fitting_with_x_and_y_errors.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting a model to data with both x and y errors with `BILBY`\n",
    "\n",
    "Usually when we fit a model to data with a Gaussian Likelihood we assume that we know x values exactly. This is almost never the case. Here we show how to fit a model with errors in both x and y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import bilby\n",
    "import inspect\n",
    "%pylab inline\n",
    "from scipy.special import logsumexp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First we create the data and plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define our model, a line\n",
    "def model(x, m, c, **kwargs):\n",
    "    y = m*x + c\n",
    "    return y\n",
    "\n",
    "#make a function to create and plot our data\n",
    "def make_data(points, m , c, xerr, yerr, seed):\n",
    "    np.random.seed(int(seed))\n",
    "    xtrue = np.linspace(0,100,points)\n",
    "    ytrue = model(x = xtrue, m = m, c = c)\n",
    "\n",
    "    xerr = xerr * np.random.randn(points)\n",
    "    yerr = yerr * np.random.randn(points)\n",
    "    xobs = xtrue + xerr\n",
    "    yobs = ytrue + yerr\n",
    "    \n",
    "    plt.errorbar(xobs, yobs, xerr = xerr, yerr = yerr, fmt = 'x')\n",
    "    plt.errorbar(xtrue, ytrue, yerr = yerr, color = 'black', alpha = 0.5)\n",
    "    plt.xlim(-20,105)\n",
    "    plt.show()\n",
    "    \n",
    "    data = {'xtrue': xtrue, 'ytrue':ytrue, 'xobs':xobs, 'yobs':yobs, 'xerr':xerr, 'yerr':yerr}\n",
    "    \n",
    "    return data\n",
    "\n",
    "data = make_data(points = 30, m = 5, c = 10, xerr = 10, yerr = 10, seed = 1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now lets set up the prior and bilby output directory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#setting up bilby priors\n",
    "priors = dict(m=bilby.core.prior.Uniform(0, 20, 'm'),\n",
    "              c=bilby.core.prior.Uniform(0, 20, 'c'))\n",
    "\n",
    "outdir = 'outdir'\n",
    "livepoints = 500\n",
    "walks = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Our first step is to recover the straight line using a simple Gaussian Likelihood that only takes into account the y errors. Under the assumption we know x exactly. In this case, we pass in xtrue for x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "15:15 bilby INFO    : Running for label 'xtrue_1D_Gaussian', output will be saved to 'outdir'\n",
      "15:15 bilby INFO    : Search parameters:\n",
      "15:15 bilby INFO    :   m = Uniform(minimum=0, maximum=20, name='m', latex_label='m', unit=None, boundary=None)\n",
      "15:15 bilby INFO    :   c = Uniform(minimum=0, maximum=20, name='c', latex_label='c', unit=None, boundary=None)\n",
      "15:15 bilby INFO    : Single likelihood evaluation took 9.316e-05 s\n",
      "15:15 bilby WARNING : Supplied argument 'walks' not an argument of 'Pymultinest', removing.\n",
      "15:15 bilby INFO    : Using sampler Pymultinest with kwargs {'importance_nested_sampling': False, 'resume': False, 'verbose': True, 'sampling_efficiency': 'parameter', 'n_live_points': 500, 'n_params': 2, 'n_clustering_params': None, 'wrapped_params': None, 'multimodal': True, 'const_efficiency_mode': False, 'evidence_tolerance': 0.5, 'n_iter_before_update': 100, 'null_log_evidence': -1e+90, 'max_modes': 100, 'mode_tolerance': -1e+90, 'outputfiles_basename': 'outdir/pm_xtrue_1D_Gaussian/', 'seed': -1, 'context': 0, 'write_output': True, 'log_zero': -1e+100, 'max_iter': 0, 'init_MPI': False, 'dump_callback': None}\n",
      "15:15 bilby INFO    : Sampling time: 0:00:02.612593\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  analysing data from outdir/pm_xtrue_1D_Gaussian/.txt\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "15:15 bilby INFO    : Summary of results:\n",
      "nsamples: 1741\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence: -90.528 +/-  0.142\n",
      "ln_bayes_factor:    nan +/-  0.142\n",
      "\n"
     ]
    }
   ],
   "source": [
    "OneDGaussian_knownx = bilby.core.likelihood.GaussianLikelihood(x = data['xtrue'], y = data['yobs'], func = model, sigma = data['yerr'])\n",
    "result_1D_xtrue = bilby.run_sampler(\n",
    "    likelihood=OneDGaussian_knownx, priors=priors, sampler='pymultinest', npoints=livepoints,\n",
    "    walks=walks, outdir=outdir, label='xtrue_1D_Gaussian', clean=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_1D_xtrue.plot_corner(truth=dict(m=5, c = 10), titles = True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "15:15 bilby INFO    : Plotting 1000 draws\n",
      "15:15 bilby INFO    : Plotting maximum likelihood\n",
      "findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n"
     ]
    }
   ],
   "source": [
    "result_1D_xtrue.plot_with_data(model = model, x = data['xtrue'], y = data['yobs'], ndraws=1000, npoints=100)\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### As expected this is easy to recover and the sampler does a good job. However this was made too easy - by passing in the 'true' values of x. Lets see what happens when we pass in the observed values of x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "15:15 bilby INFO    : Running for label 'xobs_1D_Gaussian', output will be saved to 'outdir'\n",
      "15:15 bilby INFO    : Search parameters:\n",
      "15:15 bilby INFO    :   m = Uniform(minimum=0, maximum=20, name='m', latex_label='m', unit=None, boundary=None)\n",
      "15:15 bilby INFO    :   c = Uniform(minimum=0, maximum=20, name='c', latex_label='c', unit=None, boundary=None)\n",
      "15:15 bilby INFO    : Single likelihood evaluation took 1.014e-04 s\n",
      "15:15 bilby WARNING : Supplied argument 'resume' not an argument of 'Nestle', removing.\n",
      "15:15 bilby INFO    : Using sampler Nestle with kwargs {'method': 'multi', 'npoints': 500, 'update_interval': None, 'npdim': None, 'maxiter': None, 'maxcall': None, 'dlogz': None, 'decline_factor': None, 'rstate': None, 'callback': <function print_progress at 0x1c31470840>, 'steps': 100, 'enlarge': 1.2}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[Kit=  8739 logz=-47586.261917437\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "15:15 bilby INFO    : Sampling time: 0:00:23.472091\n",
      "15:15 bilby INFO    : Summary of results:\n",
      "nsamples: 9240\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence: -47585.903 +/-  0.174\n",
      "ln_bayes_factor:    nan +/-  0.174\n",
      "\n"
     ]
    }
   ],
   "source": [
    "OneDGaussian_unknownx = bilby.core.likelihood.GaussianLikelihood(x = data['xobs'], y = data['yobs'], \n",
    "                                                                 func = model, sigma = data['yerr'])\n",
    "result_1D_xobs = bilby.run_sampler(\n",
    "    likelihood=OneDGaussian_unknownx, priors=priors, sampler='nestle', npoints=livepoints,\n",
    "    walks=walks, outdir=outdir, label='xobs_1D_Gaussian')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_1D_xobs.plot_corner(truth=dict(m=5, c = 10), titles = True)\n",
    "# result_1D_xobs.plot_with_data(model = model, x = data['xobs'], y = data['yobs'], ndraws=1000, npoints=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### As expected, this is significantly worse. Let us now define a new likelihood which takes into account x errors but you also pass in xtrue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "class TwoDGaussianLikelihood_knownxtrue(bilby.Likelihood):\n",
    "    def __init__(self, xtrue, xobs, yobs, xerr, yerr, function):\n",
    "        \"\"\"\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        xtrue: array_like \n",
    "            The true injected x values\n",
    "        xobs, yobs: array_like\n",
    "            The data to analyse\n",
    "        xerr, yerr: array_like\n",
    "            The standard deviation of the noise\n",
    "        function:\n",
    "            The python function to fit to the data\n",
    "        \"\"\"\n",
    "        self.xobs = xobs\n",
    "        self.xtrue = xtrue\n",
    "        self.yobs = yobs\n",
    "        self.yerr = yerr\n",
    "        self.xerr = xerr\n",
    "        self.function = function\n",
    "        parameters = inspect.getargspec(function).args\n",
    "        parameters.pop(0)\n",
    "        self.parameters = dict.fromkeys(parameters)\n",
    "        super(TwoDGaussianLikelihood_knownxtrue, self).__init__(parameters=dict())\n",
    "\n",
    "    def log_likelihood(self):\n",
    "        resy = self.yobs - self.function(self.xtrue, **self.parameters)\n",
    "        resx = self.xobs - self.xtrue\n",
    "        return -0.5 * (np.sum(((resy) / self.yerr) ** 2) + np.sum(((resx) / self.xerr) ** 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nsarin/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:22: DeprecationWarning: inspect.getargspec() is deprecated since Python 3.0, use inspect.signature() or inspect.getfullargspec()\n",
      "15:15 bilby INFO    : Running for label 'knownx_2D_Gaussian', output will be saved to 'outdir'\n",
      "15:15 bilby INFO    : Search parameters:\n",
      "15:15 bilby INFO    :   m = Uniform(minimum=0, maximum=20, name='m', latex_label='m', unit=None, boundary=None)\n",
      "15:15 bilby INFO    :   c = Uniform(minimum=0, maximum=20, name='c', latex_label='c', unit=None, boundary=None)\n",
      "15:15 bilby INFO    : Single likelihood evaluation took 1.016e-04 s\n",
      "15:15 bilby WARNING : Supplied argument 'resume' not an argument of 'Nestle', removing.\n",
      "15:15 bilby INFO    : Using sampler Nestle with kwargs {'method': 'multi', 'npoints': 500, 'update_interval': None, 'npdim': None, 'maxiter': None, 'maxcall': None, 'dlogz': None, 'decline_factor': None, 'rstate': None, 'callback': <function print_progress at 0x1c31470840>, 'steps': 100, 'enlarge': 1.2}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[Kit=  6040 logz=-39.998329613649\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "15:16 bilby INFO    : Sampling time: 0:00:14.583768\n",
      "15:16 bilby INFO    : Summary of results:\n",
      "nsamples: 6541\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence: -39.569 +/-  0.143\n",
      "ln_bayes_factor:    nan +/-  0.143\n",
      "\n"
     ]
    }
   ],
   "source": [
    "TwoDGaussian_knownx = TwoDGaussianLikelihood_knownxtrue(xtrue = data['xtrue'], xobs = data['xobs'], \n",
    "                                                        yobs = data['yobs'], xerr=data['xerr'], \n",
    "                                                        yerr = data['yerr'], function=model)\n",
    "result_2D_knownx = bilby.run_sampler(\n",
    "    likelihood=TwoDGaussian_knownx, priors=priors, sampler='nestle', npoints=livepoints,\n",
    "    walks=walks, outdir=outdir, label='knownx_2D_Gaussian')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_2D_knownx.plot_corner(truth=dict(m=5, c = 10), titles = True)\n",
    "# result_2D_knownx.plot_with_data(model = model, x = data['xobs'], y = data['yobs'], ndraws=1000, npoints=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### This works well, however it still is not realistic as one still needs to 'know' the true x values. Getting around this requires marginalisation of the true x values or sampling over them.  See discussion in section 7 of https://arxiv.org/pdf/1008.4686.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class TwoDGaussianLikelihood_unknownx(bilby.Likelihood):\n",
    "    def __init__(self, xobs, yobs, xerr, yerr, function):\n",
    "        \"\"\"\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        xobs, yobs: array_like\n",
    "            The data to analyse\n",
    "        xerr, yerr: array_like\n",
    "            The standard deviation of the noise\n",
    "        function:\n",
    "            The python function to fit to the data\n",
    "        \"\"\"\n",
    "        self.xobs = xobs\n",
    "        self.yobs = yobs\n",
    "        self.yerr = yerr\n",
    "        self.xerr = xerr\n",
    "        self.function = function\n",
    "        parameters = inspect.getargspec(function).args\n",
    "        parameters.pop(0)\n",
    "        self.parameters = dict.fromkeys(parameters)\n",
    "        super(TwoDGaussianLikelihood_unknownx, self).__init__(parameters=dict())\n",
    "\n",
    "    def log_likelihood(self):\n",
    "        m = self.parameters['m']\n",
    "        v = np.array([-m, 1.0])\n",
    "        \n",
    "        Sigma2 = (self.xerr*m)**2 + self.yerr**2\n",
    "        model_y = self.function(self.xobs, **self.parameters)\n",
    "        Delta = self.yobs - model_y\n",
    "\n",
    "        ll = -0.5 * np.sum(Delta**2 / Sigma2 + np.log(Sigma2))\n",
    "                \n",
    "        return ll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nsarin/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:19: DeprecationWarning: inspect.getargspec() is deprecated since Python 3.0, use inspect.signature() or inspect.getfullargspec()\n",
      "15:16 bilby INFO    : Running for label 'unknownx_2D_Gaussian', output will be saved to 'outdir'\n",
      "15:16 bilby INFO    : Search parameters:\n",
      "15:16 bilby INFO    :   m = Uniform(minimum=0, maximum=20, name='m', latex_label='m', unit=None, boundary=None)\n",
      "15:16 bilby INFO    :   c = Uniform(minimum=0, maximum=20, name='c', latex_label='c', unit=None, boundary=None)\n",
      "15:16 bilby INFO    : Single likelihood evaluation took 9.000e-05 s\n",
      "15:16 bilby WARNING : Supplied argument 'resume' not an argument of 'Nestle', removing.\n",
      "15:16 bilby INFO    : Using sampler Nestle with kwargs {'method': 'multi', 'npoints': 500, 'update_interval': None, 'npdim': None, 'maxiter': None, 'maxcall': None, 'dlogz': None, 'decline_factor': None, 'rstate': None, 'callback': <function print_progress at 0x1c31470840>, 'steps': 100, 'enlarge': 1.2}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[Kit=  3107 logz=-127.8052412152\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "15:16 bilby INFO    : Sampling time: 0:00:06.944241\n",
      "15:16 bilby INFO    : Summary of results:\n",
      "nsamples: 3608\n",
      "ln_noise_evidence:    nan\n",
      "ln_evidence: -127.361 +/-  0.095\n",
      "ln_bayes_factor:    nan +/-  0.095\n",
      "\n"
     ]
    }
   ],
   "source": [
    "TwoDGaussian_unknownx = TwoDGaussianLikelihood_unknownx(xobs = data['xobs'], yobs = data['yobs'], \n",
    "                                                        xerr= data['xerr'], yerr = data['yerr'],\n",
    "                                                        function=model)\n",
    "result_2D_unknownx = bilby.run_sampler(\n",
    "    likelihood=TwoDGaussian_unknownx, priors=priors, sampler='nestle', npoints=livepoints,\n",
    "    walks=walks, outdir=outdir, label='unknownx_2D_Gaussian')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x396 with 4 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_2D_unknownx.plot_corner(truth=dict(m=5, c = 10), titles = True)\n",
    "# result_2D_unknownx.plot_with_data(model = model, x = data['xobs'], y = data['yobs'], ndraws=1000, npoints=100)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Another approach to getting around 'knowing true values of x' is to sample over them. This is problematic for several samplers as each x data point adds a dimension.\n",
    "\n",
    "### You can use hamiltonian monte carlo/PyStan to get around this problem and fit more complicated stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# result_2D_unknownx.plot_with_data(model = model, x = data['xobs'], y = data['yobs'], ndraws=1000, npoints=100)\n",
    "# plt.show()"
   ]
  }
 ],
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