cluster_field.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Maximum Likelihood fitting\n",
    "\n",
    "Often one has complicated data sets that cannot easily be modelled by classical statistical techniques. For example, the data may be truncated, or have an additive bias or more complicated effects such that it does not well described by one of the well-known probability distributions.\n",
    "\n",
    "## Clusters and field\n",
    "\n",
    "As an example of this, consider fitting for the location and velocity dispersion of a group/cluster in redshift-space, where there is an background field population.\n",
    "\n",
    "The velocity dispersion, $\\sigma $ is of physical interest because the total mass $M \\propto \\sigma^3 $\n",
    "\n",
    "First we set up Python with imports etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "%matplotlib inline\n",
    "from pylab import *\n",
    "\n",
    "from scipy.stats import norm, uniform\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Parameters of the input cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "input_mean = 5000.\n",
    "input_sigma = 1000.\n",
    "nclus = 1000.*(input_sigma/1000.)**3\n",
    "\n",
    "dmin = 0.\n",
    "dmax = 10000.\n",
    "nfield = 100\n",
    "true_frac = float(nclus)/float(nclus+nfield)\n",
    "\n",
    "ndatabins = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of cluster members: 1000.0\n",
      "Actual mean and sigma: 5011.28064422 1010.05331245\n"
     ]
    }
   ],
   "source": [
    "def makedata(inp_mean, inp_sigma, nclus, dmin, dmax, nfield):\n",
    "    \"\"\"----------------------------------------------------------------\n",
    "    Makes a simulated redshift dataset that includes a group/cluster\n",
    "    superimposed on a uniform density background field\n",
    "    ----------------------------------------------------------------\"\"\"\n",
    "    # mock cluster data\n",
    "    cluster = norm.rvs(loc=inp_mean, scale=inp_sigma, size=int(nclus))\n",
    "    true_mean = mean(cluster)\n",
    "    true_sigma = std(cluster)\n",
    "\n",
    "    # mock field data\n",
    "    field = uniform.rvs(loc=dmin, scale = dmax-dmin, size = nfield)\n",
    "    # Put the cluster and field data together into a data sample\n",
    "    data = concatenate((cluster, field))\n",
    "    \n",
    "    return (data, true_mean, true_sigma)\n",
    "\n",
    "# Generate the cluster\n",
    "(data, true_mean, true_sigma) = makedata(input_mean, input_sigma, nclus, dmin, dmax, nfield)\n",
    "print(\"Number of cluster members:\", nclus)\n",
    "print(\"Actual mean and sigma:\", true_mean, true_sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Here are the data\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1130a6410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11337cd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_data(data, true_mean=None, true_sigma=None, ndatabins=100):\n",
    "    \"\"\"--------------------------------------------------\n",
    "    Plots a histogram of the input data set.\n",
    "    Optionally also shows the cluster mean and dispersion\n",
    "    -----------------------------------------------------\"\"\"\n",
    "    hist(data, ndatabins)\n",
    "    title('Data')\n",
    "    xlabel(r\"$cz$\"+\" (km/s)\")\n",
    "    ylabel(\"N per bin\")\n",
    "\n",
    "    if true_mean: axvline(true_mean, ls='dotted')\n",
    "    if true_sigma:\n",
    "        axvline(true_mean+2*true_sigma, ls='dotted')\n",
    "        axvline(true_mean-2*true_sigma, ls='dotted')\n",
    "\n",
    "print(\"Here are the data\")\n",
    "plot_data(data, true_mean, true_sigma)\n",
    "show()\n",
    "clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "A common way of dealing with the background is sigma-clipping.\n",
    "\n",
    "(Of course, it's not obvious which is the appropriate multiple of sigma is to clip. 2.5? 3? 5?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def sigma_clip(data, mean_in, sigma_in=1000., n_sigma=2.5):\n",
    "    \"\"\"--------------------------------------------------\n",
    "    Rejects data that are outside the +- n_sigma range\n",
    "\n",
    "    Returns new mean, new sigma and clipped data set\n",
    "    --------------------------------------------------\"\"\"\n",
    "    vlo = mean_in - n_sigma*sigma_in\n",
    "    vhi = mean_in + n_sigma*sigma_in\n",
    "\n",
    "    inrange = logical_and(data > vlo, data < vhi)\n",
    "    select = data[inrange]\n",
    "\n",
    "    new_mean = mean(select)\n",
    "    new_std = std(select)\n",
    "    \n",
    "    return (new_mean, new_std, select)\n",
    "\n",
    "def clip_loop(data, mean_in, sigma_in=1500., n_sigma=2.5, verbose=True):\n",
    "    \"\"\"----------------------------------------------------------\n",
    "    Repeatedly sigma_clips until no further data are rejected\n",
    "\n",
    "    Returns final mean, final sigma and final clipped data set\n",
    "    ----------------------------------------------------------\"\"\"\n",
    "\n",
    "    done = False\n",
    "    # First pass\n",
    "    (new_mean, new_std, select) = sigma_clip(data, mean_in,\n",
    "                                             sigma_in=sigma_in,\n",
    "                                             n_sigma=n_sigma)\n",
    "    n_select_old = len(select)\n",
    "\n",
    "    while not done:\n",
    "        (new_mean, new_std, select) = sigma_clip(data, true_mean,\n",
    "                                                 new_std, n_sigma=n_sigma)\n",
    "        n_select = len(select)\n",
    "        if verbose: print(n_select, \"galaxies selected range from:\",min(select), \" to:\", max(select))\n",
    "        if verbose: print(\"mean:\", new_mean, \"and sigma:\", new_std)\n",
    "        if n_select == n_select_old: done = True\n",
    "        n_select_old = n_select\n",
    "    return (new_mean, new_std, select)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now we do the actual interative clipping."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1051 galaxies selected range from: 2201.88682939  to: 7820.80869449\n",
      "mean: 4999.78323514 and sigma: 1031.34735404\n",
      "1040 galaxies selected range from: 2454.38948783  to: 7549.74801179\n",
      "mean: 4996.82426312 and sigma: 999.081442304\n",
      "1035 galaxies selected range from: 2546.96150981  to: 7492.31527491\n",
      "mean: 4994.35822934 and sigma: 985.826302644\n",
      "1033 galaxies selected range from: 2546.96150981  to: 7465.0727843\n",
      "mean: 4989.52428938 and sigma: 980.633825645\n",
      "1030 galaxies selected range from: 2587.84701239  to: 7424.63003158\n",
      "mean: 4991.86166136 and sigma: 973.094798558\n",
      "1030 galaxies selected range from: 2587.84701239  to: 7424.63003158\n",
      "mean: 4991.86166136 and sigma: 973.094798558\n"
     ]
    }
   ],
   "source": [
    "(clip_mean, clip_std, select) = clip_loop(data, true_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The final result is generaly OK for rich clusters with a high contrast between cluster and field.\n",
    "\n",
    "For poorer systems its not clear how well it works. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Maximum likelihood\n",
    "\n",
    "The better way to do this is *maximum likelihood*.\n",
    "\n",
    "For a choice of mean and sigma, and the (prior) probability that one is in the cluster, one can calculate the probabiilty of observing a galaxy between\n",
    "$v$ and $v+dv$. In fact we drop the $dv $ term since it doesn't matter:\n",
    "with likelihoods we only care about relative probabilities: a small quantity $dv $ would rescale all probabilities by some constant factor.\n",
    "\n",
    "We will be varying the parameters of the model (in this case: mean, sigma, p_clus) to find which combination maximises the posterior likelihood\n",
    "\n",
    "(Note that the priors here are assumed to be uniform, but they need not be: a non-uniform prior could easily be added to the functions below.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def likelihood(mean, sigma, p_clus, data):\n",
    "\n",
    "    \"\"\"---------------------------------------------------------------\n",
    "    Calculate the likelihood of each member of the data set\n",
    "    for a given model based on a cluster with a mean and dispersion\n",
    "    plus a prior probability that a data point is in the cluster.\n",
    "    \n",
    "    Returns an array of probabilities same length as data.\n",
    "    ---------------------------------------------------------------\"\"\"\n",
    "    p_field = 1. - p_clus\n",
    "    \n",
    "    clus = norm(loc=mean, scale=sigma)\n",
    "    field = uniform(dmin, dmax-dmin)\n",
    "    \n",
    "    p = p_clus*clus.pdf(data) + p_field*field.pdf(data)\n",
    "\n",
    "    return p\n",
    "\n",
    "def loglikelihood(mean, sigma, p_clus, data):\n",
    "\n",
    "    p = likelihood(mean, sigma, p_clus, data)\n",
    "    logp = log(p)\n",
    "    loglike = sum(logp)\n",
    "    return loglike"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def gridsearch(means, sigmas, fracs, data):\n",
    "    \"\"\"---------------------------------------------\n",
    "    Brute force grid search for maximum\n",
    "\n",
    "    Input: means, sigmas, fracs are numpy arrays.\n",
    "    ---------------------------------------------\"\"\"\n",
    "\n",
    "    maxlike = None\n",
    "    for mean in means:\n",
    "        for sigma in sigmas:\n",
    "            for frac in fracs:\n",
    "                like = loglikelihood(mean, sigma, frac, data)\n",
    "                if maxlike:\n",
    "                    if like > maxlike:\n",
    "                        maxlike = like\n",
    "                        maxmean = mean\n",
    "                        maxsig = sigma\n",
    "                        maxfrac = frac\n",
    "                else:\n",
    "                    maxlike =  like\n",
    "                    maxmean = mean\n",
    "                    maxsig = sigma\n",
    "                    maxfrac = frac\n",
    "\n",
    "    return (maxmean, maxsig, maxfrac, maxlike)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def findmax(data, frac):\n",
    "    \"\"\"-------------------------------------------------------------------\n",
    "    Finds the global maximum\n",
    "    \n",
    "    First do a coarse grid search over a wide range of plausible values.\n",
    "\n",
    "    Then refine with a smaller step size\n",
    "    --------------------------------------------------------------------\"\"\"\n",
    "    means = arange(dmin,dmax,100.)\n",
    "    sigmas = arange(100.,2000.,100.)\n",
    "    (maxmean, maxsig, maxfrac, maxlike) = gridsearch(means, sigmas, frac, data)\n",
    "\n",
    "    means = arange(maxmean-100., maxmean+100., 10.)\n",
    "    sigmas = arange(maxsig-100., maxsig+100., 10.)\n",
    "    (maxmean, maxsig, maxfrac, maxlike) = gridsearch(means, sigmas, frac, data)\n",
    "\n",
    "    return (maxmean, maxsig, maxfrac, maxlike)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now we actually find the maximum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4990.0 1000.0 0.909090909091 -9386.5179244\n"
     ]
    }
   ],
   "source": [
    "frac = array([true_frac])\n",
    "(maxmean, maxsig, maxfrac, maxlike) = findmax(data, frac)\n",
    "print(maxmean, maxsig, maxfrac, maxlike)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def plotlike(x, xlike, xtrue=None, type='log',\n",
    "             xlab=None,ylab=None, plot_title=None):\n",
    "\n",
    "    if type is not 'log':\n",
    "        plot(x, exp(xlike))\n",
    "        ylim(0.,1.)\n",
    "        axhline(0., ls='dashed')\n",
    "        axhline(exp(-2.), ls='dashed')\n",
    "        axhline(exp(-8.), ls='dashed')\n",
    "        if not ylab: ylab = r\"$\\mathcal{L}$\"\n",
    "    else:\n",
    "        plot(x, xlike)\n",
    "        ylim(-18.,1.)\n",
    "        axhline(0., ls='dashed')\n",
    "        axhline(-2., ls='dashed')\n",
    "        axhline(-8., ls='dashed')\n",
    "        if not ylab: ylab = r\"$\\ln \\, \\mathcal{L}$\"\n",
    "        \n",
    "    if xtrue: axvline(xtrue, ls='dotted') \n",
    "    if xlab: xlabel(xlab)\n",
    "    ylabel(ylab)\n",
    "    if plot_title: title(plot_title)\n",
    "    show()\n",
    "    clf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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QTZNqhsjSpTByZLiyb+fO1dmG5EtdHOJrZoWniZ0APBerFsmOhx9O11FZLaoVIAA77AB9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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11318ae50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Kjt90VP+q+yZptqS70mX/LemkzLqd1rdlkn6d9uWudNlkSbdK+h9JP5S0f2b9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1130c3310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1134a8050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PEyJibUfr7OQsfRlfwBvI9jpaDnx0jGv5C7I5gNuB2/KvucAM4KfAvcBPgOlV\nz/lYXvtS4PVjUPMJ7NwbqufqBF4K3ALcQfbJaJ9eq5NscnMxcCfZpPH4XqiRrGt8ENhCNrd3Wjt1\nAUfn72058OUu1Pl+YBnw+6rfo6/2UJ1PV76fNY+vIN8bqtfqzP9Pfjd/3d8AQ52u0wflmZlZU70+\nDGVmZj3AYWFmZk05LMzMrCmHhZmZNeWwMDOzphwWZmbWlMPCzMyacliYmVlTDguzOpRd4Oj/KTO7\n3gVx2tjm1yS9qsFr/UySfx+tZ/k/p1l97wT+Izp7ioNjgV/VLoyIp4Eb6fB1D8w6yWFhVt+pwL/X\nLpT0/PzaG0fnHcfS/Hoc90j6vqQTJf1C2WVNj6l63mFk52vaW9KPJN2eX9Lyr/JVFuavadaTHBa2\nR5L0JkmLJD2k7Lrqf1f12ADwooi4t+Y5LyQ7jfp7I+I3+eKDgfOBPwNeCJwSEX8OfJjsBG4VbwCu\nJjvx5JqIeFlEvJjscp2QnZxytyEqs14xONYFmHWbpOcCJ0fEyZLeQnZN4h9WrTIT2FDztD8hO4Xz\nf46IpVXL74+Ixfl2F5Od8RXgLrJrIVScCLwPmAp8XtKnyYa5fg7ZUJSkcZL2il1P2W3WE9xZ2J7o\nPcCX8tv7AY/XWaf2imiPkZ1S+7ia5U9X3d5Bdhruyu1BeOaKa9Mju4b7MrLL8d4J/Kukj9e8pk8D\nbT3JnYXtifYlu6Y2ZFe9+07N42uBKTXLtgBvBa6VtDEiLmnh9V4NXA/PXL1ufUR8X9LjwF/nyycC\n2/PJbrOe47CwPdE3yK4eJuBLEbG1+sGI2C7pLkkvjIh7di6Ozfn1za+TtIGsO6jtBKLO7Tew85rI\nLwY+J2kHsBU4I19+JHX2lDLrFb74kVkd+fWh94+Iz3RgW78B5kTE9hHW+SRwS83ciVnPcFiY1ZFf\n8/2nwAkdPtai3mtNBK7rxmuZtcthYWZmTXlvKDMza8phYWZmTTkszMysKYeFmZk15bAwM7OmHBZm\nZtaUw8LMzJpyWJiZWVP/HxqlMBrR64mdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1134fb0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1131248d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meanlike = []\n",
    "means = arange(4500.,5500.,10.)\n",
    "for mean1 in means:\n",
    "    meanlike.append(loglikelihood(mean1, maxsig, maxfrac, data)-maxlike)\n",
    "\n",
    "xlab=\"Mean $cz$(km/s)\"\n",
    "plot_title=\"Probability of mean\"\n",
    "plotlike(means, meanlike, true_mean, xlab=xlab, plot_title=plot_title)\n",
    "plotlike(means, meanlike, true_mean, type='linear',\n",
    "         xlab=xlab, plot_title=plot_title)\n",
    "\n",
    "siglike = []\n",
    "sigmas = arange(10.,1500.,10.)\n",
    "for sigma1 in sigmas:\n",
    "    siglike.append(loglikelihood(maxmean, sigma1, maxfrac, data)-maxlike)\n",
    "\n",
    "xlab = r\"$\\sigma$\"+\" (km/s)\"\n",
    "plot_title = \"Probability of \"+r\"$\\sigma$\"\n",
    "plotlike(sigmas, siglike, true_sigma, xlab=xlab, plot_title=plot_title)\n",
    "plotlike(sigmas, siglike, true_sigma, xlab=xlab, type='linear',\n",
    "         plot_title=plot_title)\n",
    "\n",
    "def plot_data_and_model(data, true_mean=None, true_sigma=None,\n",
    "                        maxmean=None, maxsig=None, maxfrac=None,\n",
    "                        ndatabins=ndatabins):\n",
    "\n",
    "    plot_data(data, true_mean, true_sigma, ndatabins=ndatabins)\n",
    "\n",
    "    d = arange(0.,10010.,10.)\n",
    "    p = likelihood(maxmean, maxsig, maxfrac, d)\n",
    "    norm = sum(p)\n",
    "    nexp = p/norm*len(data)*len(d)/ndatabins\n",
    "\n",
    "    plot(d, nexp)\n",
    "    title('Data and model')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Here are the data and the best fitting model\n"
     ]
    },
    {
     "data": {
      "image/png": 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rh3LoBMwcEnUkUtskeGDSA1FHITlAiUJS0uSjxgPvh8lAZcs0RiNpMRvmrZrH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\nEZGk/j+xXcxs67hdHgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113319710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1131d6b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Here are the data and the best fitting model\")\n",
    "plot_data_and_model(data, true_mean, true_sigma, maxmean, maxsig, maxfrac)\n",
    "show()\n",
    "clf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def do_all(input_mean = 5000., input_sigma = 1000., nclus=None,\n",
    "           dmin=0., dmax=10000., nfield=100,\n",
    "           ndatabins=50,\n",
    "           doclip=False):\n",
    "           \n",
    "    if not nclus: nclus = 1000.*(input_sigma/1000.)**3\n",
    "\n",
    "    true_frac = float(nclus)/float(nclus+nfield)\n",
    "\n",
    "    (data, true_mean, true_sigma) = makedata(input_mean, input_sigma, nclus,\n",
    "                                             dmin, dmax, nfield)\n",
    "\n",
    "    if doclip: (clip_mean, clip_std, select) = clip_loop(data, true_mean)\n",
    "\n",
    "    frac = array([true_frac])\n",
    "    (maxmean, maxsig, maxfrac, maxlike) = findmax(data, frac)\n",
    "    print(maxmean, maxsig, maxfrac, maxlike)\n",
    "\n",
    "    meanlike = []\n",
    "    means = arange(4500.,5500.,10.)\n",
    "    for mean1 in means:\n",
    "        meanlike.append(loglikelihood(mean1, maxsig, maxfrac, data)-maxlike)\n",
    "\n",
    "    xlab=\"Mean $cz$(km/s)\"\n",
    "    plot_title=\"Probability of mean\"\n",
    "    plotlike(means, meanlike, true_mean, xlab, plot_title=plot_title)\n",
    "\n",
    "    siglike = []\n",
    "    sigmas = arange(10.,1500.,10.)\n",
    "    for sigma1 in sigmas:\n",
    "        siglike.append(loglikelihood(maxmean, sigma1, maxfrac, data)-maxlike)\n",
    "\n",
    "    xlab = r\"$\\sigma$\"+\" (km/s)\"\n",
    "    plot_title = \"Probability of \"+r\"$\\sigma$\"\n",
    "    plotlike(sigmas, siglike, true_sigma, xlab=xlab, plot_title=plot_title)\n",
    "\n",
    "    print(\"Here are the data and the best fitting model\")\n",
    "    plot_data_and_model(data, true_mean, true_sigma,\n",
    "                        maxmean, maxsig, maxfrac, ndatabins=ndatabins)\n",
    "    show()\n",
    "    clf()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "198 galaxies selected range from: 1872.63164167  to: 8539.18173639\n",
      "mean: 5118.18713944 and sigma: 1261.02625174\n",
      "193 galaxies selected range from: 1872.63164167  to: 8081.72499219\n",
      "mean: 5032.77196328 and sigma: 1158.49958123\n",
      "188 galaxies selected range from: 2312.95683426  to: 7880.43503305\n",
      "mean: 4986.15993998 and sigma: 1064.62156753\n",
      "184 galaxies selected range from: 2436.56061172  to: 7665.35684\n",
      "mean: 4983.6672595 and sigma: 994.893002433\n",
      "179 galaxies selected range from: 2635.80560429  to: 7428.18861022\n",
      "mean: 4939.16720809 and sigma: 908.196642615\n",
      "176 galaxies selected range from: 2823.16382014  to: 7267.33780483\n",
      "mean: 4950.80051849 and sigma: 863.172095152\n",
      "173 galaxies selected range from: 2891.40502887  to: 7107.30908127\n",
      "mean: 4936.49409206 and sigma: 818.770867003\n",
      "169 galaxies selected range from: 2981.82145023  to: 7012.46024854\n",
      "mean: 4959.68915527 and sigma: 764.62825122\n",
      "165 galaxies selected range from: 3136.22141612  to: 6839.87999185\n",
      "mean: 4934.83428306 and sigma: 706.983195642\n",
      "161 galaxies selected range from: 3374.86100587  to: 6746.20283865\n",
      "mean: 4955.72439557 and sigma: 657.089870325\n",
      "159 galaxies selected range from: 3374.86100587  to: 6515.26804589\n",
      "mean: 4933.42837589 and sigma: 630.21942534\n",
      "158 galaxies selected range from: 3483.55581931  to: 6515.26804589\n",
      "mean: 4943.29272633 and sigma: 619.853804867\n",
      "158 galaxies selected range from: 3483.55581931  to: 6515.26804589\n",
      "mean: 4943.29272633 and sigma: 619.853804867\n",
      "4960.0 520.0 0.555555555556 -1965.32569705\n"
     ]
    },
    {
     "data": {
      "image/png": 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03DFJ/NzhRz8KQySf/jR89atJRxSfWs9ZlDvpJPjLX+CKK8Jt/frkYpF8izVZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113090210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VfFqVlImKSEZlqTtL4jvssHDI78svx04ieaMiklFZGlhXSyQ+M03KKOWhIpJR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\niIgUTUVERESK9n9aAq1hdfVA2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b8d650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Here are the data and the best fitting model\n"
     ]
    },
    {
     "data": {
      "image/png": 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RuPs77j4qfIx09+8nEYekXI834cA34a3gpc6gA6cPOZ3lm5bzhepZSYciZSLp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113539bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113116750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "do_all(input_sigma=500., doclip=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102 galaxies selected range from: 315.339284767  to: 9681.80144958\n",
      "mean: 5086.63405445 and sigma: 2418.27994001\n",
      "108 galaxies selected range from: 16.1070503215  to: 9681.80144958\n",
      "mean: 4812.09505155 and sigma: 2608.64517272\n",
      "108 galaxies selected range from: 16.1070503215  to: 9681.80144958\n",
      "mean: 4812.09505155 and sigma: 2608.64517272\n",
      "5250.0 280.0 0.0740740740741 -991.49851304\n"
     ]
    },
    {
     "data": {
      "image/png": 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uKi0tpbS0NOOvm41pqM7AwJRpqAFAmXNuUFq7jsB4oMQ5t7CC19E0lNTa7bfD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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111d40dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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47vTPalbZHFhSt9mWFLfLfk9mzq1pfyQz55T7nUNxB12A2RTPohhwNPDXwMbA\nuRFxNsVw2X9AMaQVEetExMRc9dboUiXYE5EG/RVwfjn/JmDxEOvUP8HuBYpblx9W1760Zn4lxe3O\nB+bHw+tPyNs0Mxdl5oMUj1WeBfxTRHyp7pjebluVZE9EGrQZxTPToXhK4Q/rlj8DbFTX9hrwXuC6\niHgpMy9p4HhHADfB608bfD4zL46IxcBHy/b1gBVlkV2qHJOINOi7FE98C+D8zFxWuzAzV0TE7IjY\nJTP/MNicr5TPsL8hIpZQ9Cbqew45xPyxDD73eg/gaxGxElgGfLxs/zOGOHNLqgofSiU1oHz+95TM\nPKcF+7oL2D8zV6xmna8Cd9TVZqTKMIlIDYiIdSmK5Ie3+FqRoY61HnDDaBxLapZJRJLUNM/OkiQ1\nzSQiSWqaSUSS1DSTiCSpaSYRSVLTTCKSpKaZRCRJTTOJSJKa9v8BuTOhoPd6gwAAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11338e550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Here are the data and the best fitting model\n"
     ]
    },
    {
     "data": {
      "image/png": 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1nXX3ncAmM+uXrfCkEkLV9GSbWQ9gOvBNd9+SOs6j1N3p68LMTgXWuPs8IO25\n09VSF0R7aocSNeUPBbYStZB3qZa6MLNRwH8T7SUPAXqY2Tmp01RLXaSTxLonlRBWAMNTPg9nzyzX\nKZhZF6JkcLu7/zEMXm1mg8L4wcCaMLx1nQwjqpMV4X3q8BVxxh2Do4HTzewN4C5gspndTnXWxXJg\nubvPDZ//QJQgVlVhXRwOPOvu68Ie7H1Eh5OrsS5aFOM3sTxlnv3CsuqA3qFVllFSCeE54INmNsLM\n9iLq8HggoVhiYWYG3AIscvefp4x6gKjjjPD3jynDP21me5nZSOCDwBx3XwVsDmeiGHBuyjwVwd2/\n6+7D3X0k0THOJ9z9XKqzLlYBy8xsdBh0IrCQ6Ph5VdUF0fHyiWbWLazDicAiqrMuWhTjN/GnNMv6\nd2BGztIT7Ew5hahD6VVgatKdOzGs37FEx8vnA/PC62SijrTHgVeAvwJ9Uub5bqiPJcBJKcMPAxaE\ncdcnvW4drJfj2X2WUVXWBfAvwFzgRaK94t5VXBcXEyXEBURnX3Wplrogai2vBN4nOtZ/fjHXHdgb\nuAdYCvwdGJErJl2YJiIigB6hKSIigRKCiIgASggiIhIoIYiICKCEICIigRKCiIgASggiIhIoIYiI\nCKCEIFUqPDzkKYuMSH1ISYHL+5WZHZ2lrL+ZmX5vUtb0BZVq9Z/An714l+ofCcxKN8LdtwNPA/9W\npLJEYqGEINXqM+y+CdguZnZAeE7B4eFRhbea2ctm9jsz+5iZzQyPNzwiZZ6xRPee6WZmD5nZ/PBI\nw/9IWfQDoUyRslWXdAAixWBmnwAGAh8jevTgaeH1IvCyu/8mZdpa4EPu/kqrZYwhuuHY54AtwCjg\nLKI7cM4Fznb3Y8zsdKIbjX0yzHoK8DDRzQtXuPsnwvJ6pSx+PtFtwEXKlloIUvHCraSnuPutwHnu\n/k93/1/gS0S3Cf6/VrMMINrgpxpIdKvhz7p7S3/CG+6+MBxWWkh0F0qAl4ge6tLiY0SPK1wA/KuZ\n/djMjnX3zS0ThMNGNWbWtYOrKxIbJQTpDM4D7oBdG17MrA/wv8CXPXr4Smutn9y2EXiL6MHnLban\nvG8muk1xy/u6UE53olsUr3L3pYSHpgM/NLPvpylTtxeWsqVDRtIZ1BE9lxczG0a04f0R0eMZt5vZ\nge6+JGX6tUCPVst4HzgTeNTM3iFDB3EaJwBPhLIHAxvc/Xdmtgn4QstEZrY30NSSsETKkRKCdAa/\nAs42s/0NIjsPAAAAtElEQVSI9sCbgMuBbxFt+C9Indjdm8zsJTMb4+4v7x7s28Lznx8jOqzUem/e\n07w/heghJAAfBn5iZi2tia+kTD+e/JOMSCL0gBypSmZ2HrCvu1/dweU8D0xw96Yc010FzHX3+ztS\nnkiclBCkKoVneT8OHF/EaxEylbU3Uasj9rJEOkIJQUREAJ1lJCIigRKCiIgASggiIhIoIYiICKCE\nICIigRKCiIgASggiIhIoIYiICAD/H5aDXNW0a/oyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11313fe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11361cdd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "do_all(input_sigma=200., doclip=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}