{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "**This is a fixed-text formatted version of a Jupyter notebook**\n", "\n", "- Try online [![Binder](https://static.mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/master?urlpath=lab/tree/spectrum_analysis.ipynb)\n", "- You can contribute with your own notebooks in this\n", "[GitHub repository](https://github.com/gammapy/gammapy/tree/master/docs/tutorials).\n", "- **Source files:**\n", "[spectrum_analysis.ipynb](../_static/notebooks/spectrum_analysis.ipynb) |\n", "[spectrum_analysis.py](../_static/notebooks/spectrum_analysis.py)\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Modeling and fitting\n", "\n", "\n", "## Prerequisites\n", "\n", "- Knowledge of spectral analysis to produce 1D On-Off datasets, [see the following tutorial](spectrum_analysis.ipynb)\n", "- Reading of pre-computed datasets [see the MWL tutorial](analysis_mwl.ipynb)\n", "- General knowledge on statistics and optimization methods\n", "\n", "## Proposed approach\n", "\n", "This is a hands-on tutorial to `~gammapy.modeling`, showing how the model, dataset and fit classes work together. As an example we are going to work with HESS data of the Crab Nebula and show in particular how to :\n", "- perform a spectral analysis\n", "- use different fitting backends\n", "- acces covariance matrix informations and parameter errors\n", "- compute likelihood profile\n", "- compute confidence contours\n", "\n", "See also: [Models gallery tutorial](models.ipynb) and `docs/modeling/index.rst`.\n", "\n", "\n", "## The setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from astropy import units as u\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as st\n", "from gammapy.modeling import Fit\n", "from gammapy.datasets import Datasets, SpectrumDatasetOnOff\n", "from gammapy.modeling.models import LogParabolaSpectralModel, SkyModel\n", "from gammapy.visualization.utils import plot_contour_line\n", "from itertools import combinations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model and dataset\n", "\n", "First we define the source model, here we need only a spectral model for which we choose a log-parabola" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "crab_spectrum = LogParabolaSpectralModel(\n", " amplitude=1e-11 / u.cm ** 2 / u.s / u.TeV,\n", " reference=1 * u.TeV,\n", " alpha=2.3,\n", " beta=0.2,\n", ")\n", "\n", "crab_spectrum.alpha.max = 3\n", "crab_spectrum.alpha.min = 1\n", "crab_model = SkyModel(spectral_model=crab_spectrum, name=\"crab\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data and background are read from pre-computed ON/OFF datasets of HESS observations, for simplicity we stack them together.\n", "Then we set the model and fit range to the resulting dataset." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "datasets = []\n", "for obs_id in [23523, 23526]:\n", " dataset = SpectrumDatasetOnOff.from_ogip_files(\n", " f\"$GAMMAPY_DATA/joint-crab/spectra/hess/pha_obs{obs_id}.fits\"\n", " )\n", " datasets.append(dataset)\n", "\n", "dataset_hess = Datasets(datasets).stack_reduce(name=\"HESS\")\n", "\n", "# Set model and fit range\n", "dataset_hess.models = crab_model\n", "e_min = 0.66 * u.TeV\n", "e_max = 30 * u.TeV\n", "dataset_hess.mask_fit = dataset_hess.counts.geom.energy_mask(e_min, e_max)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting options\n", "\n", "\n", "\n", "First let's create a `Fit` instance:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "fit = Fit([dataset_hess], store_trace=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default the fit is performed using MINUIT, you can select alternative optimizers and set their option using the `optimize_opts` argument of the `Fit.run()` method. In addition we have specified to store the trace of parameter values of the fit.\n", "\n", "Note that, for now, covaraince matrix and errors are computed only for the fitting with MINUIT. However depending on the problem other optimizers can better perform, so somethimes it can be usefull to run a pre-fit with alternative optimization methods.\n", "\n", "For the \"scipy\" backend the available options are desribed in detail here: \n", "https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "No covariance estimate - not supported by this backend.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 158 ms, sys: 1.25 ms, total: 159 ms\n", "Wall time: 159 ms\n" ] } ], "source": [ "%%time\n", "scipy_opts = {\"method\": \"L-BFGS-B\", \"options\": {\"ftol\": 1e-4, \"gtol\": 1e-05}}\n", "result_scipy = fit.run(backend=\"scipy\", optimize_opts=scipy_opts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the \"sherpa\" backend you can choose the optimization algorithm between method = {\"simplex\", \"levmar\", \"moncar\", \"gridsearch\"}. \n", "Those methods are described and compared in detail on http://cxc.cfa.harvard.edu/sherpa/methods/index.html. \n", "The available options of the optimization methods are described on the following page https://cxc.cfa.harvard.edu/sherpa/methods/opt_methods.html" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "No covariance estimate - not supported by this backend.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 362 ms, sys: 5.7 ms, total: 368 ms\n", "Wall time: 370 ms\n" ] } ], "source": [ "%%time\n", "sherpa_opts = {\"method\": \"simplex\", \"ftol\": 1e-3, \"maxfev\": int(1e4)}\n", "results_simplex = fit.run(backend=\"sherpa\", optimize_opts=sherpa_opts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the \"minuit\" backend see https://iminuit.readthedocs.io/en/latest/reference.html for a detailed description of the available options. If there is an entry ‘migrad_opts’, those options will be passed to [iminuit.Minuit.migrad](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.migrad). Additionnaly you can set the fit tolerance using the [tol](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.tol\n", ") option. The minimization will stop when the estimated distance to the minimum is less than 0.001*tol (by default tol=0.1). The [strategy](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.strategy) option change the speed and accuracy of the optimizer: 0 fast, 1 default, 2 slow but accurate. If you want more reliable error estimates, you should run the final fit with strategy 2.\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 107 ms, sys: 1.92 ms, total: 109 ms\n", "Wall time: 109 ms\n" ] } ], "source": [ "%%time\n", "minuit_opts = {\"tol\": 0.001, \"strategy\": 1}\n", "result_minuit = fit.run(backend=\"minuit\", optimize_opts=minuit_opts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit quality assessment\n", "\n", "There are various ways to check the convergence and quality of a fit. Among them:\n", "\n", "- Refer to the automatically-generated results dictionary" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : scipy\n", "\tmethod : L-BFGS-B\n", "\tsuccess : True\n", "\tmessage : b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n", "\tnfev : 60\n", "\ttotal stat : 30.35\n", "\n" ] } ], "source": [ "print(result_scipy)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : sherpa\n", "\tmethod : simplex\n", "\tsuccess : True\n", "\tmessage : Optimization terminated successfully\n", "\tnfev : 135\n", "\ttotal stat : 30.35\n", "\n" ] } ], "source": [ "print(results_simplex)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : minuit\n", "\tmethod : minuit\n", "\tsuccess : True\n", "\tmessage : Optimization terminated successfully.\n", "\tnfev : 39\n", "\ttotal stat : 30.35\n", "\n" ] } ], "source": [ "print(result_minuit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Check the trace of the fit e.g. in case the fit did not converge properly" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "Table length=39\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
total_statcrab.spectral.amplitudecrab.spectral.alphacrab.spectral.beta
float64float64float64float64
30.349530528486243.8122426567655013e-112.1957469632607970.22648270775624538
30.3510341440583533.822242656765501e-112.1957469632607970.22648270775624538
30.3510021829727143.8022426567655015e-112.1957469632607970.22648270775624538
30.3495472402856453.813242656765501e-112.1957469632607970.22648270775624538
30.3495435693018583.811242656765501e-112.1957469632607970.22648270775624538
30.370145276360093.8122426567655013e-112.2080054788741340.22648270775624538
30.3707431868993573.8122426567655013e-112.1834577827489220.22648270775624538
30.3497324900103543.8122426567655013e-112.1969742264672730.22648270775624538
30.3497468299198453.8122426567655013e-112.19451939340137250.22648270775624538
30.3495366891642143.8122426567655013e-112.19597900049804370.22648270775624538
............
30.349538056083343.8122170725955735e-112.1957554196278170.22635140580397067
30.349530752787823.812358837258474e-112.1957554196278170.22648881542336197
30.3495307362047133.812075307932674e-112.1957554196278170.22648881542336197
30.3495307856020283.8122170725955735e-112.195801827878430.22648881542336197
30.3495307033490573.8122170725955735e-112.1957090109387970.22648881542336197
30.3495307175463153.8122170725955735e-112.1957554196278170.22651629734724024
30.3495307713953443.8122170725955735e-112.1957554196278170.22646133349948372
30.3495357930781153.812925895910074e-112.19598745649473060.22648881542336197
30.349537136883193.812925895910074e-112.1957554196278170.2266262250427533
30.349559344877233.8122170725955735e-112.19598745649473060.2266262250427533
" ], "text/plain": [ "\n", " total_stat crab.spectral.amplitude ... crab.spectral.beta\n", " float64 float64 ... float64 \n", "------------------ ----------------------- ... -------------------\n", " 30.34953052848624 3.8122426567655013e-11 ... 0.22648270775624538\n", "30.351034144058353 3.822242656765501e-11 ... 0.22648270775624538\n", "30.351002182972714 3.8022426567655015e-11 ... 0.22648270775624538\n", "30.349547240285645 3.813242656765501e-11 ... 0.22648270775624538\n", "30.349543569301858 3.811242656765501e-11 ... 0.22648270775624538\n", " 30.37014527636009 3.8122426567655013e-11 ... 0.22648270775624538\n", "30.370743186899357 3.8122426567655013e-11 ... 0.22648270775624538\n", "30.349732490010354 3.8122426567655013e-11 ... 0.22648270775624538\n", "30.349746829919845 3.8122426567655013e-11 ... 0.22648270775624538\n", "30.349536689164214 3.8122426567655013e-11 ... 0.22648270775624538\n", " ... ... ... ...\n", " 30.34953805608334 3.8122170725955735e-11 ... 0.22635140580397067\n", " 30.34953075278782 3.812358837258474e-11 ... 0.22648881542336197\n", "30.349530736204713 3.812075307932674e-11 ... 0.22648881542336197\n", "30.349530785602028 3.8122170725955735e-11 ... 0.22648881542336197\n", "30.349530703349057 3.8122170725955735e-11 ... 0.22648881542336197\n", "30.349530717546315 3.8122170725955735e-11 ... 0.22651629734724024\n", "30.349530771395344 3.8122170725955735e-11 ... 0.22646133349948372\n", "30.349535793078115 3.812925895910074e-11 ... 0.22648881542336197\n", " 30.34953713688319 3.812925895910074e-11 ... 0.2266262250427533\n", " 30.34955934487723 3.8122170725955735e-11 ... 0.2266262250427533" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_minuit.trace" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Check that the fitted values and errors for all parameters are reasonable, and no fitted parameter value is \"too close\" - or even outside - its allowed min-max range" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "Table length=4\n", "
\n", "\n", "\n", "\n", "\n", "\n", "\n", "
namevalueunitminmaxfrozenerror
str9float64str14float64float64boolfloat64
amplitude3.8122e-11cm-2 s-1 TeV-1nannanFalse3.546e-12
reference1.0000e+00TeVnannanTrue0.000e+00
alpha2.1958e+001.000e+003.000e+00False2.626e-01
beta2.2649e-01nannanFalse1.397e-01
" ], "text/plain": [ "\n", " name value unit min max frozen error \n", " str9 float64 str14 float64 float64 bool float64 \n", "--------- ---------- -------------- --------- --------- ------ ---------\n", "amplitude 3.8122e-11 cm-2 s-1 TeV-1 nan nan False 3.546e-12\n", "reference 1.0000e+00 TeV nan nan True 0.000e+00\n", " alpha 2.1958e+00 1.000e+00 3.000e+00 False 2.626e-01\n", " beta 2.2649e-01 nan nan False 1.397e-01" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_minuit.parameters.to_table()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Plot fit statistic profiles for all fitted prameters, using `~gammapy.modeling.Fit.stat_profile()`. For a good fit and error estimate each profile should be parabolic" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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dilJK9UpBnQRGD0hkcEocC1fvcTsUpZTqlYI6CYgIs/M8fLylgv012iSklFLegjoJAMzK89DUbHhjrTYJKaWUt6BPAqM8iQxJi+e1NbvdDkUppXqdoE8CLU1Cy7ZUUHao3u1wlFKqV/FrEhCRviLyoohsFJENInKaiKSIyNsiUmS/J/szBrCahJoNvKFnCSml1DH8vSfwIPCGMSYXGAtsAOYBi40xOcBi+7tfjcjswwkZCSz8QpuElFLKyW9JQEQSgbOAxwGMMQ3GmIPAHGCB3dsC4Hx/xeCIhVljPHxSsp/Sqjp//5xSSgUMf+4JDAXKgCdF5DMReUxE4oFMY8weAPs9o7WBReQ6ESkQkYKysrLjDmZ2ngdjYNEavWZAKaVa+DMJRAAnA381xowDauhE048xZr4xJt8Yk5+e3u5zkn2Sk9mHEZl9eE2TgFJKHeXPJLAT2GmMWWF/fxErKewTEQ+A/V7qxxiOMTvPw8qSA+ypPNxTP6mUUr2a35KAMWYvsENERtidzgXWA68Cc+1uc4FX/BWDt1l5HgAWrdGzhJRSCvx/dtCNwLMisho4CfgdcDcwTUSKgGn29x4xND2BUZ5EFq7Ws4SUUgqsdnu/McZ8DuS3UnSuP3+3PbPyPPzpzU3sPFDLwOQ4t8JQSqleIeivGPY2+2iTkB4gVkqpkEsCWanxjBmQxGt6e2mllAq9JADW3sAXOyvZsb/W7VCUUspVIZkEzhtjNQnpw2aUUqEuJJPAoJQ4ThrUV28vrZQKeSGZBMBqElq7q4qS8hq3Q1FKKdeEbBJoaRLS20gopUJZyCaB/n1jOSUrmf/q7aWVUiEsZJMAwKwxHjbuPcTm0mq3Q1FKKVeEdBI4b4wHEfSaAaVUyArpJNAvKYZTs1L0LCGlVMgK6SQAMHush8J91RTuO+R2KEop1eNCPgnMGN2PMNELx5RSoSnkk0BGnxgmDEll4erdGGPcDkcppXpUyCcBsG4vXVxWw8a92iSklAotmgSAmUebhPQAsVIqtGgSAFITojl9WBqvrd6jTUJKqZCiScA2O89DSUUt63ZXuR2KUkr1GE0Ctq+d2I+IMNGzhJRSIUWTgC05PopJJ6Tx2ho9S0gpFTo0CTjMyvOwY/9hVu+sdDsUpZTqEZoEHL42qh+R4aK3l1ZKhQy/JgERKRGRNSLyuYgU2N1SRORtESmy35P9GUNnJMVFcmZOup4lpJQKGT2xJzDFGHOSMSbf/j4PWGyMyQEW2997jVljPOw6eJjPdhx0OxSllPI7N5qD5gAL7M8LgPNdiKFN007MJCo8jIVfaJOQUir4+TsJGOAtEVklItfZ3TKNMXsA7PeM1gYUketEpEBECsrKyvwc5pcSYyI5a3g6i9bsoblZm4SUUsHN30lgkjHmZGAm8EMROcvXAY0x840x+caY/PT0dP9F2Iqvj/Wwt6qOVdsP9OjvKqVUT/NrEjDG7LbfS4GXgfHAPhHxANjvpf6MoSvOHZlJdESYPnFMKRX0/JYERCReRPq0fAamA2uBV4G5dm9zgVf8FUNXJURHMGVEBq+t2UOTNgkppYKYP/cEMoEPReQL4BPgNWPMG8DdwDQRKQKm2d97nVl5HsoO1bOyZL/boSillN9E+GvExphiYGwr3SuAc/31u93l3JEZxERaTUITh6a6HY5SSvmFXjHchrioCM7NzeT1tXtobGp2OxyllPILTQLtmJ3noby6gU+2apOQUio4aRJox+QRGcRFhfNfPUtIKRWkNAm0IzYqnKkjM3lDm4SUUkFKk0AHZuV5OFB7hI+3VLgdilJKdTtNAh04e3g6CdEReuGYUiooaRLoQExkONNGZfLGur00NGqTkFIquGgS8MHsPA+Vh4/w0ZZyt0NRSqlupUnAB2fkpNEnJkJvL62UCjqaBHwQHRHO9FH9eGv9Xuobm9wORymluo0mAR/NHuvhUF0jHxRqk5BSKnhoEvDRpGFpJMVG6kPolVJBRZOAj6IiwphxYj/eXr+PuiPaJKSUCg6aBDphVp6H6vpGlhb23OMulVLKnzQJdMLpw1JJjovUC8eUUkFDk0AnRISHMWO0h3c27ONwgzYJKaUCnyaBTvp6nofahiaWbOp1j0ZWSqlO0yTQSeOHpJCWEMVCbRJSSgUBTQKdFBEexszRHhZv3EdtQ6Pb4Sil1HHRJNAFs/I81B1pZvEGbRJSSgU2TQJdcGp2Chl9ovUsIaVUwNMk0AXhYcJ5Yzy8t6mU6nptElJKBS6/JwERCReRz0Rkof09RUTeFpEi+z3Z3zH4w+w8D/WNzSzesM/tUJRSqst6Yk/gJmCD4/s8YLExJgdYbH8POCcPTqZfYgz/1dtLK6UCmF+TgIgMBGYBjzk6zwEW2J8XAOf7MwZ/CQsTZuV5eL+wjKq6I26Ho5RSXeLvPYEHgNsA53MZM40xewDs9ww/x+A3s/I8NDQ18/Y6bRJSSgUmvyUBEZkNlBpjVnVx+OtEpEBECsrKeucN28YN6suAvrF6e2mlVMDy557AJOAbIlICPAecIyLPAPtExANgv7d6sr0xZr4xJt8Yk5+enu7HMLtOxGoS+qCojMpabRJSSgUevyUBY8ztxpiBxphs4FLgXWPMFcCrwFy7t7nAK/6KoSfMGuPhSJPhzfV73Q5FKaU6zY3rBO4GpolIETDN/h6w8gYmMSglVi8cU0oFpIie+BFjzBJgif25Aji3J363J4gIs8b057EPijlQ00ByfJTbISmllM/0iuFuMDvPQ2Oz4c112iSklAosmgS6wYn9E8lOjdPbSyulAk6bSUBEskQkyfF9iog8KCI/ERFt83AQEWbn9efjLeVUVNe7HY5SSvmsvT2B54F4ABE5CXgB2A6MBR72f2iBZVaeh2YDr6/VJiGlVOBoLwnEGmN225+vAJ4wxtwLfBcY7/fIAkxuvz4MS4/Xs4SUUgGlvSQgjs/nYN3sDWNMc+u9hzbrwrH+rNhaQemhOrfDUUopn7SXBN4TkedF5EEgGXgXjl7l29ATwQWa2XaT0BvaJKSUChDtJYGbgJeAEuAMY0zLfRH6AT/zc1wBaXhmH4ZnJrBQby+tlAoQ7V0s9qYxZrp3R2PMZ36MJ+DNzuvP/e8Usreyjn5JMW6Ho5RS7WpvT6B33rWtl5uV58EYWKR3FlVKBYD29gSSROSbbRUaY17yQzwBb1h6AiM9iby2Zg9XnzHE7XCUUqpd7SYBYDbHniXUwmAdL1CtmJ3n4U9vbmL3wcP07xvrdjhKKdWm9pLANmPM1T0WSRCZnefhnrc28dTHJdxx3ki3w1FKqTb5ep2A6oSs1Hi+OW4gT31cws4DtW6Ho5RSbWovCVzZY1EEoVunD0eAe98qdDsUpZRqU5tJwBizticDCTb9+8Zy9RlDePmzXazdVel2OEop1Sq9lbQffX/yMJLjIvn96xswxrgdjlJKfYUmAT9KjInkx+fm8NHmCpYWlrkdjlJKfUWHSUBEckTkRRFZLyLFLa+eCC4YXD4hi8Epcfx+0UaamnVvQCnVu/iyJ/Ak8FegEZgC/B142p9BBZOoiDBumzGCTfsO8e9Pd7odjlJKHcOXJBBrjFkMiDFmmzHmTqxbSysfzRrjYeygvtz3ViGHG5rcDkcppY7yJQnUiUgYUCQiPxKRC4AMP8cVVESEO2bmsreqjic+2up2OEopdZQvSeBmIA74MXAK1lPGrvJnUMFowtBUpo7M5K9LtuhziJVSvYYvSSDbGFNtjNlpjPmuMeZbwOCOBhKRGBH5RES+EJF1IvJru3uKiLwtIkX2e/LxViJQzJuZy+EjTTz07ma3Q1FKKcC3JHC7j9281QPnGGPGAicBM0RkIjAPWGyMycF6ZOU8X4MNdCdkJHDJqYN4Zvk2tpbXuB2OUkq1nQREZKaIPAQMEJE/O15PYZ0p1C5jqba/RtovA8wBFtjdFwDnH08FAs3NU3OIigjjT29udDsUpZRqd09gN7AKqLPfW16vAl/zZeQiEi4inwOlwNvGmBVApjFmD4D93upBZhG5TkQKRKSgrCx4LrTK6BPDdWcNZdGavXy6/YDb4SilQpx0dDsDEYkwxnS45d/BOPoCLwM3Ah8aY/o6yg4YY9o9LpCfn28KCgqOJ4Repaa+kcn3LCErJY4XbjgNEb1hq1Kq+4nIKmNMfnv9tNcctEZEVgOfishq71dnAjHGHASWADOAfSLisX/Dg7WXEFLioyO4ZepwCrYd4K31+9wORykVwtp7qMzs4xmxiKQDR4wxB0UkFpgK/AGrOWkucLf9/srx/E6gujh/II9/WMwfXt/IObkZRIbrbZyUUj2vvVtJb2t52Z1y7M+lwH4fxu0B3rP3GlZiHRNYiLXynyYiRcA0+3vIiQgPY97MkRSX1/Dcyh1uh6OUClHt7QkAICLfA64DUoBhwEDgb8C57Q1njFkNjGule0VHw4aKqSMzGD8khQffKeSCcQNIiO7w71BKqW7lSxvED4FJQBWAMaYIvW1EtxAR7jhvJOXVDcxfusXtcJRSIciXJFBvjGlo+SIiEVjn+6tucNKgvszK8/DoB1vZV1XndjhKqRDjSxJYKiJ3ALEiMg14Afivf8MKLbd9bQSNzc088I4+j1gp1bN8SQLzgDJgDXA9sAj4uT+DCjVZqfFcMTGLf63cQeG+Q26Ho5QKIR0mAWNMM/Af4AfGmAuNMY8afWBut/vxOTnER0fwh9f1dhJKqZ7T3sViIiJ3ikg5sBHYJCJlIvLLngsvdCTHR/GDySeweGMpy7ZUuB2OUipEtLcncDPWWUGnGmNSjTEpwARgkojc0iPRhZjvTsqmf1IMv399A836PGKlVA9oLwlcBVxmjDn6KCxjTDH6UBm/iYkM59bpI1i9s5KFa/a4HY5SKgS0lwQijTHl3h2NMWVYt4VWfnD+uAGM9CTyxzc2Ut+ozyNWSvlXe0mgoYtl6jiEhwm3z8xl54HDPL1sW8cDKKXUcWgvCYwVkapWXoeAMT0VYCg6a3g6Z+ak8dC7m6msPeJ2OEqpINbeDeTCjTGJrbz6GGO0OcjP5s3MparuCA8v0ecRK6X8R+9f3Eud2D+JC8YN4MmPS9h5oNbtcJRSQUqTQC/20+kjALj3Lb2dhFLKPzQJ9GL9+8Zy9aQhvPzZLtbuqnQ7HKVUENIk0Mv9YMowkuMi+f3rG9C7dSilupsmgV4uMSaSG8/J4aPNFSwtLHM7HKVUkNEkEACumJjF4JQ47n59I016OwmlVDfSJBAAoiLCuG3GCDbuPcRLn+50OxylVBDRJBAgZo3xMHZgEve+VcjhBr2dhFKqe2gSCBAtzyPeW1XHEx9t7XgApZTygSaBADJhaCpTR2by1yVbqKiudzscpVQQ8FsSEJFBIvKeiGwQkXUicpPdPUVE3haRIvs92V8xBKN5M0dQ29DIQ+/q7SSUUsfPn3sCjcCtxpiRwETghyIyCuuZxYuNMTnAYvu78tEJGX245NTBPLN8GyXlNW6Ho5QKcH5LAsaYPcaYT+3Ph4ANwABgDrDA7m0BcL6/YghWt0zLISoijD++qc8jVkodnx45JiAi2cA4YAWQaYzZA1aiADLaGOY6ESkQkYKyMr1IyimjTwzfO3Moi9bs5dPtB9wORykVwPyeBEQkAfg3cLMxpsrX4Ywx840x+caY/PT0dP8FGKCuO2soaQnR/H6R3k5CKdV1fk0CIhKJlQCeNca8ZHfeJyIeu9wDlPozhmAVHx3BLdNyWFlygLfW73M7HKVUgPLn2UECPA5sMMbc5yh6FZhrf54LvOKvGILdJfmDGJYezx9e38iRpma3w1FKBSB/7glMAq4EzhGRz+3XecDdwDQRKQKm2d9VF0SEhzFv5kiKy2t4buUOt8NRSnWzreU1fm/ujfDXiI0xHwLSRvG5/vrdUDN1ZAbjs1N48J1CLhg3gIRov/2lSqkesq+qjnvf2sQLq3by2FX5nDsy02+/pVcMBzgR4fbzcimvbmD++8Vuh6OUOg6HG5r48+IiptyzhJc/28X3zhxKfnaKX39TNxuDwLjByczK8/Do+8VcPmEwmYkxboeklOqE5mbDfz7fxR/f2MTeqjrOG9OP/5mRS1ZqvN9/W/cEgsRtXxtBY3MzD7yjzyNWKpCsKCJc9NAAABH/SURBVK5gzv99xE+e/4KMxGheuOE0Hr78lB5JAKB7AkEjKzWeKyZmseDjEq6eNISczD5uh6SUakdJeQ13v76RN9btxZMUwwOXnMQ3xvYnLKytQ6n+oUkgiNx4Tg4vFuzkF6+s5e9XTyAqQnf0lOptKmuP8NC7RSxYVkJkeBg/nT6ca84YSmxUuCvxaBIIIinxUfzy66P4fy+u5qbnPuOhy8YREa6JQKne4EhTM88u38YDi4uoPHyES/IH8ZNpw8lw+RieJoEgc1H+IKrqGrlr4Xpue3E191w0tsd3L5VSXzLGsHhDKb9btIHi8homnZDKz84bxaj+iW6HBmgSCErXnDGE2vpG7n27kNiocH5z/misC7iVUj1p3e5KfvvaBj7eUsHQ9Hie+E4+U0Zk9KrlUZNAkPrROSdQ3dDII0uLiY+O4PaZub1qxlMqmJVW1XGPfbFX39hIfv2NE/n2hMFE9sLmWU0CQUpEmDcjl9r6Jua/X0x8VAQ3Tc1xOyylgtrhhiYe/aCYvy3dwpGmZq49Ywg/mpJDUlyk26G1SZNAEBMRfv2NE6ltaOL+dwqJiwrne2cNdTsspYKO98VeM0f3Y97MnrnY63hpEghyYWHCH741hrojTfx20QZio8K5YmKW22EpFTRWFFfwm9c2sGZXJXkDk/jzZeMYP8S/t3roTpoEQkBEeBj3X3ISh4808YtX1hIfHc4F4wa6HZZSAc37Yq/7LxnLnLEDAu5sPE0CISIqIoyHLz+Z7z65kp++sJrYyHBmjPa4HZZSAcf7Yq9bpw3n2jPdu9jreGkSCCExkeE8NjefKx9fwY3//IxHrwpn8ohWH/GslPLifbHXxacM4tbp7l/sdbx63/lKyq/ioyN48rvjycnow/VPr2J5cYXbISnVqxljeGf9Pr52//vc+d/1jPIk8tqNZ/KHC/MCPgGAJoGQlBQbydPXjGdQShzXPLWSz7YfcDskpXqlZVsquGT+cq79ewEIPD43n2evndBrrvbtDpoEQlRqQjTPXjuB1IRo5j7xCet3V7kdklK9xrItFVzyyDIue3Q5JeU1/O+cE3nz5rM4d2Rm0F10Kf5+fmV3yM/PNwUFBW6HEZR27K/l4keW0dDYzL+uP40TMhLcDkkp1ywvruCBdwpZXryfjD7RfH/yMC4bP5iYyMA86Csiq4wx+e32o0lAbSmr5pJHlhERFsYLN5zGoJQ4t0NSqketKK7gfnvln94nmh8E+Mq/hSYB5bMNe6q4dP5yEmMjeOH60+mXFPgHvJTqyIriCh54p4hlxRWk94nm+2cP49sTAn/l30KTgOqUL3Yc5PLHVpCZGM2/rj+NtIRot0NSyi8+2bqfB94p5OMtwbnyb+FLEvDbgWEReUJESkVkraNbioi8LSJF9nuyv35fdd7YQX15fG4+uw4e5qrHP6Gy9ojbISnVrVaW7Ofyx5Zz8SPLKNxXzS9mj+KD26Zw9RlDgi4B+MqfZwc9Bczw6jYPWGyMyQEW299VLzJhaCqPXJlPUekhvvPUJ1TXN7odklLHrWXlf9HflrFpbzU/nzWSD26bwjUhvPJv4dfmIBHJBhYaY0bb3zcBk40xe0TEAywxxozoaDzaHNTz3li7lx/+41NOzU7mqe+OD/kFRQWmgpL9PPBOER9uLictIZobzh7K5ROyAvYWD53lS3NQT982ItMYswfATgR6z4Jeasboftx70Vhuef5zbnhmFfOvzNcH16uAsWqbtfL/oKictIQofj5rZEit/Duj1947SESuA64DGDx4sMvRhKbzxw3g8JEmbn9pDTf/6zP+fKk+uF71bt4r/5+dN5LLJw4mLqrXrupc19NTZp+IeBzNQaVt9WiMmQ/MB6s5qKcCVMe6bPxgauob+c1rG4iJXM09F+qD61Xvs2rbAR54p5APispJjdeVf2f09BR6FZgL3G2/v9LDv6+64Nozh1Lb0MR9b1tPJ7trjj64XvUOq7Yd4MHFRbxfWEZqfBR3nJfLFROzdOXfCX6bUiLyT2AykCYiO4FfYa38nxeRa4DtwEX++n3VvW485wRq7AfXx0Xpg+uVuz7dfoAH3rFW/inxUdw+M5crT9OVf1f4bYoZYy5ro+hcf/2m8h99cL3qDT6zV/5LHSv/KyZmER+tK/+u0imnfOb94Pr46HCuPVMfXK/8q7nZsLSojCc/Kjm65T9vZi5X6sq/W+gUVJ3S8uD6w0esg8VxURF8e4KevaW63/6aBl4o2MGzK7azfX8taQnR/M+MXK46TVf+3UmnpOq0iPAwHrhkHIcbCvjZf9YQGxWmD65X3cIYw+c7DvL08m0sXL2HhsZmJgxJ4bYZI5g+qp9eq+IHmgRUl0RFhPHXK05xPLg+ghmj+7kdlgpQhxuaePWLXTy9fBtrd1WREB3BpacO4oqJWQzP7ON2eEFN7yKqjktNfSNXPr6CNbsqefSqfH1wveqULWXVPLt8Oy+s2sGhukZy+/XhiolZnD9uAAna5HPceuNtI1SQaXlw/WXzl3P906v4/uRhXHPGEPrERLodmuqlGpuaeWfDPp5Zvp0PN5cTGS7MHO3hytOyyM9K1lOPe5juCahuUVFdz89eXssb6/bSNy6S688axtzT9bxt9aXSqjr++ckO/vnJdvZW1dE/KYbLJ2Zxcf4g0vvosyv8QR8qo3rcmp2V3Pf2Jt7bVEZaQjQ/nBIcj+lTXWOMYXnxfp5Zvo031+2lsdlw1vB0rpyYxTm5GYTrLUj8SpOAcs2qbfu5581ClhVX4EmK4cZzcrgofyCRegO6kFBVd4SXP7UO9G4urSYpNpKL8wdy+YQsstPi3Q4vZGgSUK77eHM597y1iU+3H2RwShw3nZvD+eMG6BZgkFq/u4pnVmzjP5/torahibEDk7hiYhZfH9tf9wZdoElA9QrGGJZsKuOetzaxbncVw9LjuWXacM4b7dE7kgaB+sYm3li7l6eXbaNg2wGiI8L4xtj+XDExi7GD+rodXkjTJKB6FWMMb67by31vF1K4r5rcfn24dfoIpo7M0DNCAtCO/bX845PtPL9yBxU1DWSnxnHFxCwuPGUgfeOi3A5PoUlA9VJNzYaFq3dz/9uFlFTUMnZgErdOH8GZOWmaDHq5pmbD+0VlPLNsG+9uKkWAqSMzufK0LCYNS9M9u15Gk4Dq1Rqbmnnp0108uLiIXQcPMz47hVunD2fC0FS3Q1MOB2sbWFpYxpJNZSwtLGN/TQNpCdFcNn4Ql40fTP++sW6HqNqgSUAFhPrGJp5fuYOH3t1M6aF6zsxJ4yfThjNucLLboYUkYwzr91SxZFMZ720s5dPtB2g2kBIfxdnD05k6MpNpozL1Pj4BQJOACih1R5p4Zvk2Hl6yhf01DUwdmcEt04ZzYv8kt0MLetX1jXxYVM6STaW8t6mUfVX1AIwZkMSUEelMyc0gb2BfPasrwGgSUAGpur6RBR+X8MjSLVTVNTJrjIdbpuVwQobeSKy7GGMoLq/hvY3WSv+Trfs50mToEx3BmcPTmDwig8nD08lIjHE7VHUcNAmogFZ5+AiPf1DM4x9u5fCRJs4/aQA3Tc0hK1UvNuqKuiNNLC+usFf8ZWzfXwvA8MwEpozIYPKIDPKzk/WCviCiSUAFhf01DTyydAsLlpXQ2GS4KH8gPzonhwF6QLJDOw/U8t6mMpZsLOWjLeXUHWkmJjKMScPSmJxrbe0PSolzO0zlJ5oEVFAprarj4SVb+MeK7QB8e8JgfjBlGBl9tMmixZGmZgpKDrBkUynvbiylqLQagMEpcZyTm8HkEelMHJqqV++GCE0CKijtOniYv7xbxPMFO4kMF+aels1F+QMZnBIfkmeslB6qY8mmMpZsKuWDwnIO1TcSGS5MGJLKZPug7tC0eL0GIwRpElBBraS8hgcXF/Gfz3dhDIQJDEiOJTs1niFp8V++p8UzMDk2KNq6Gxqb2VdVx44DtSzfUsF7m8pYs6sSgH6JMUzJTWfyiAwmnZCmD2VRmgRUaNhaXsNn2w9QUl7D1opaSsprKCmv4VB949F+wsOEQcmxZHslhyGp8fTvG0NEL0gQjU3NlB6qZ0/lYXYfrDvmfW9lHbsr6yivrqdlkQ0TOHlwMlNyM5gyIoORnj66ta+O0WufLCYiM4AHgXDgMWPM3W7EoYLDkDRrpe5kjKGipsFKDOU1lFTUUFJey9byGj7Zup/ahqaj/UaGC4NS4hiSGm8nibijyaJ/39huOTe+udlQVl3Pnso69hw8zG77fU9lHbsrD7PnYB2lh+po9tomi48Kx9M3Fk9SDLn9EvH0jaF/Uiz9kmLIG5ik9+hRx63Hk4CIhAP/B0wDdgIrReRVY8z6no5FBS8RIS0hmrSEaPKzU44pM8ZQdqj+aHLYWm7vPVTUHD2DpkVURBiDU+LsvYe4o3sP2Wnx9EuMISxMjiacPfZWu3PF3rI1v6+qjkavNXxMZNjRFfqkE9Lo3zcGT1Ls0RW9p28MfaIjdOte+ZUbewLjgc3GmGIAEXkOmANoElA9QkTISIwhIzHmK/cpam427DtUZyWI8lo7SVjNS+8XldHQ+GWCiIkMIzU+mrLq+mO6A0SFh9EvKQZPUgzjh6TgsT87V/J94yJ1Ba9c50YSGADscHzfCUzw7klErgOuAxg8eHDPRKZCXliYWCvqpFhOH3ZsWXOzYXflYatZqcJKDBXV9WQm2it4u9nGkxRLanyU3lFTBQQ3kkBrS8ZXjk4bY+YD88E6MOzvoJTqSFiYMDA5joHJcZyRk+Z2OEp1CzdOidgJDHJ8HwjsdiEOpZQKeW4kgZVAjogMEZEo4FLgVRfiUEqpkNfjzUHGmEYR+RHwJtYpok8YY9b1dBxKKaVcuk7AGLMIWOTGbyullPqS+5dJKqWUco0mAaWUCmGaBJRSKoRpElBKqRAWEHcRFZEyYJvbcXRCGlDudhB+EKz1guCtW7DWC4K3bt1ZryxjTHp7PQREEgg0IlLQ0e1bA1Gw1guCt27BWi8I3rr1dL20OUgppUKYJgGllAphmgT8Y77bAfhJsNYLgrduwVovCN669Wi99JiAUkqFMN0TUEqpEKZJQCmlQpgmgeMgIjNEZJOIbBaRea2Ui4j82S5fLSInuxFnZ/lQr1wRWSYi9SLyUzdi7Cof6na5/V+tFpGPRWSsG3F2lg/1mmPX6XMRKRCRM9yIsys6qpujv1NFpElELuzJ+LrKh/9ssohU2v/Z5yLyS78EYozRVxdeWLfB3gIMBaKAL4BRXv2cB7yO9TS1icAKt+PupnplAKcCvwV+6nbM3Vy304Fk+/PMIPrPEvjyGGAesNHtuLurbo7+3sW6O/GFbsfdTf/ZZGChv2PRPYGuGw9sNsYUG2MagOeAOV79zAH+bizLgb4i4unpQDupw3oZY0qNMSuBI24EeBx8qdvHxpgD9tflWE++6+18qVe1sdcsQDytPNK1l/JlOQO4Efg3UNqTwR0HX+vld5oEum4AsMPxfafdrbP99DaBGLOvOlu3a7D25Ho7n+olIheIyEbgNeDqHorteHVYNxEZAFwA/K0H4zpevs6Lp4nIFyLyuoic6I9ANAl0nbTSzXvrypd+eptAjNlXPtdNRKZgJYH/8WtE3cOnehljXjbG5ALnA3f5Paru4UvdHgD+xxjT1APxdBdf6vUp1r1/xgIPAf/xRyCaBLpuJzDI8X0gsLsL/fQ2gRizr3yqm4jkAY8Bc4wxFT0U2/Ho1H9mjHkfGCYiaf4OrBv4Urd84DkRKQEuBB4WkfN7Jrwu67BexpgqY0y1/XkREOmP/0yTQNetBHJEZIiIRAGXAq969fMqcJV9ltBEoNIYs6enA+0kX+oVqDqsm4gMBl4CrjTGFLoQY1f4Uq8TRETszydjHYwMhATXYd2MMUOMMdnGmGzgReAHxhi/bDV3I1/+s36O/2w81vq62/8zV54xHAyMMY0i8iPgTawj/U8YY9aJyA12+d+wzlQ4D9gM1ALfdSteX/lSLxHpBxQAiUCziNyMdWZDlWuB+8DH/+yXQCrW1iRAo+nld6r0sV7fwtogOQIcBi5xHCjutXysW8DxsV4XAt8XkUas/+xSf/xnetsIpZQKYdocpJRSIUyTgFJKhTBNAkopFcI0CSilVAjTJKCUUiFMk4BSSoUwTQJKKRXC/j9oFlLhX8ZfBgAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "total_stat = result_minuit.total_stat\n", "\n", "for par in dataset_hess.models.parameters:\n", " if par.frozen is False:\n", " profile = fit.stat_profile(parameter=par)\n", " plt.plot(\n", " profile[f\"{par.name}_scan\"], profile[\"stat_scan\"] - total_stat\n", " )\n", " plt.xlabel(f\"{par.unit}\")\n", " plt.ylabel(\"Delta TS\")\n", " plt.title(f\"{par.name}: {par.value} +- {par.error}\")\n", " plt.show()\n", " plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Inspect model residuals. Those can always be accessed using `~Dataset.residuals()`, that will return an array in case a the fitted `Dataset` is a `SpectrumDataset` and a full cube in case of a `MapDataset`. For more details, we refer here to the dedicated fitting tutorials: [analysis_3d.ipynb](analysis_3d.ipynb) (for `MapDataset` fitting) and [spectrum_analysis.ipynb](spectrum_analysis.ipynb) (for `SpectrumDataset` fitting)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Covariance and parameters errors\n", "\n", "After the fit the covariance matrix is attached to the model. You can get the error on a specific parameter by accessing the `.error` attribute:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.26258179523184855" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crab_model.spectral_model.alpha.error" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, this step is needed to produce a butterfly plot showing the envelope of the model taking into account parameter uncertainties." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "energy_range = [1, 10] * u.TeV\n", "crab_spectrum.plot(energy_range=energy_range, energy_power=2)\n", "ax = crab_spectrum.plot_error(energy_range=energy_range, energy_power=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Confidence contours\n", "\n", "\n", "In most studies, one wishes to estimate parameters distribution using observed sample data.\n", "A 1-dimensional confidence interval gives an estimated range of values which is likely to include an unknown parameter.\n", "A confidence contour is a 2-dimensional generalization of a confidence interval, often represented as an ellipsoid around the best-fit value.\n", "\n", "Gammapy offers two ways of computing confidence contours, in the dedicated methods `Fit.minos_contour()` and `Fit.stat_profile()`. In the following sections we will describe them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An important point to keep in mind is: *what does a $N\\sigma$ confidence contour really mean?* The answer is it represents the points of the parameter space for which the model likelihood is $N\\sigma$ above the minimum. But one always has to keep in mind that **1 standard deviation in two dimensions has a smaller coverage probability than 68%**, and similarly for all other levels. In particular, in 2-dimensions the probability enclosed by the $N\\sigma$ confidence contour is $P(N)=1-e^{-N^2/2}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing contours using `Fit.minos_contour()` " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After the fit, MINUIT offers the possibility to compute the confidence confours.\n", "gammapy provides an interface to this functionnality throught the `Fit` object using the `minos_contour` method.\n", "Here we defined a function to automatize the contour production for the differents parameterer and confidence levels (expressed in term of sigma):" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def make_contours(fit, result, npoints, sigmas):\n", " cts_sigma = []\n", " for sigma in sigmas:\n", " contours = dict()\n", " for par_1, par_2 in combinations([\"alpha\", \"beta\", \"amplitude\"], r=2):\n", " contour = fit.minos_contour(\n", " result.parameters[par_1],\n", " result.parameters[par_2],\n", " numpoints=npoints,\n", " sigma=sigma,\n", " )\n", " contours[f\"contour_{par_1}_{par_2}\"] = {\n", " par_1: contour[par_1].tolist(),\n", " par_2: contour[par_2].tolist(),\n", " }\n", " cts_sigma.append(contours)\n", " return cts_sigma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can compute few contours." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 9.72 s, sys: 38.6 ms, total: 9.76 s\n", "Wall time: 9.79 s\n" ] } ], "source": [ "%%time\n", "sigma = [1, 2]\n", "cts_sigma = make_contours(fit, result_minuit, 10, sigma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we prepare some aliases and annotations in order to make the plotting nicer." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "pars = {\n", " \"phi\": r\"$\\phi_0 \\,/\\,(10^{-11}\\,{\\rm TeV}^{-1} \\, {\\rm cm}^{-2} {\\rm s}^{-1})$\",\n", " \"alpha\": r\"$\\alpha$\",\n", " \"beta\": r\"$\\beta$\",\n", "}\n", "\n", "panels = [\n", " {\n", " \"x\": \"alpha\",\n", " \"y\": \"phi\",\n", " \"cx\": (lambda ct: ct[\"contour_alpha_amplitude\"][\"alpha\"]),\n", " \"cy\": (\n", " lambda ct: np.array(1e11)\n", " * ct[\"contour_alpha_amplitude\"][\"amplitude\"]\n", " ),\n", " },\n", " {\n", " \"x\": \"beta\",\n", " \"y\": \"phi\",\n", " \"cx\": (lambda ct: ct[\"contour_beta_amplitude\"][\"beta\"]),\n", " \"cy\": (\n", " lambda ct: np.array(1e11)\n", " * ct[\"contour_beta_amplitude\"][\"amplitude\"]\n", " ),\n", " },\n", " {\n", " \"x\": \"alpha\",\n", " \"y\": \"beta\",\n", " \"cx\": (lambda ct: ct[\"contour_alpha_beta\"][\"alpha\"]),\n", " \"cy\": (lambda ct: ct[\"contour_alpha_beta\"][\"beta\"]),\n", " },\n", "]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we produce the confidence contours figures." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(16, 5))\n", "colors = [\"m\", \"b\", \"c\"]\n", "for p, ax in zip(panels, axes):\n", " xlabel = pars[p[\"x\"]]\n", " ylabel = pars[p[\"y\"]]\n", " for ks in range(len(cts_sigma)):\n", " plot_contour_line(\n", " ax,\n", " p[\"cx\"](cts_sigma[ks]),\n", " p[\"cy\"](cts_sigma[ks]),\n", " lw=2.5,\n", " color=colors[ks],\n", " label=f\"{sigma[ks]}\" + r\"$\\sigma$\",\n", " )\n", " ax.set_xlabel(xlabel)\n", " ax.set_ylabel(ylabel)\n", "plt.legend()\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing contours using `Fit.stat_surface()`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This alternative method for the computation of confidence contours, although more time consuming than `Fit.minos_contour()`, is expected to be more stable. It consists of a generalization of `Fit.stat_profile()` to a 2-dimensional parameter space. The algorithm is very simple:\n", "- First, passing two arrays of parameters values, a 2-dimensional discrete parameter space is defined;\n", "- For each node of the parameter space, the two parameters of interest are frozen. This way, a likelihood value ($-2\\mathrm{ln}\\,\\mathcal{L}$, actually) is computed, by either freezing (default) or fitting all nuisance parameters;\n", "- Finally, a 2-dimensional surface of $-2\\mathrm{ln}(\\mathcal{L})$ values is returned.\n", "Using that surface, one can easily compute a surface of $TS = -2\\Delta\\mathrm{ln}(\\mathcal{L})$ and compute confidence contours.\n", "\n", "Let's see it step by step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First of all, we can notice that this method is \"backend-agnostic\", meaning that it can be run with MINUIT, sherpa or scipy as fitting tools. Here we will stick with MINUIT, which is the default choice:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "optimize_opts = {\"backend\": \"minuit\", \"print_level\": 0}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, we can compute the confidence contour for the `alpha` and `beta` parameters of the `dataset_hess`. Here we define the parameter space:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "result = result_minuit\n", "par_1 = result.parameters[\"alpha\"]\n", "par_2 = result.parameters[\"beta\"]\n", "\n", "x = par_1\n", "y = par_2\n", "x_values = np.linspace(1.55, 2.7, 20)\n", "y_values = np.linspace(-0.05, 0.55, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we run the algorithm, by choosing `reoptimize=False` for the sake of time saving. In real life applications, we strongly recommend to use `reoptimize=True`, so that all free nuisance parameters will be fit at each grid node. This is the correct way, statistically speaking, of computing confidence contours, but is expected to be time consuming." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "stat_surface = fit.stat_surface(\n", " x, y, x_values, y_values, reoptimize=False, **optimize_opts\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to easily inspect the results, we can convert the $-2\\mathrm{ln}(\\mathcal{L})$ surface to a surface of statistical significance (in units of Gaussian standard deviations from the surface minimum):" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "# Compute TS\n", "TS = stat_surface[\"stat_scan\"] - result.total_stat" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# Compute the corresponding statistical significance surface\n", "gaussian_sigmas = np.sqrt(TS.T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that, as explained before, $1\\sigma$ contour obtained this way will not contain 68% of the probability, but rather " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# Compute the corresponding statistical significance surface\n", "# p_value = 1 - st.chi2(df=1).cdf(TS)\n", "# gaussian_sigmas = st.norm.isf(p_value / 2).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can plot the surface values together with contours:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "# We choose to plot 1 and 2 sigma confidence contours\n", "levels = [1, 2]\n", "\n", "contours = plt.contour(gaussian_sigmas, levels=levels, colors=\"white\")\n", "plt.clabel(contours, fmt=\"%.0f$\\,\\sigma$\", inline=3, fontsize=15)\n", "\n", "im = plt.imshow(\n", " gaussian_sigmas,\n", " extent=[0, len(x_values) - 1, 0, len(y_values) - 1],\n", " origin=\"lower\",\n", ")\n", "fig.colorbar(im)\n", "\n", "plt.xticks(range(len(x_values)), np.around(x_values, decimals=2), rotation=45)\n", "plt.yticks(range(len(y_values)), np.around(y_values, decimals=2));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that, if computed with `reoptimize=True`, this plot would be completely consistent with the third panel of the plot produced with `Fit.minos_contour` (try!)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, it is always remember that confidence contours are approximations. In particular, when the parameter range boundaries are close to the contours lines, it is expected that the statistical meaning of the countours is not well defined. That's why we advise to always choose a parameter space that com contain the contours you're interested in." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.0" }, "nbsphinx": { "orphan": true } }, "nbformat": 4, "nbformat_minor": 4 }