{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Preamble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "code_folding": [],
    "collapsed": false,
    "hidden": true,
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "#Initialization Cell\n",
    "import numpy as np\n",
    "import scipy.integrate as si\n",
    "import matplotlib.pyplot as plt\n",
    "import lmfit\n",
    "\n",
    "plt.style.use('fivethirtyeight')\n",
    "%matplotlib inline\n",
    "\n",
    "plt.rcParams['figure.figsize']=[12.8*0.75, 9.6*0.75]\n",
    "plt.rcParams['font.size']=20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'seaborn-darkgrid',\n",
       " u'seaborn-notebook',\n",
       " u'classic',\n",
       " u'seaborn-ticks',\n",
       " u'grayscale',\n",
       " u'bmh',\n",
       " u'seaborn-talk',\n",
       " u'dark_background',\n",
       " u'ggplot',\n",
       " u'fivethirtyeight',\n",
       " u'_classic_test',\n",
       " u'seaborn-colorblind',\n",
       " u'seaborn-deep',\n",
       " u'seaborn-whitegrid',\n",
       " u'seaborn-bright',\n",
       " u'seaborn-poster',\n",
       " u'seaborn-muted',\n",
       " u'seaborn-paper',\n",
       " u'seaborn-white',\n",
       " u'seaborn-pastel',\n",
       " u'seaborn-dark',\n",
       " u'seaborn',\n",
       " u'presentation',\n",
       " u'seaborn-dark-palette']"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.style.available"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "x=np.array([i for i in range(100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7faa05fd5350>"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LM9u0jX1ERERE1lis90bEagZHHUbVqZpk2cwuIPhC38sEM8qfr6TtiPIjsMPyfYHTw9t7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\nTU5bZWQMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faa062f2f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,x**2)\n",
    "plt.plot(x,2*x**2)\n",
    "plt.plot(x,3*x**2,ls=':',marker='')\n",
    "plt.xlabel(r'$\\gamma$')\n",
    "plt.ylabel(r'$d\\,P_S/d\\,\\gamma$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Bayesian Inference (Wikipedia)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import HTML, YouTubeVideo, Markdown, IFrame\n",
    "import wikipedia as wiki\n",
    "import pypandoc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "Bayesian inference is a method of statistical inference in which Bayes'\n",
       "theorem is used to update the probability for a hypothesis as more\n",
       "evidence or information becomes available. Bayesian inference is an\n",
       "important technique in statistics, and especially in mathematical\n",
       "statistics. Bayesian updating is particularly important in the dynamic\n",
       "analysis of a sequence of data. Bayesian inference has found application\n",
       "in a wide range of activities, including science, engineering,\n",
       "philosophy, medicine, sport, and law. In the philosophy of decision\n",
       "theory, Bayesian inference is closely related to subjective probability,\n",
       "often called \"Bayesian probability\".\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bayes=wiki.page(\"Bayesian Inference\")\n",
    "Markdown(pypandoc.convert_text(bayes.summary,'md','mediawiki'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/0F0QoMCSKJ4\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7faa08eeb290>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('0F0QoMCSKJ4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Bayesian vs Frequentist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Frequentist Interpretation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in a large number of trials. This interpretation supports the statistical needs of experimental scientists and pollsters; probabilities can be found (in principle) by a repeatable objective process (and are thus ideally devoid of opinion). It does not support all needs; gamblers typically require estimates of the odds without experiments.\n",
       "The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the classical interpretation. In the classical interpretation, probability was defined in terms of the principle of indifference, based on the natural symmetry of a problem, so, e.g. the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. This classical interpretation stumbled at any statistical problem that has no natural symmetry for reasoning."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq=wiki.page(\"Frequentist probability\")\n",
    "Markdown(freq.summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### Bayesian Interpretation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.\n",
       "The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses, i.e., the propositions whose truth or falsity is uncertain. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability.\n",
       "Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies some prior probability, which is then updated to a posterior probability in the light of new, relevant data (evidence). The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation.\n",
       "The term Bayesian derives from the 18th century mathematician and theologian Thomas Bayes, who provided the first mathematical treatment of a non-trivial problem of Bayesian inference. Mathematician Pierre-Simon Laplace pioneered and popularised what is now called Bayesian probability.\n",
       "Broadly speaking, there are two views on Bayesian probability that interpret the probability concept in different ways. According to the objectivist view, probability is a reasonable expectation that represents the state of knowledge, can be interpreted as an extension of logic, and its rules can be justified by Cox's theorem. According to the subjectivist view, probability quantifies a personal belief, and its rules can be justified by requirements of rationality and coherence following from the Dutch book argument or from the decision theory and de Finetti's theorem."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bayes=wiki.page(\"Bayesian probability\")\n",
    "Markdown(bayes.summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Bayes theorem redux"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": true,
    "hidden": true,
    "init_cell": true
   },
   "source": [
    "The Bayesian inference is built upon the Bayes-theorem:\n",
    "$$P(H|D)=\\frac{P(H)\\times P(D|H)}{P(D)}$$\n",
    "where, M and D stands for the hypothesis being tested and D is the data.\n",
    "\n",
    "The Bayes theorem should be interpreted as follows:\n",
    "1. P(H|D) is called the **posterior** the probability of the hypothesis given the observed data.\n",
    "2. P(H) is called the **prior**. It quantifies your **a priori** degree of belief in the Hypothesis. In other words, it quantify your confidence/prejudice on the hypothesis **before** looking on the **new** data\n",
    "3. P(D|H) is called the **likelihood**. It is the probability of obtaining the data from a random sampling the hypothesis.\n",
    "4. P(D) is called the **evidence** or **marginal likelihood**. The second name is due to the fact that since the posterior has to be normalized to unity this term is a normalization factor coming from the integration of the dividend over the hypothesis (this operation is called **marginalization**). *In summa*, It quantifies the overall performance of your hypothesis explaining the occurrence of the data;\n",
    "    1. Unimportant for parameter estimation.\n",
    "    2. Extremely important for model judgment.\n",
    "    \n",
    "An important note! The **posterior** is many times confused with the **likelihood**. That's due to the fact that in the case of a *flat* prior they are numerically equal. But remember that one is function of the data and the other is a function of the hypothesis!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Likelihood construction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In many analysis cosmologists begin their analysis upon the hypothesis that the likelihood is a Gaussian distribution on the Data. In other words, the observed data is a random sample that obeys a multi-variated distribution. Many reasons justify why it is a good hypothesis (but not always!). Usually those reasons are related with the *central limit theorem*.\n",
    "\n",
    "- Many distributions has the normal distribution as a limit\n",
    "    - Binomial\n",
    "    - Poisson\n",
    "    - (...)\n",
    "- If a process is resulted by the convolution of many other sub-processes the distribution of the process tend to be Gaussian. (Challenge: test that! Start with a very skewed distribution and iteratively convolve it with itself. After how many iterations you are not able to distinguish it anymore from a gaussian?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " A Gaussian distribution is defined by two quantities:\n",
    " - The mean:\n",
    "     - For this case it coincides with the most probable value.\n",
    " - The variance:\n",
    "     - The spread of the distribution around the mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SNe Likelihood (Union 2.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Union2.1 catalog has a simplistic likelihood where each SN is assumed to be independent.\n",
    "\n",
    "1. Let's import Union 2.1 data (http://supernova.lbl.gov/union/figures/SCPUnion2.1_mu_vs_z.txt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "--2017-05-18 12:49:25--  http://supernova.lbl.gov/union/figures/SCPUnion2.1_mu_vs_z.txt\n",
      "Resolving supernova.lbl.gov (supernova.lbl.gov)... 128.3.28.216\n",
      "Connecting to supernova.lbl.gov (supernova.lbl.gov)|128.3.28.216|:80... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 33899 (33K) [text/plain]\n",
      "Saving to: ‘SCPUnion2.1_mu_vs_z.txt’\n",
      "\n",
      "     0K .......... .......... .......... ...                  100% 44.1K=0.8s\n",
      "\n",
      "2017-05-18 12:49:27 (44.1 KB/s) - ‘SCPUnion2.1_mu_vs_z.txt’ saved [33899/33899]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%%bash \n",
    "wget supernova.lbl.gov/union/figures/SCPUnion2.1_mu_vs_z.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "union21=np.loadtxt('SCPUnion2.1_mu_vs_z.txt',dtype={'names': ('name', 'z', 'mu','mu_error','XXX'),\n",
    "...                      'formats': ('S6', 'f', 'f','f','f')})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7faa06a1f150>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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0ZhRnA5+bHuKpw36eqeldov3tYT/fWQifajB7tp65MzKPG5fpX9+YyDSuuXwSv2g7x3M3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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faa069ce4d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(union21['z'],union21['mu'],ls='None',marker='x')\n",
    "plt.xlabel(r'$z$')\n",
    "plt.ylabel(r'$\\mu$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Challenge: \n",
    " 1. Write the union21 likelihood function!\n",
    " 2. Add this to your Cosmology Class!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data=union21['mu'][(union21['z']>0.5) & (union21['z']<0.6)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mean=data.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data_zero_mean=data-mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.,  1.,  1.,  2.,  5.,  9.,  8.,  4.,  3.,  1.,  2.,  3.,  1.,\n",
       "         0.,  0.]),\n",
       " array([-1.        , -0.86666667, -0.73333333, -0.6       , -0.46666667,\n",
       "        -0.33333333, -0.2       , -0.06666667,  0.06666667,  0.2       ,\n",
       "         0.33333333,  0.46666667,  0.6       ,  0.73333333,  0.86666667,  1.        ]),\n",
       " <a list of 15 Patch objects>)"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A6IyABwDQGQEPAKAzAh4AQGcEPACAzgh4AACdEfAAADoj4AEAdEbAAwDojIAHANCZPTtd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faa05c45e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data_zero_mean,bins=15,range=(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from cosmolopy.distance import luminosity_distance as dl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def mu (z,om,ol,h):\n",
    "\n",
    "    cosmo = {'omega_M_0' : om, 'omega_lambda_0' : ol, 'h' : h,'omega_k_0':0}\n",
    "    return 5*np.log10(dl(z,**cosmo))+5+19.3081547178\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def lhood_sne (om,ol,h):\n",
    "    \n",
    "    mu_teo=mu(union21['z'],om,ol,h)\n",
    "    chiq=((mu_teo-union21['mu'])/union21['mu_error'])**2\n",
    "    return np.exp(-1./2*chiq.sum())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
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