0909217206.ipynb

{
 "worksheets": [
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   "cells": [
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<center><img src=\"http://identity.stanford.edu/overview/images/emblems/SU_BlockStree_2color.png\" width=\"200\" style=\"display: inline-block\"><img src=\"http://upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Main_fermi_logo_HI.jpg/682px-Main_fermi_logo_HI.jpg\" width=\"200\" style=\"display: inline-block\"><img src=\"http://www.astro.wisc.edu/~russell/HAWCLogo.png\" width=\"200\" style=\"display: inline-block\"></center>\n<h1> Example of a spectral analysis with 3ML</h1>\n<br/>\nGiacomo Vianello (Stanford University)\n<a href=\"mailto:giacomov@stanford.edu\">giacomov@stanford.edu</a>\n\n<h2>IPython Notebook setup (only if you are using the <a href=http://ipython.org/notebook.html>IPython Notebook</a>)</h2>\nThis line will activate the support for inline display of matplotlib images:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "%matplotlib inline",
     "prompt_number": 1,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Import 3ML and see the available plug-ins</h2>"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "from threeML import *\ngetAvailablePlugins()",
     "prompt_number": 2,
     "outputs": [
      {
       "output_type": "stream",
       "text": "Plugins:\n\n* FermiLATUnbinnedLike for Fermi LAT (standard classes)        available\n* FermiGBMLike for Fermi GBM (all detectors)                   available\n",
       "stream": "stdout"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Define some general features for the source of interest</h2>\nHere we define a name and the coordinates (Equatorial J2000). In this case, we are analyzing a GRB:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "triggerName = 'bn090217206'\nra = 204.9\ndec = -8.4",
     "prompt_number": 3,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Setup the use of LAT data</h2>\nHere we instanciate a plugin to handle Fermi/LAT data:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "datadir = '/home/giacomov/science/hawc/jointLikelihood/examples/090217206/'\neventFile   = os.path.join(datadir,'gll_ft1_tr_bn090217206_v00_filt.fit')\nft2File = '/home/giacomov/FermiData/bn090217206/gll_ft2_tr_bn090217206_v00.fit'\nexpomap = os.path.join(datadir,'gll_ft1_tr_bn090217206_v00_filt_expomap.fit')\nltcube = os.path.join(datadir,'gll_ft1_tr_bn090217206_v00_filt_ltcube.fit')\nxmlModel = os.path.join(datadir,\"bn090217206_LAT_xmlmodel.xml\")\nirf = \"P7REP_TRANSIENT_V15\"\n\nfl = FermiLATUnbinnedLike(\"LAT_p7rep_transient\",eventFile,ft2File,expomap,ltcube,xmlModel,irf)",
     "prompt_number": 4,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Setup of GBM data</h2>\nHere we create 3 instances of the plugin which handle GBM data, for 3 different GBM detectors (NaI6, NaI9, BGO1). We also define the channels (or energies) we want to use, by using setActiveMeasurements():"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "obsSpectrum = os.path.join(datadir,\"bn090217206_n6_srcspectra.pha{1}\")\nbakSpectrum = os.path.join(datadir,\"bn090217206_n6_bkgspectra.bak{1}\")\nrspFile = os.path.join(datadir,\"bn090217206_n6_weightedrsp.rsp{1}\")\n#Plugin instance\nNaI6 = FermiGBMLike(\"NaI6\",obsSpectrum,bakSpectrum,rspFile)\n#Choose chanels to use\nNaI6.setActiveMeasurements(\"10.0-30.0\",\"40.0-950.0\")\n\n\nobsSpectrum = os.path.join(datadir,\"bn090217206_n9_srcspectra.pha{1}\")\nbakSpectrum = os.path.join(datadir,\"bn090217206_n9_bkgspectra.bak{1}\")\nrspFile = os.path.join(datadir,\"bn090217206_n9_weightedrsp.rsp{1}\")\n#Plugin instance\nNaI9 = FermiGBMLike(\"NaI9\",obsSpectrum,bakSpectrum,rspFile)\n#Choose chanels to use\nNaI9.setActiveMeasurements(\"10.0-30.0\",\"40.0-950.0\")\n\n\nobsSpectrum = os.path.join(datadir,\"bn090217206_b1_srcspectra.pha{1}\")\nbakSpectrum = os.path.join(datadir,\"bn090217206_b1_bkgspectra.bak{1}\")\nrspFile = os.path.join(datadir,\"bn090217206_b1_weightedrsp.rsp{1}\")\n#Plugin instance\nBGO1 = FermiGBMLike(\"BGO1\",obsSpectrum,bakSpectrum,rspFile)\n#Choose chanels to use\nBGO1.setActiveMeasurements(\"140-40000\")",
     "prompt_number": 5,
     "outputs": [
      {
       "output_type": "stream",
       "text": "Now using 117 channels out of 128\nNow using 115 channels out of 128\nNow using 124 channels out of 128",
       "stream": "stdout"
      },
      {
       "output_type": "stream",
       "text": "\n",
       "stream": "stdout"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Create a dataList object to collect all our data</h2>"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "datalist = dataList(fl,NaI6,NaI9,BGO1)",
     "prompt_number": 6,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Define our model</h2>\nWe have to define a spatial model and a spectral model for each source.\n\n<h3>Spatial model</h3>\nA source can be a point source, or an extended one (not yet implemented). Let's define our source as a point source at the position R.A., and Dec: \n"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "ps = spatialModels.PointSource(ra,dec)",
     "prompt_number": 7,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h3>Spectral model</h3>\nHere we define our spectral model. In this case we are using a Band function (Band et al., 1993), a typical spectrum for a Gamma-Ray Burst:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "band = spectralModels.Band()",
     "prompt_number": 8,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Now let us put all together and define our complete model:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "mod = ModelManager(triggerName,ps,band,datalist)",
     "prompt_number": 9,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "We can obtain all the information about the defined model by printing it:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "print(mod)",
     "prompt_number": 10,
     "outputs": [
      {
       "output_type": "stream",
       "text": "Spatial model: Point source\nFormula:\n\n",
       "stream": "stdout"
      },
      {
       "text": "<IPython.core.display.Latex at 0x4c85c90>",
       "latex": "\\begin{equation}f(RA',Dec') = \\delta(RA'-RA)\\delta(Dec'-Dec)\\end{equation}",
       "output_type": "display_data",
       "metadata": {}
      },
      {
       "output_type": "stream",
       "text": "\nCurrent parameters:\n\n",
       "stream": "stdout"
      },
      {
       "html": "<table>\n<tr><th>Name</th><th>Value</th><th>Minimum</th><th>Maximum</th><th>Delta</th><th>Status</th><th>Unit</th></tr>\n<tr><td>RA</td><td>204.9</td><td>0.0</td><td>360.0</td><td>0.01</td><td>fixed</td><td>deg</td></tr>\n<tr><td>Dec</td><td>-8.4</td><td>-90.0</td><td>90.0</td><td>0.01</td><td>fixed</td><td>deg</td></tr>\n</table>",
       "text": "<IPython.core.display.HTML at 0x1ce0b90>",
       "output_type": "display_data",
       "metadata": {}
      },
      {
       "output_type": "stream",
       "text": "\nSpectral model: Band function (Band et al. 1993)\nFormula:\n\n",
       "stream": "stdout"
      },
      {
       "text": "<IPython.core.display.Latex at 0x1cdd150>",
       "latex": "\n    \\[f(E) = \\left\\{ \\begin{eqnarray}\nK \\left(\\frac{E}{100 \\mbox{ keV}}\\right)^{\\alpha} & \\exp{\\left(\\frac{-E}{E_{c}}\\right)} & \\mbox{ if } E < (\\alpha-\\beta)E_{c} \\\\\n    K \\left[ (\\alpha-\\beta)\\frac{E_{c}}{100}\\right]^{\\alpha-\\beta}\\left(\\frac{E}{100 \\mbox{ keV}}\\right)^{\\beta} & \\exp{(\\beta-\\alpha)} & \\mbox{ if } E \\ge (\\alpha-\\beta)E_{c}\n    \\end{eqnarray}\n    \\right.\n    \\]\n    ",
       "output_type": "display_data",
       "metadata": {}
      },
      {
       "output_type": "stream",
       "text": "\nCurrent parameters:\n\n",
       "stream": "stdout"
      },
      {
       "html": "<table>\n<tr><th>Name</th><th>Value</th><th>Minimum</th><th>Maximum</th><th>Delta</th><th>Status</th><th>Unit</th></tr>\n<tr><td>alpha</td><td>-1.0</td><td>-10</td><td>10</td><td>0.1</td><td>free</td><td></td></tr>\n<tr><td>beta</td><td>-2.0</td><td>-10</td><td>10</td><td>0.1</td><td>free</td><td></td></tr>\n<tr><td>E0</td><td>500</td><td>10</td><td>100000.0</td><td>50</td><td>free</td><td>keV</td></tr>\n<tr><td>K</td><td>1</td><td>0.0001</td><td>1000.0</td><td>0.1</td><td>free</td><td></td></tr>\n</table>",
       "text": "<IPython.core.display.HTML at 0x4c85b50>",
       "output_type": "display_data",
       "metadata": {}
      },
      {
       "output_type": "stream",
       "text": "\n\n",
       "stream": "stdout"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "We can now change the values for any of the parameters of the model by using its name. For example, we can set the parameter alpha to -1.0 and set its minimum and maximum values to -10:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "mod['alpha'].setValue(-1.0)\nmod['alpha'].setBounds(-10,10)",
     "prompt_number": 11,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Create a jointLikelihood object</h2>"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "jl = JointLikelihood(mod,verbose=False)\n\n#If we want, we can set explicitly the minimizer (default=MINUIT)\njl.setMinimizer(\"MINUIT\")",
     "prompt_number": 12,
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Profile likelihood maximization</h2>\nIf you want to use the profile likelihood, just perform the fit:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "(p_mle, logLikeMin) = jl.fit()",
     "prompt_number": 13,
     "outputs": [
      {
       "output_type": "stream",
       "text": "Minimum of -logLikelihood is: 1530.45841106\nContributions to the -logLikelihood at the minimum:\nLAT_p7rep_transient : 84.7995896323\nNaI6                : 512.837258219\nNaI9                : 461.250193116\nBGO1                : 471.571370093\n\nValues for the parameters at the minimum are:\nalpha                = -0.805\nbeta                 =  -2.56\nE0                   =    493\nK                    = 0.0181\n",
       "stream": "stdout"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "We can now compute the errors on the parameters. By default, 3ML computes the 1-sigma confidence level errors:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "p_1SigmaErr = jl.getErrors()",
     "prompt_number": 14,
     "outputs": [
      {
       "output_type": "stream",
       "text": "Computing 0.683 c.l. errors (chisq critical value: 1.000, equivalent sigmas: 1.000 sigma)\nComputing error for parameter alpha...\nComputing error for parameter beta...\n",
       "stream": "stdout"
      },
      {
       "output_type": "stream",
       "text": "Computing error for parameter E0...\nComputing error for parameter K...\n",
       "stream": "stdout"
      },
      {
       "output_type": "stream",
       "text": "\nBest fit values and their errors are:\nalpha                = -0.805 [-0.02427,0.02466]\nbeta                 =  -2.56 [-0.04988,0.04703]\nE0                   =    493 [-33.83, 35.45]\nK                    = 0.0181 [-0.0004198,0.000436]\n",
       "stream": "stdout"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "If we want another confidence level, we can specify it either by giving it explicitly or by using the sigma keyword. We can also obtain a plot of the profile of the log-likelihood, by specifying \"profiles=True\". This for example will compute the 90% c.l. and plot the profiles:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "p_90cl = jl.getErrors(0.90, profiles=True)",
     "prompt_number": 15,
     "outputs": [
      {
       "output_type": "stream",
       "text": "Computing 0.900 c.l. errors (chisq critical value: 2.706, equivalent sigmas: 1.645 sigma)\nComputing error for parameter alpha...\nComputing error for parameter beta...\n",
       "stream": "stdout"
      },
      {
       "output_type": "stream",
       "text": "Computing error for parameter E0...\nComputing error for parameter K...\n",
       "stream": "stdout"
      },
      {
       "output_type": "stream",
       "text": "\nBest fit values and their errors are:\nalpha                = -0.805 [-0.03968,0.04084]\nbeta                 =  -2.56 [-0.1055,0.07673]\nE0                   =    493 [-55.19, 59.51]\nK                    = 0.0181 [-0.0006809,0.0007278]\n",
       "stream": "stdout"
      },
      {
       "output_type": "stream",
       "text": "/home/giacomov/science/hawc/jointLikelihood/threeML/spectralModels.py:95: RuntimeWarning: invalid value encountered in power\n  out[nidx]                = numpy.maximum(K*numpy.power((alpha-beta)*E0/100.0,alpha-beta)*numpy.exp(beta-alpha)*numpy.power(energies[nidx]/100.0,beta),1e-30)\n",
       "stream": "stderr"
      },
      {
       "png": 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73e5YtmxZludMTEx0AP/9SnSY9cdZf40dm/P4s3tuzaE5NIfm0ByaQ3O4wxx/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MR1XLp0iaNHjwLg4eFB3bp1s3Sevn37OsYr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8PWDAAL1JbaLSaNQosaBkpUpAcDDg4wMkJJi6V0SlS1ycuIL55EmxiGtwMJPaREAZT2znVqtW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\nc+vWLY2TkL4k5qVLl+R2NWrU0Bt033zzjdz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       "text": "<matplotlib.figure.Figure at 0x4cb5e50>",
       "output_type": "display_data",
       "metadata": {}
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "This instead will compute the 2 sigma error contours:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "p_2sigma_cl = jl.getErrors(sigma=2)",
     "prompt_number": 16,
     "outputs": [
      {
       "output_type": "stream",
       "text": "Computing 0.954 c.l. errors (chisq critical value: 4.000, equivalent sigmas: 2.000 sigma)\nComputing error for parameter alpha...\nComputing error for parameter beta...\n",
       "stream": "stdout"
      },
      {
       "output_type": "stream",
       "text": "Computing error for parameter E0...\nComputing error for parameter K...\n",
       "stream": "stdout"
      },
      {
       "output_type": "stream",
       "text": "\nBest fit values and their errors are:\nalpha                = -0.805 [-0.0481,0.04984]\nbeta                 =  -2.56 [-0.1283,0.08627]\nE0                   =    493 [-66.87, 73.27]\nK                    = 0.0181 [-0.0008217,0.000892]\n",
       "stream": "stdout"
      }
     ],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h2>Full Bayesian analysis</h2>\n<ul><li>\nDefine your model and its initial values (as before):</li></ul>"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "mod = ModelManager(triggerName,ra,dec,\"grbm\",datalist)\nmod.setParameterValue(\"grbm.alpha\",\"-1.01482\")\nmod.setParameterValue(\"grbm.beta\",\"-2.21990\")\nmod.setParameterValue(\"grbm.tem\",\"526.247\")\nmod.setParameterValue(\"grbm.norm\",[0.0173822,0.001,1e-12,1e-12,1e5,1e5])",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<ul><li>Define the priors for all your parameters:</li></ul>"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "#Define priors for model parameters\nmod.setParameterPrior(\"grbm.alpha\",Priors.UniformPrior(-10,10))\nmod.setParameterPrior(\"grbm.beta\",Priors.UniformPrior(-10,10))\nmod.setParameterPrior(\"grbm.tem\",Priors.UniformPrior(10,1e4))\n\n#Use a log-uniform (Jeffrey's) prior for the normalization\nmod.setParameterPrior(\"grbm.norm\",Priors.LogUniformPrior(1e-3,1e6))\n\n#Define priors for the nuisance parameters\nmod.setNuisanceParameterPrior(\"IsotropicTemplate-Normalization\",Priors.UniformPrior(0.85,1.15))\nmod.setNuisanceParameterPrior(\"bn090217206-Normalization\",Priors.UniformPrior(0.85,1.15))\nmod.setNuisanceParameterValue(\"IsotropicTemplate-Normalization\",1.0)\n\nprint mod",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<ul><li>Create a jointLikelihood object:</li></ul>"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "jl = JointLikelihood(mod)",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<ul><li>Run the Markov Chain MC and explore the parameter space: (this will take some time, depending on the number of samples)</li></ul>"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "nwalkers = 100\nsamplesPerWalker = 3000\njl.explore(nwalkers,samplesPerWalker)",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "<h3>Getting some useful information from the Bayesian analysis</h3>\nNow that we have our MCMC sample of parameters, we can extract a lot of useful information. We can start by taking the usual median values, and the credibility intervals (the Bayesian equivalent of confidence intervals). This is made with the getPercentiles method, which uses 1-sigma intervals by default (i.e., 16 and 84 percentiles):"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "percentiles = jl.getPercentiles()",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "If we want instead the 90% interval, we can request the appropriate percentiles:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "percentiles = jl.getPercentiles(levels=[50,5,95])",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "We can also easily produce a triangle plot which show all the monodimensional and bidimensional marginal distribution, with the latter being the equivalent of countour plots in frequentist analysis:"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "import triangle\nfig = triangle.corner(jl.samples,\n                      labels=[r'$\\alpha$',r'$\\beta$','tem',r'A$_{Band}$','N','N1'],\n                      quantiles=[0.16, 0.5, 0.84],\n                      show_titles=True, label_args={\"fontsize\": 16})",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    },
    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "By using the MCMC samples we can also plot the best fit model along with its \"1-sigma contour\":"
    },
    {
     "metadata": {},
     "cell_type": "code",
     "input": "bestFitParam = map(lambda x:x[0],percentiles.values())\nnufnu = mod.plotWithChain(bestFitParam,jl.samples,kind=\"nufnu\",ymin=1e-19,emin=1e-3,emax=1e12,nbins=1000)",
     "outputs": [],
     "language": "python",
     "trusted": true,
     "collapsed": false
    }
   ],
   "metadata": {}
  }
 ],
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