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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Mean and Intrinsic Dispersion Maximum-Likelihood Estimates "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Author:** Yannick Copin <y.copin@ipnl.in2p3.fr>\n",
"$\n",
"\\renewcommand{\\d}{\\mathrm{d}}\n",
"\\renewcommand{\\v}[1]{\\boldsymbol{#1}} % Vector\n",
"\\renewcommand{\\m}[1]{\\mathsf{#1}} % Matrix\n",
"\\DeclareMathOperator{\\Var}{Var}\n",
"\\DeclareMathOperator{\\Cov}{Cov}\n",
"\\DeclareMathOperator{\\argmin}{argmin}\n",
"$\n",
"\n",
"**Abstract:** When computing the mean value of a measurement sample, standard supposedly-optimal inverse-variance weighted-mean usually omits the presence of *intrinsic* dispersion. On the other hand, various methods have been used to compute intrinsic dispersion *a posteriori* from $\\chi^2$ statistic. I present unified mean and intrinsic dispersion maximum-likelihood estimates. \n",
"\n",
"**Changelog:** 21/12/28: Ported to Python 3.x, iminuit 2.x\n",
"\n",
"Online versions:\n",
"* [gist](https://gist.github.com/ycopin/65c01f5cd52e6820fb3a/#file-intrinsicdispersion-ipynb)\n",
"* [nbviewer](http://nbviewer.jupyter.org/gist/ycopin/65c01f5cd52e6820fb3a/intrinsicDispersion.ipynb)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Numpy 1.21.4\n",
"Scipy 1.7.2\n",
"Matplotlib 3.5.0\n",
"iminuit v 2.8.4\n",
"mar. 28 déc. 2021 19:16:45 CET\n"
]
}
],
"source": [
"import numpy as N\n",
"print(\"Numpy\", N.__version__)\n",
"import scipy as S\n",
"print(\"Scipy\", S.__version__)\n",
"import matplotlib.pyplot as P\n",
"print(\"Matplotlib\", P.matplotlib.__version__)\n",
"\n",
"import iminuit\n",
"print(\"iminuit v\", iminuit.__version__)\n",
"\n",
"!date"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"P.rcParams['figure.figsize'] = 12, 9\n",
"\n",
"import scipy.stats as SS\n",
"import scipy.optimize as SO"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Analytics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Independent measurements"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let $\\v{x}$ be a collection of independent observations derived from (unknown) normal population $\\cal{N}(\\mu, \\sigma^2)$ with (known) normal observational errors $\\d\\v{x}$. The underlying distribution of each observation $x_i$ is therefore normal $\\cal{N}(\\mu, \\sigma^2 + \\d x_i^2)$, and the likelihood $\\cal{L}$ of the observations is defined as:\n",
"$$\\begin{align}\n",
"\\cal{L} &= \\prod_i \\frac{1}{\\sqrt{2\\pi(\\sigma^2 + \\d x_i^2})}\\exp\\left(-\\frac{1}{2}\\frac{(x_i - \\mu)^2}{\\sigma^2 + \\d x_i^2}\\right) \\\\\n",
"-2\\ln\\cal{L} &\\equiv \\sum_i \\frac{(x_i - \\mu)^2}{\\sigma^2 + \\d x_i^2} + \\sum_i \\ln(\\sigma^2 + \\d x_i^2) \\\\\n",
" &= \\chi^2(\\mu,\\sigma) + \\delta\\chi^2(\\sigma) \\\\\n",
" &= \\chi_T^2(\\mu,\\sigma) \n",
"\\end{align}$$\n",
"Minimizing the $\\chi^2$ against $\\mu$ leads to the traditional variance-weighted average maximum-likelihood (ML) estimate of $\\mu$:\n",
"$$\n",
"\\frac{\\partial\\chi^2}{\\partial\\mu} = 0 \\quad\\text{for}\\quad\n",
"\\hat{\\mu} = \\frac{1}{\\sum_i w_i} \\sum_i w_i x_i\n",
"\\quad\\text{with}\\quad\n",
"w_i = \\frac{1}{(\\sigma^2 + \\d x_i^2)^{2}}\n",
"$$\n",
"where the variance weighting *includes* the yet-unknown intrinsic dispersion $\\sigma$. Unfortunately, the expression cannot be minimized analytically against $\\sigma$, but the numerical minimization is easy:\n",
"$$\n",
"(\\hat{\\mu},\\hat{\\sigma}) = \\argmin_{\\mu,\\sigma} \\chi_T^2(\\mu,\\sigma)\n",
"$$\n",
"\n",
"Note that in the error-free case ($\\d\\v{x}=\\v{0}$), one correctly retrieves:\n",
"$$\\begin{align}\n",
"\\hat{\\mu} &= \\frac{1}{N}\\sum_i x_i \\\\\n",
"\\hat{\\sigma}^2 &= \\frac{1}{N}\\sum_i (x_i - \\hat{\\mu})^2\n",
"\\end{align}$$\n",
"the latter being the (biased) ML-estimator of the variance of $\\v{x}$ (see [Oliphant, 2006](http://contentdm.lib.byu.edu/cdm/ref/collection/IR/id/558)).\n",
"\n",
"Note furthermore that the partial $\\chi^2$ as defined above properly **follows** a $\\chi^2$-distribution with $N-2$ degrees of freedom, and provides therefore a way to assert goodness-of-fit of the model, in the present case the validity of the errors $\\d\\v{x}$. On the contrary, the total $\\chi_T^2$ which is minimized does not follow a $\\chi^2$-distribution."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def chi2(mu, sig, x, dx):\n",
" return N.sum((x - mu)**2 / (dx**2 + sig**2)) # Standard chi2\n",
" \n",
"def delta_chi2(sig, dx):\n",
" return N.sum(N.log(dx**2 + sig**2)) # Complementary term\n",
"\n",
"def chi2total(mu, sig, x, dx):\n",
" return chi2(mu, sig, x, dx) + delta_chi2(sig, dx)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correlated measurements"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For normally distributed $\\mathcal{N}(\\mu,\\sigma^2)$ measurements $\\v{x}$ with correlated errors described by covariance matrix $\\m{\\Sigma}$, the likelihood can be written from the total covariance matrix $\\m{\\Sigma} + \\m{1}\\sigma^2$:\n",
"$$\\begin{align}\n",
"\\mathcal{L} &= (2\\pi)^{-N/2}|\\m{\\Sigma} + \\m{1}\\sigma^2|^{-1/2}\\,\\exp\\left(-\\frac{1}{2}(\\v{x}-\\mu)^{T}(\\m{\\Sigma} + \\m{1}\\sigma^2)^{-1}(\\v{x}-\\mu)\\right), \\\\\n",
"-2\\ln\\mathcal{L} &\\equiv (\\v{x}-\\mu)^{T}(\\m{\\Sigma} + \\m{1}\\sigma^2)^{-1}(\\v{x}-\\mu) + \\ln|\\m{\\Sigma} + \\m{1}\\sigma^2| \\\\\n",
" &= \\chi^2(\\mu,\\sigma) + \\delta\\chi^2(\\sigma) \\\\\n",
" &= \\chi_T^2(\\mu,\\sigma) \n",
"\\end{align}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Numerical simulations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Dataset"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The *x* dataset is defined as originating from a single null value observed with log-normally distributed errors *dx*, therefore µ=0 and σ=0 (no intrinsic dispersion).\n",
"\n",
"The *y* dataset is defined as originating from normal population (µ=0, intrinsic dispersion σ=2), observed with the same log-normally distributed errors *dx*."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"n = 500 # Sample size\n",
"mu0 = 0 # Intrinsic mean\n",
"sig0 = 2 # Intrinsic scatter\n",
"\n",
"N.random.seed(1234)\n",
"dx = N.sqrt(N.random.lognormal(sigma=1, size=n)) # Log-normally distributed uncertainties\n",
"x = N.random.normal(loc=mu0, scale=dx) # x: No intrinsic dispersion: mu=mu0, sig=0\n",
"y = x + N.random.randn(n)*sig0 # y: Gaussian uncertainties + intrinsic dispersion"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x648 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = P.subplots(1, 1)\n",
"ax.errorbar(N.arange(n), x, yerr=dx, fmt='b.', label='x: no intrinsic dispersion')\n",
"ax.errorbar(N.arange(n), y, yerr=dx, fmt='r.', label='y: x + intrinsic dispersion')\n",
"#ax.hist(x, bins='auto', orientation='horizontal', histtype='stepfilled', color='b', alpha=0.5)\n",
"#ax.hist(y, bins='auto', orientation='horizontal', histtype='step', color='r')\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Estimates *without* accounting for intrinsic dispersion"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plain: µ = 0.093 ± 0.111, σ = 2.472 ± 0.078\n"
]
}
],
"source": [
"mup = N.average(y) # Sample mean\n",
"var = N.var(y, ddof=1) # Sample variance\n",
"dvar2 = 2 * var**2 / len(y) # Error on var**2 in normal approximation\n",
"std = N.sqrt(var) # Sample stddev\n",
"dmup = std/N.sqrt(len(y)) # Error on sample mean\n",
"dstd = N.sqrt(dvar2)/(2*std) # Error on stddev in normal approximation\n",
"print(f\"Plain: µ = {mup:.3f} ± {dmup:.3f}, σ = {std:.3f} ± {dstd:.3f}\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Weighted, NO intrinsic: µ = 0.148 ± 0.035 (χ²/DoF=3602.66/499, p=0.0%)\n"
]
}
],
"source": [
"muw, sumw = N.average(y, weights=dx**(-2), returned=True) # Optimally weighted mean\n",
"dmuw = sumw**(-0.5) # Uncertainty on weighted mean\n",
"chi2w = chi2(muw, 0, y, dx)\n",
"pw = SS.distributions.chi2.sf(chi2w, len(x) - 1) # SS.chisqprob deprecated in v0.17.0\n",
"print(f\"Weighted, NO intrinsic: µ = {muw:.3f} ± {dmuw:.3f} (χ²/DoF={chi2w:.2f}/{len(x)-1}, p={pw:.1%})\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Poor man's minimization"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum: χ² = 1381.09 at µ = 0.100, σ = 2.100\n"
]
}
],
"source": [
"mus = N.linspace(-1, +1, 21)\n",
"sigs = N.linspace(0, 4, 41)\n",
"chi2ts = N.array([ [ chi2(mu,sig, y, dx) for mu in mus ] for sig in sigs ])\n",
"chi2ds = N.array([ [ delta_chi2(sig, dx) for mu in mus ] for sig in sigs ])\n",
"chi2s = chi2ts + chi2ds\n",
"jmin, imin = N.unravel_index(chi2s.argmin(), chi2s.shape)\n",
"print(f\"Minimum: χ² = {chi2s.min():.2f} at µ = {mus[imin]:.3f}, σ = {sigs[jmin]:.3f}\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### scipy minimization"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Scipy: total χ² = 1380.98 at µ = 0.067 ± 0.108, σ = 2.087 ± 0.084\n"
]
}
],
"source": [
"res = SO.minimize(lambda p: chi2total(p[0], p[1], y, dx), (y.mean(), y.std()), tol=1e-3)\n",
"mu, sig = res.x\n",
"dmu, dsig = N.sqrt((2*res.hess_inv).diagonal())\n",
"print(f\"Scipy: total χ² = {res.fun:.2f} at µ = {mu:.3f} ± {dmu:.3f}, σ = {sig:.3f} ± {dsig:.3f}\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### minuit minimization\n",
"\n",
"**Note:** the `iminuit.Minuit` interface changed between versions 1.x and 2.x; however, the `minimize` interface (introduced in v1.3) remained unchanged."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Case with intrinsic dispersion (*y*)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
" <tr>\n",
" <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
" </tr>\n",
" <tr>\n",
" <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 1381 </td>\n",
" <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 31 </td>\n",
" </tr>\n",
" <tr>\n",
" <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.59e-06 (Goal: 0.0002) </td>\n",
" <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\"> </td>\n",
" </tr>\n",
" <tr>\n",
" <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
" <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
" </tr>\n",
" <tr>\n",
" <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
" <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
" </tr>\n",
" <tr>\n",
" <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
" <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
" <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
" <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
" <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
" </tr>\n",
"</table><table>\n",
" <tr>\n",
" <td></td>\n",
" <th title=\"Variable name\"> Name </th>\n",
" <th title=\"Value of parameter\"> Value </th>\n",
" <th title=\"Hesse error\"> Hesse Error </th>\n",
" <th title=\"Minos lower error\"> Minos Error- </th>\n",
" <th title=\"Minos upper error\"> Minos Error+ </th>\n",
" <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
" <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
" <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
" </tr>\n",
" <tr>\n",
" <th> 0 </th>\n",
" <td> mu </td>\n",
" <td> 0.07 </td>\n",
" <td> 0.11 </td>\n",
" <td> </td>\n",
" <td> </td>\n",
" <td> </td>\n",
" <td> </td>\n",
" <td> </td>\n",
" </tr>\n",
" <tr>\n",
" <th> 1 </th>\n",
" <td> sig </td>\n",
" <td> 2.09 </td>\n",
" <td> 0.08 </td>\n",
" <td> </td>\n",
" <td> </td>\n",
" <td> </td>\n",
" <td> </td>\n",
" <td> </td>\n",
" </tr>\n",
"</table><table>\n",
" <tr>\n",
" <td></td>\n",
" <th> mu </th>\n",
" <th> sig </th>\n",
" </tr>\n",
" <tr>\n",
" <th> mu </th>\n",
" <td> 0.0112 </td>\n",
" <td style=\"background-color:rgb(250,250,250);color:black\"> 2.67e-05 <strong>(0.003)</strong> </td>\n",
" </tr>\n",
" <tr>\n",
" <th> sig </th>\n",
" <td style=\"background-color:rgb(250,250,250);color:black\"> 2.67e-05 <strong>(0.003)</strong> </td>\n",
" <td> 0.00713 </td>\n",
" </tr>\n",
"</table>"
],
"text/plain": [
"┌─────────────────────────────────────────────────────────────────────────┐\n",
"│ Migrad │\n",
"├──────────────────────────────────┬──────────────────────────────────────┤\n",
"│ FCN = 1381 │ Nfcn = 31 │\n",
"│ EDM = 1.59e-06 (Goal: 0.0002) │ │\n",
"├──────────────────────────────────┼──────────────────────────────────────┤\n",
"│ Valid Minimum │ No Parameters at limit │\n",
"├──────────────────────────────────┼──────────────────────────────────────┤\n",
"│ Below EDM threshold (goal x 10) │ Below call limit │\n",
"├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
"│ Covariance │ Hesse ok │ Accurate │ Pos. def. │ Not forced │\n",
"└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
"┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
"│ │ Name │ Value │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit- │ Limit+ │ Fixed │\n",
"├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
"│ 0 │ mu │ 0.07 │ 0.11 │ │ │ │ │ │\n",
"│ 1 │ sig │ 2.09 │ 0.08 │ │ │ │ │ │\n",
"└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
"┌─────┬───────────────────┐\n",
"│ │ mu sig │\n",
"├─────┼───────────────────┤\n",
"│ mu │ 0.0112 2.67e-05 │\n",
"│ sig │ 2.67e-05 0.00713 │\n",
"└─────┴───────────────────┘"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"minuit = iminuit.Minuit(lambda mu, sig: chi2total(mu, sig, y, dx), mu=y.mean(), sig=y.std())\n",
"minuit.errordef = iminuit.Minuit.LEAST_SQUARES\n",
"minuit.migrad()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minuit.migrad: total χ² = 1380.98 at µ = 0.067 ± 0.106, σ = 2.088 ± 0.084\n"
]
}
],
"source": [
"mu, sig = minuit.values['mu'], abs(minuit.values['sig'])\n",
"dmu, dsig = minuit.errors['mu'], minuit.errors['sig']\n",
"print(f\"Minuit.migrad: total χ² = {minuit.fval:.2f} at µ = {mu:.3f} ± {dmu:.3f}, σ = {sig:.3f} ± {dsig:.3f}\")"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minuit.minimize: total χ² = 1380.98 at µ = 0.067 ± 0.106, σ = 2.088 ± 0.084\n"
]
}
],
"source": [
"res = iminuit.minimize(lambda p: chi2total(p[0], p[1], y, dx), (y.mean(), y.std())) # tol=1e-3\n",
"mu, sig = res.x\n",
"dmu, dsig = N.sqrt((2*res.hess_inv).diagonal())\n",
"print(f\"Minuit.minimize: total χ² = {res.fun:.2f} at µ = {mu:.3f} ± {dmu:.3f}, σ = {sig:.3f} ± {dsig:.3f}\")"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def musig(x, dx, verbose=False):\n",
" \"\"\"\n",
" Compute maximum-likelihood estimate of mean and intrinsic dispersion.\n",
" \n",
" Warning: does not support masked arrays nor invalid measurement errors.\n",
" \"\"\"\n",
" \n",
" def chi2(mu, sig, x, dx):\n",
" return N.sum((x - mu)**2 / (dx**2 + sig**2)) # Standard chi2\n",
"\n",
" def delta_chi2(sig, dx):\n",
" return N.sum(N.log(dx**2 + sig**2)) # Complementary term\n",
" \n",
" def chi2total(mu, sig, x, dx):\n",
" return chi2(mu, sig, x, dx) + delta_chi2(sig, dx)\n",
" \n",
" # Initial guess\n",
" mu = x.mean()\n",
" sig = x.std()\n",
" minuit = iminuit.Minuit(lambda mu, sig: chi2total(mu, sig, x, dx), mu=mu, sig=sig)\n",
" minuit.errordef = iminuit.Minuit.LEAST_SQUARES\n",
" minuit.migrad() # Minimization\n",
" if not minuit.valid:\n",
" raise ValueError(\"Convergence issue.\")\n",
" \n",
" mu, sig = minuit.values['mu'], abs(minuit.values['sig'])\n",
" dmu, dsig = minuit.errors['mu'], minuit.errors['sig'] \n",
" if verbose:\n",
" fval = minuit.fval # Minimal total chi2\n",
" c1 = chi2(mu, sig, x, dx) # Traditional chi2\n",
" c2 = delta_chi2(sig, dx) # Complementary term\n",
" dof = len(x) - 2 # DoF\n",
" p = SS.distributions.chi2.sf(c1, dof) # p-value of *traditional* chi2\n",
" print(f\"Minuit: χ² = {c1:.2f}, δχ² = {c2:.2f}\"\n",
" f\" at µ = {mu:.3f} ± {dmu:.3f}, σ = {sig:.3f} ± {dsig:.3f} (DoF={dof}, p={p:.1%})\")\n",
" \n",
" return (mu, dmu), (sig, dsig)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minuit: χ² = 505.80, δχ² = 875.18 at µ = 0.067 ± 0.106, σ = 2.088 ± 0.084 (DoF=498, p=39.5%)\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x648 with 3 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = P.subplots(1, 1)\n",
"\n",
"cnt = ax.contourf(mus, sigs, chi2ts/(n-2), \n",
" cmap='gist_heat_r', levels=N.arange(11)/2, extend='max')\n",
"cntf = ax.contour(mus, sigs, chi2s/(n-2), \n",
" cmap='gray', levels=N.arange(2.7,3.4,0.1), extend='max')\n",
"ax.clabel(cntf, fmt='%.1f')\n",
"ax.set(xlabel=\"µ\", ylabel=\"σ\")\n",
"cbf = fig.colorbar(cntf)\n",
"cbf.ax.set_ylabel('Total χ²/DoF')\n",
"cb = fig.colorbar(cnt)\n",
"cb.ax.set_ylabel('χ²/DoF')\n",
"\n",
"ax.plot([mu0], [sig0], 'y*', ms=10, label=f\"Truth: µ={mu0:.1f}, σ={sig0:.1f}\")\n",
"ax.errorbar([mup], [std], xerr=[dmup], yerr=[dstd], fmt='rs', ecolor='r',\n",
" label=f\"Plain: µ={mup:.3f}±{dmup:.3f}, σ={std:.3f}±{dstd:.3f}\")\n",
"(mu, dmu), (sig, dsig) = musig(y, dx, verbose=True)\n",
"ax.errorbar([mu], [sig], xerr=[dmu], yerr=[dsig], fmt='g*', ecolor='g',\n",
" label=f\"MLE: µ={mu:.3f}±{dmu:.3f}, σ={sig:.3f}±{dsig:.3f}\")\n",
"\n",
"ax.legend(loc=2, numpoints=1, frameon=False);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Case without intrinsic dispersion (*x*)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minuit: χ² = 486.71, δχ² = 4.87 at µ = -0.001 ± 0.035, σ = 0.000 ± 0.106 (DoF=498, p=63.3%)\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x648 with 3 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"chi2ts = N.array([ [ chi2(mu,sig, x, dx) for mu in mus ] for sig in sigs ])\n",
"chi2ds = N.array([ [ delta_chi2(sig, dx) for mu in mus ] for sig in sigs ])\n",
"chi2s = chi2ts + chi2ds\n",
"\n",
"fig, ax = P.subplots(1, 1)\n",
"\n",
"cnt = ax.contourf(mus, sigs, chi2ts/(n-2), \n",
" cmap='gist_heat_r', levels=N.arange(0, 2.1, 0.2), extend='max')\n",
"cntf = ax.contour(mus, sigs, chi2s/(n-2), \n",
" cmap='gray', levels=N.arange(0.8, 2.1, 0.2), extend='max')\n",
"ax.clabel(cntf, fmt='%.1f')\n",
"ax.set(xlabel=\"µ\", ylabel=\"σ\")\n",
"cbf = fig.colorbar(cntf)\n",
"cbf.ax.set_ylabel('Total χ²/DoF')\n",
"cb = fig.colorbar(cnt)\n",
"cb.ax.set_ylabel('χ²/DoF')\n",
"\n",
"ax.plot([mu0], [0], 'y*', ms=10, label=f\"Truth: µ={mu0:.1f}, σ={0:.1f}\")\n",
"\n",
"mup = N.average(x) # Sample mean\n",
"var = N.var(x, ddof=1) # Sample variance\n",
"dvar2 = 2*var**2/len(x) # Error on var**2 in normal approximation\n",
"std = N.sqrt(var) # Sample stddev\n",
"dmup = std/N.sqrt(len(x)) # Error on sample mean\n",
"dstd = N.sqrt(dvar2)/(2*std) # Error on stddev in normal approximation\n",
"ax.errorbar([mup], [std], xerr=[dmup], yerr=[dstd], fmt='rs', ecolor='r',\n",
" label=f\"Plain: µ={mup:.3f}±{dmup:.3f}, σ={std:.3f}±{dstd:.3f}\")\n",
"\n",
"(mu, dmu), (sig, dsig) = musig(x, dx, verbose=True)\n",
"ax.errorbar([mu], [sig], xerr=[dmu], yerr=[dsig], fmt='g*', ecolor='g',\n",
" label=f\"MLE: µ={mu:.3f}±{dmu:.3f}, σ={sig:.3f}±{dsig:.3f}\")\n",
"\n",
"ax.legend(loc=2, numpoints=1, frameon=False);"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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