LVr1/TJJ5/oySeflJubm7183rx5qlChgurVq6e4uDhdvnz5pu2kp6crNTXVYQEAALhVTj8CdL1ly5bpwoULGjRokL3siSeeUJUqVRQREaGdO3dq9OjR2r9/v5YsWZJvO/Hx8ZowYYIruwoAACzEzRhjXNV4TEyMvLy89O9//zvfOt988406dOiggwcPqnr16nnWSU9PV3p6uv11amqqIiMjlZKSIj8/P6f3G/9Vdczy4u4CbtPhhK7F3QUAkPTb97e/v3+J+P522RGgX375RatXr77pkR1Jio6OlqSbBiCbzSabzeb0PgIAAGty2TlAc+bMUUhIiLp2vfl/fe7YsUOSFB4e7qquAAAAOHDJEaDs7GzNmTNHsbGx8vT87y4SExM1f/58denSRUFBQdq5c6dGjhypNm3aqEGDBq7oCmB5rvwZk5/XAJRWLglAq1ev1pEjR/Tkk086lHt5eWn16tV6++23denSJUVGRqpnz54aO3asK7oBAACQJ5cEoIcfflh5nVsdGRmpb7/91hW7BAAAKDSeBQYAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACyHAAQAACzHs7g7AOeoOmZ5cXcBAIBSgyNAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcghAAADAcngYKoBb5qqH8B5O6OqSdgEgB0eAAACA5RCAAACA5RCAAACA5RCAAACA5RCAAACA5RCAAACA5Tg9AI0fP15ubm4OS61atezrr169qmHDhikoKEjlypVTz549dfLkSWd3AwAAIF8uOQJUt25dnThxwr5s2LDBvm7kyJH697//rUWLFunbb7/V8ePH9dhjj7miGwAAAHlyyY0QPT09FRYWlqs8JSVF//znPzV//nw9+OCDkqQ5c+aodu3a+v7773X//fe7ojsAAAAOXHIE6MCBA4qIiFC1atXUv39/HTlyRJK0bds2ZWRkqGPHjva6tWrVUuXKlbVp0yZXdAUAACAXpx8Bio6O1ty5c1WzZk2dOHFCEyZMUOvWrbV7924lJyfLy8tLAQEBDtuEhoYqOTk53zbT09OVnp5uf52amursbgMAAAtxegDq3Lmz/e8GDRooOjpaVapU0b/+9S/5+PjcUpvx8fGaMGGCs7oIAAAszuWXwQcEBKhGjRo6ePCgwsLCdO3aNV24cMGhzsmTJ/M8ZyhHXFycUlJS7MvRo0dd3GsAAHA3c3kASktLU2JiosLDw9W0aVPdc889WrNmjX39/v37deTIEbVo0SLfNmw2m/z8/BwWAACAW+X0n8BefPFFdevWTVWqVNHx48c1btw4eXh4qF+/fvL399eQIUM0atQoBQYGys/PTyNGjFCLFi24AgwAANwxTg9Av/76q/r166ezZ88qODhYrVq10vfff6/g4GBJ0t/+9je5u7urZ8+eSk9PV0xMjN577z1ndwMAACBfbsYYU9ydKKrU1FT5+/srJSWFn8P+T9Uxy4u7C4DTHE7oWtxdAOACJen7m2eBAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAyyEAAQAAy/Es7g4AwI2qjlnusrYPJ3R1WdsASg+OAAEAAMshAAEAAMshAAEAAMshAAEAAMshAAEAAMshAAEAAMshAAEAAMshAAEAAMshAAEAAMshAAEAAMtxegCKj4/XfffdJ19fX4WEhKhHjx7av3+/Q5127drJzc3NYXn22Wed3RUAAIA8OT0Affvttxo2bJi+//57rVq1ShkZGXr44Yd16dIlh3pPP/20Tpw4YV+mTJni7K4AAADkyekPQ125cqXD67lz5yokJETbtm1TmzZt7OVlypRRWFiYs3cPAABQIJefA5SSkiJJCgwMdCifN2+eKlSooHr16ikuLk6XL192dVcAAAAkueAI0PWys7P1wgsvqGXLlqpXr569/IknnlCVKlUUERGhnTt3avTo0dq/f7+WLFmSZzvp6elKT0+3v05NTXVltwEAwF3OpQFo2LBh2r17tzZs2OBQPnToUPvf9evXV3h4uDp06KDExERVr149Vzvx8fGaMGGCK7t6R1Qds7y4uwAAAOTCn8CGDx+uL774QmvXrlWlSpVuWjc6OlqSdPDgwTzXx8XFKSUlxb4cPXrU6f0FAADW4fQjQMYYjRgxQkuXLtW6desUFRVV4DY7duyQJIWHh+e53mazyWazObObAADAwpwegIYNG6b58+frs88+k6+vr5KTkyVJ/v7+8vHxUWJioubPn68uXbooKChIO3fu1MiRI9WmTRs1aNDA2d0BAADIxekBaMaMGZJ+u9nh9ebMmaNBgwbJy8tLq1ev1ttvv61Lly4pMjJSPXv21NixY53dFQAAgDy55Cewm4mMjNS3337r7N0CAAAUGs8CAwAAlkMAAgAAlkMAAgAAlkMAAgAAlkMAAgAAlkMAAgAAlkMAAgAAlkMAAgAAlkMAAgAAluP0O0EDQElWdcxyl7R7OKGrS9oF4BocAQIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJZDAAIAAJbD0+Dz4KqnRQMAgJKBI0AAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByuA8QAJRwpfHeZIcTuhZ3F4Cb4ggQAACwHAIQAACwHAIQAACwHAIQAACwHAIQAACwHK4CAwAnKI1XarmSq+aDq8vgLMV6BGj69OmqWrWqvL29FR0drR9++KE4uwMAACyi2ALQ//zP/2jUqFEaN26ctm/froYNGyomJkanTp0qri4BAACLKLYA9NZbb+npp5/W4MGDVadOHb3//vsqU6aMZs+eXVxdAgAAFlEs5wBdu3ZN27ZtU1xcnL3M3d1dHTt21KZNm4qjSwCAUqA0nmvlyvOWXDkfd/v5VsUSgM6cOaOsrCyFhoY6lIeGhuo///lPrvrp6elKT0+3v05JSZEkpaamuqR/2emXXdIuAMB6XPVdJbn2+8oV/c5p0xjj9LaLqlRcBRYfH68JEybkKo+MjCyG3gAAUHj+bxd3D26NK/t98eJF+fv7u24HhVAsAahChQry8PDQyZMnHcpPnjypsLCwXPXj4uI0atQo++vs7GydO3dOQUFBcnNzc3l/7yapqamKjIzU0aNH5efnV9zdKbWYR+dhLp2DeXQe5tJ5bpxLY4wuXryoiIiI4u5a8QQgLy8vNW3aVGvWrFGPHj0k/RZq1qxZo+HDh+eqb7PZZLPZHMoCAgLuQE/vXn5+fnywnYB5dB7m0jmYR+dhLp3n+rks7iM/OYrtJ7BRo0YpNjZWzZo1U/PmzfX222/r0qVLGjx4cHF1CQAAWESxBaDHH39cp0+f1muvvabk5GQ1atRIK1euzHViNAAAgLMV60nQw4cPz/MnL7iOzWbTuHHjcv2kiKJhHp2HuXQO5tF5mEvnKclz6WZKwrVoAAAAdxBPgwcAAJZDAAIAAJZDAAIAAJZDACpBpk+frqpVq8rb21vR0dH64Ycfblp/0aJFqlWrlry9vVW/fn2tWLHCYb0xRq+99prCw8Pl4+Ojjh076sCBAw51zp07p/79+8vPz08BAQEaMmSI0tLSHOrs3LlTrVu3lre3tyIjIzVlypQi9+VOK61zOWvWLLVu3Vrly5dX+fLl1bFjxwL77kqldR6vt3DhQrm5udnvOVZcSvNcXrhwQcOGDVN4eLhsNptq1KhRbJ/x0jyPb7/9tmrWrCkfHx9FRkZq5MiRunr16i3OxO0riXN59epVDRo0SPXr15enp2e+n9t169apSZMmstlsuvfeezV37tyiT4BBibBw4ULj5eVlZs+ebfbs2WOefvppExAQYE6ePJln/f/93/81Hh4eZsqUKWbv3r1m7Nix5p577jG7du2y10lISDD+/v5m2bJl5qeffjLdu3c3UVFR5sqVK/Y6nTp1Mg0bNjTff/+9+e6778y9995r+vXrZ1+fkpJiQkNDTf/+/c3u3bvNggULjI+Pj/nggw+K1Jc7qTTP5RNPPGGmT59ufvzxR7Nv3z4zaNAg4+/vb3799VcXzNTNleZ5zJGUlGQqVqxoWrdubR555BHnTU4Rlea5TE9PN82aNTNdunQxGzZsMElJSWbdunVmx44dLpipmyvN8zhv3jxjs9nMvHnzTFJSkvnqq69MeHi4GTlypAtmqmAldS7T0tLMs88+a2bOnGliYmLy/NweOnTIlClTxowaNcrs3bvXTJs2zXh4eJiVK1cWaQ4IQCVE8+bNzbBhw+yvs7KyTEREhImPj8+zfp8+fUzXrl0dyqKjo80zzzxjjDEmOzvbhIWFmalTp9rXX7hwwdhsNrNgwQJjjDF79+41ksyWLVvsdb788kvj5uZmjh07Zowx5r333jPly5c36enp9jqjR482NWvWLHRf7rTSPJc3yszMNL6+vubDDz8s7PCdprTPY2ZmpnnggQfMP/7xDxMbG1usAag0z+WMGTNMtWrVzLVr1251+E5Tmudx2LBh5sEHH3Toy6hRo0zLli2LNAfOUlLn8nr5fW7//Oc/m7p16zqUPf744yYmJqaAUTviJ7AS4Nq1a9q2bZs6duxoL3N3d1fHjh21adOmPLfZtGmTQ31JiomJsddPSkpScnKyQx1/f39FR0fb62zatEkBAQFq1qyZvU7Hjh3l7u6uzZs32+u0adNGXl5eDvvZv3+/zp8/X6i+3EmlfS5vdPnyZWVkZCgwMLAo03Db7oZ5nDhxokJCQjRkyJBbnQanKO1z+fnnn6tFixYaNmyYQkNDVa9ePU2aNElZWVm3My1FVtrn8YEHHtC2bdvsPzMdOnRIK1asUJcuXW55Tm5VSZ7LwnDWdw4BqAQ4c+aMsrKyct0FOzQ0VMnJyXluk5ycfNP6Of9bUJ2QkBCH9Z6engoMDHSok1cb1++joL7cSaV9Lm80evRoRURE5Pqwu1ppn8cNGzbon//8p2bNmlW4AbtQaZ/LQ4cOafHixcrKytKKFSv06quv6s0339Trr79euAlwktI+j0888YQmTpyoVq1a6Z577lH16tXVrl07vfzyy4WbACcqyXNZGPn1JTU1VVeuXCl0OwQgoIRKSEjQwoULtXTpUnl7exd3d0qNixcvauDAgZo1a5YqVKhQ3N0p9bKzsxUSEqKZM2eqadOmevzxx/XKK6/o/fffL+6ulSrr1q3TpEmT9N5772n79u1asmSJli9frr/85S/F3TXLIgCVABUqVJCHh4dOnjzpUH7y5EmFhYXluU1YWNhN6+f8b0F1Tp065bA+MzNT586dc6iTVxvX76OgvtxJpX0uc7zxxhtKSEjQ119/rQYNGtx80C5QmucxMTFRhw8fVrdu3eTp6SlPT0999NFH+vzzz+Xp6anExMRCz4MzlOa5lKTw8HDVqFFDHh4e9jq1a9dWcnKyrl27VsDonae0z+Orr76qgQMH6qmnnlL9+vX16KOPatKkSYqPj1d2dnbhJsFJSvJcFkZ+ffHz85OPj0+h2yEAlQBeXl5q2rSp1qxZYy/Lzs7WmjVr1KJFizy3adGihUN9SVq1apW9flRUlMLCwhzqpKamavPmzfY6LVq00IULF7Rt2zZ7nW+++UbZ2dmKjo6211m/fr0yMjIc9lOzZk2VL1++UH25k0r7XErSlClT9Je//EUrV650+K38TirN81irVi3t2rVLO3bssC/du3dX+/bttWPHDkVGRt7m7BRNaZ5LSWrZsqUOHjzo8CX9888/Kzw83OGcF1cr7fN4+fJlubs7fuXmhEpzh59IVZLnsjCc9p1TpFOm4TILFy40NpvNzJ071+zdu9cMHTrUBAQEmOTkZGOMMQMHDjRjxoyx1//f//1f4+npad544w2zb98+M27cuDwvSQwICDCfffaZ2blzp3nkkUfyvCSxcePGZvPmzWbDhg3md7/7ncMliRcuXDChoaFm4MCBZvfu3WbhwoWmTJkyuS6DL6gvd1JpnsuEhATj5eVlFi9ebE6cOGFfLl686Mopy1NpnscbFfdVYKV5Lo8cOWJ8fX3N8OHDzf79+80XX3xhQkJCzOuvv+7KKctTaZ7HcePGGV9fX7NgwQJz6NAh8/XXX5vq1aubPn36uHLK8lVS59IYY/bs2WN+/PFH061bN9OuXTvz448/mh9//NG+Pucy+Jdeesns27fPTJ8+ncvgS7tp06aZypUrGy8vL9O8eXPz/fff29e1bdvWxMbGOtT/17/+ZWrUqGG8vLxM3bp1zfLlyx3WZ2dnm1dffdWEhoYam81mOnToYPbv3+9Q5+zZs6Zfv36mXLlyxs/PzwwePDjXl+1PP/1kWrVqZWw2m6lYsaJJSEjI1feC+nKnlda5rFKlipGUaxk3btztT8otKK3zeKPiDkDGlO653Lhxo4mOjjY2m81Uq1bN/PWvfzWZmZm3OSO3prTOY0ZGhhk/frypXr268fb2NpGRkea5554z58+fv/1JuUUldS7z+3fwemvXrjWNGjUyXl5eplq1ambOnDlFHj9PgwcAAJbDOUAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCECAE509e1YhISE6fPiwy/Zx+PBhubm5aceOHS7bx93Mzc1Ny5Yty3f93r17ValSJV26dOnOdeo2FTQmALkRgAAn+utf/6pHHnlEVatWdUp7gwYNUo8ePRzKIiMjdeLECdWrV88p+8jPnQ5a48ePV6NGjYq9vTp16uj+++/XW2+9Vaj6H374oVq1auXUPuTH2e0BVkYAApzk8uXL+uc//6khQ4a4dD8eHh4KCwuTp6enS/dTUmVkZLh8H4MHD9aMGTOUmZlZYN3PPvtM3bt3v6393YkxAbhBkR+fCiBPixYtMsHBwbnKd+3aZTp16mTKli1rQkJCzIABA8zp06cdtqtXr57x9vY2gYGBpkOHDiYtLc2MGzcu19OQ165da5KSkowk8+OPPxpjfnsqsiSzcuVK06hRI+Pt7W3at29vTp48aVasWGFq1aplfH19Tb9+/cylS5fs+/3yyy9Ny5Ytjb+/vwkMDDRdu3Y1Bw8etK+/cd9t27a1r5s1a5apVauWsdlspmbNmmb69Om3NXdz5szJtb+cpztLMu+9957p1q2bKVOmjBk3bpyZM2eO8ff3d2hj6dKl9idGF9TerFmzTI8ePYyPj4+59957zWeffebQVnp6urHZbGb16tU37feVK1dM2bJlzb59+0r8mAA4IgABTvL888+bTp06OZSdP3/eBAcHm7i4OLNv3z6zfft289BDD5n27dsbY4w5fvy48fT0NG+99ZZJSkoyO3fuNNOnTzcXL140Fy9eNH369DGdOnUyJ06cMCdOnDDp6en5BqD777/fbNiwwWzfvt3ce++9pm3btubhhx8227dvN+vXrzdBQUEmISHB3rfFixebTz/91Bw4cMD8+OOPplu3bqZ+/fomKyvLGGPMDz/8YCSZ1atXmxMnTpizZ88aY4z55JNPTHh4uPn000/NoUOHzKeffmoCAwPN3Llzb3nuLl++bP7f//t/pm7duvaxXr582Rjz25d7SEiImT17tklMTDS//PJLgWGhoPYqVapk5s+fbw4cOGCef/55U65cOfv4ckRHR5tx48bdtN9ffPGFqVGjRqkZE4D/suYxdMAFfvnlF0VERDiUvfvuu2rcuLEmTZpkL5s9e7YiIyP1888/Ky0tTZmZmXrsscdUpUoVSVL9+vXtdX18fJSenq6wsLAC9//666+rZcuWkqQhQ4YoLi5OiYmJqlatmiSpV69eWrt2rUaPHi1J6tmzp8P2s2fPVnBwsPbu3at69eopODhYkhQUFOSw/3HjxunNN9/UY489JkmKiorS3r179cEHHyg2NrZwk3UDHx8flStXTp6ennmO9YknntDgwYOd1t6gQYPUr18/SdKkSZP0zjvv6IcfflCnTp3sdSIiIvTLL7/cdD83+/mrJI4JwH9xDhDgJFeuXJG3t7dD2U8//aS1a9eqXLly9qVWrVqSpMTERDVs2FAdOnRQ/fr11bt3b82aNUvnz5+/pf03aNDA/ndoaKjKlCljDz85ZadOnbK/PnDggPr166dq1arJz8/PfuL2kSNH8t3HpUuXlJiYqCFDhjiM6fXXX1diYmKe28ybN8+h7nfffVfksTVr1qzI29zM9XNVtmxZ+fn5OcyN9FvguHz5cr5tGGP073//+5bP/ymOMQH4L44AAU5SoUKFXOElLS1N3bp10+TJk3PVDw8Pl4eHh1atWqWNGzfq66+/1rRp0/TKK69o8+bNioqKKtL+77nnHvvfbm5uDq9zyrKzs+2vu3XrpipVqmjWrFmKiIhQdna26tWrp2vXruW7j7S0NEnSrFmzFB0d7bDOw8Mjz226d+/uULdixYqFH9T/KVu2rMNrd3d3GWMcyopyInFBcyNJ586dU/Xq1fNt44cfflBmZqYeeOCBQu/3esUxJgD/RQACnKRx48b65JNPHMqaNGmiTz/9VFWrVs33qi03Nze1bNlSLVu21GuvvaYqVapo6dKlGjVqlLy8vJSVleX0vp49e1b79+/XrFmz1Lp1a0nShg0bHOp4eXlJksP+Q0NDFRERoUOHDql///6F2pevr698fX0LrFeUsQYHB+vixYu6dOmSPUjceLn+7c7d7t271atXr3zXf/bZZ+ratWu+wa+ofbgTYwLwX/wEBjhJTEyM9uzZ43AUaNiwYTp37pz69eunLVu2KDExUV999ZUGDx6srKwsbd68WZMmTdLWrVt15MgRLVmyRKdPn1bt2rUlSVWrVtXOnTu1f/9+nTlzxmmXS5cvX15BQUGaOXOmDh48qG+++UajRo1yqBMSEiIfHx+tXLlSJ0+eVEpKiiRpwoQJio+P1zvvvKOff/5Zu3bt0pw5cwp935z8VK1aVUlJSdqxY4fOnDmj9PT0fOtGR0erTJkyevnll5WYmKj58+dr7ty5t9zejQ4fPqxjx46pY8eO+db5/PPPC/z5qySNCcANivkkbOCu0rx5c/P+++87lP3888/m0UcfNQEBAcbHx8fUqlXLvPDCCyY7O9vs3bvXxMTEmODgYGOz2UyNGjXMtGnT7NueOnXKPPTQQ6ZcuXIFXgZ//vx5+3Z5XVE0btw407BhQ/vrVatWmdq1axubzWYaNGhg1q1bZySZpUuX2uvMmjXLREZGGnd3d4fL4OfNm2caNWpkvLy8TPny5U2bNm3MkiVLbmvurl69anr27GkCAgJyXeJ9fZ9yLF261Nx7773Gx8fH/P73vzczZ8401/+TVpT2/P397euNMWbSpEkmJiYm374ePHjQ2Gw2k5aWVmrGBMCRmzE3/OgM4JYtX75cL730knbv3i13dw6wlkbXrl3T7373O82fP99+Vd2N3nrrLa1evVorVqy4w70D4CycAwQ4UdeuXXXgwAEdO3ZMkZGRxd0d3IIjR47o5Zdfzjf8SFKlSpUUFxd3B3sFwNk4AgQAACyHY/QAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMByCEAAAMBy/j8vkWJ+VPn1rQAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.title(\"$\\\\lambda$ estimate\")\n", + "plt.hist(lambd1, bins=20, alpha=0.5, label=f\"ExtendedBinnedNLL\\nvalid={np.mean(valid1)*100:.0f}%\\nmean = {np.mean(lambd1):.2f}\\nstd.dev. = {np.std(lambd1):.3f}\")\n", + "plt.hist(lambd2, bins=20, alpha=0.5, label=f\"BinnedNLL\\nvalid={np.mean(valid2)*100:.0f}%\\nmean = {np.mean(lambd2):.2f}\\nstd.dev. = {np.std(lambd2):.3f}\")\n", + "plt.legend()\n", + "\n", + "plt.figure()\n", + "plt.hist(ntot1 / ntot - 1, bins=20)\n", + "plt.title(f\"ExtendedBinnedNLL: $n_\\\\mathrm{{tot}}$ estimate\\n(mean-truth)/truth = {np.mean(ntot1) / np.mean(ntot) - 1:.3f}\")\n", + "plt.xlabel(\"(estimate - truth) / truth\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now find negligible bias for $\\lambda$ and $n_\\text{tot}$. The precision is also greatly improved, since the weight distribution is so narrow that it can effectively be neglected as a source of additional uncertainty to the underlying Poisson process.\n", + "\n", + "The estimates from `ExtendedBinnedNLL` and `BinnedNLL` for $\\lambda$ become equal in this case (and their precision), because the ordinary likelihood for unweighted samples factorizes into a part for $n_\\text{tot}$ and another for $\\lambda$. This means that the estimates for $n_\\text{tot}$ and $\\lambda$ are independent. This factorization is broken for weighted histograms in general, and only restored here, because the weight variance is negligible.\n", + "\n", + "Finally, we have another look at the function minimum values." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n", + "\n", + "plt.sca(ax[0])\n", + "plt.hist(minval1, bins=50, density=True)\n", + "x = np.linspace(0, 100)\n", + "plt.plot(x, chi2(bins-2).pdf(x))\n", + "plt.title(f\"ExtendedBinnedNLL minimum value\\nndf = {bins-2} mean = {np.mean(minval1):.2f} median = {np.median(minval1):.2f}\")\n", + "\n", + "plt.sca(ax[1])\n", + "plt.hist(minval2, bins=50, density=True)\n", + "x = np.linspace(0, 100)\n", + "plt.plot(x, chi2(bins-2).pdf(x))\n", + "plt.title(f\"BinnedNLL minimum value\\nndf = {bins-2} mean = {np.mean(minval2):.2f} median = {np.median(minval2):.2f}\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The minimum values now follow the theoretical chi-square distribution very well, since bins with a negative sum of weights do not occur anymore." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/studies.rst b/doc/studies.rst index 6c612a95..cda4eba5 100644 --- a/doc/studies.rst +++ b/doc/studies.rst @@ -11,6 +11,7 @@ The following studies explore different aspects of the library, including its pe :maxdepth: 1 notebooks/binned_vs_unbinned + notebooks/weighted_histograms notebooks/hesse_and_minos notebooks/numba notebooks/automatic_differentiation diff --git a/src/iminuit/cost.py b/src/iminuit/cost.py index 2ee0e7ee..f4ddb854 100644 --- a/src/iminuit/cost.py +++ b/src/iminuit/cost.py @@ -1446,9 +1446,14 @@ def _update_cache(self): if self._bohm_zech_s is not None: val = n[..., 0] var = n[..., 1] - self._bohm_zech_s = np.ones_like(val) - np.divide(np.abs(val), var, out=self._bohm_zech_s, where=var > 0) - self._bohm_zech_n = val * self._bohm_zech_s + s = np.zeros_like(val) + ma = var > 0 + s[ma] = np.abs(val[ma]) / var[ma] + # Use median of s from bins with entries to bins which have zero entries. + # This is arbitrary, but still better than other arbitrary choices. + s[~ma] = np.median(s[ma]) + self._bohm_zech_s = s + self._bohm_zech_n = val * s else: self._bohm_zech_n = n