MCMC Likelihood Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example MCMC analysis\n",
    "\n",
    "This tutorial will go through running a likelihood analysis with CCL. It will compare \"data\" and \"model\" angular shear power spectra, to infer values for the $\\Omega_c$ and $\\sigma_8$ parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import emcee # MCMC package https://emcee.readthedocs.io/en/stable/user/install/\n",
    "import matplotlib.pyplot as plt \n",
    "import pyccl as ccl\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "# for nicer plots http://seaborn.pydata.org -- optional\n",
    "# if you don't want to use it, you can comment this and the next line\n",
    "import seaborn as sns; sns.set_style('darkgrid')\n",
    "sns.set_context(\"talk\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The \"Data\"\n",
    "\n",
    "Let's create the \"data\" in the form of $C_\\ell$ As a proof of point, we'll make the \"data\" using CCL (as a proof of concept $-$ normally you will want to input your real data here)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First, we have to define a redshift distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = np.linspace(0., 3., 1024)\n",
    "i_lim = 26. # Limiting i-band magnitude\n",
    "z0 = 0.0417 * i_lim - 0.744\n",
    "\n",
    "ell = np.arange(2, 2000)\n",
    "delta_ell = ell[1] - ell[0]\n",
    "Ngal = 46. * 100.31 * (i_lim - 25.) # Normalisation, galaxies/arcmin^2\n",
    "pz = 1. / (2. * z0) * (z / z0)**2. * np.exp(-z / z0) # Redshift distribution, p(z)\n",
    "dNdz = Ngal * pz # Number density distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's set the cosmological parameters for our \"data\" and create it as an angular shear $C_\\ell$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "cosmo = ccl.Cosmology(Omega_c=0.27, \n",
    "                      Omega_b=0.045, \n",
    "                      h=0.67, \n",
    "                      n_s=0.96,  \n",
    "                      sigma8=0.83, \n",
    "                      transfer_function='bbks')\n",
    "\n",
    "tracer1 = ccl.WeakLensingTracer(cosmo, dndz=(z, dNdz))\n",
    "tracer2 = ccl.WeakLensingTracer(cosmo, dndz=(z, dNdz))\n",
    "data    = ccl.angular_cl(cosmo, tracer1, tracer2, ell) #C_ell"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple plot to see how this looks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ell, data)\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'$\\ell$')\n",
    "plt.ylabel(r'$C_\\ell$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make a covariance matrix:\n",
    "For the purpose of demonstration, we'll simply make a simplified diagonal covariance matrix without shape noise. Again you will want to input the actual covariance matrix here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# C_ell^2/(Area of LSST survey*ell*delta ell)\n",
    "cov = np.diag(data**2) * 2 * np.pi / ((4 * np.pi * 18000) * (np.pi / 180)**2 * ell * delta_ell) \n",
    "icov = np.linalg.inv(cov) #inverse of cov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the MCMC:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define our model that we want to test against our data. We'll use the same redshift distribution as above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will define `ln(probability)` (easier computationally that `probability`). Theta is the set of $\\Omega_c$ and $\\sigma_8$\n",
    "\n",
    "For the likelihood analysis, we'll use MCMC to find the set of parameters that minimises $\\chi^2 =(d - t)^T \\cdot \\Sigma^{-1} \\cdot (d-t)$, with $\\Sigma$: the covariance matrix $d$: data, and $t$: theory. The likelihood is then $L = e^{- \\chi^2 / 2}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lnprob(theta):\n",
    "    cosmo = ccl.Cosmology(\n",
    "        Omega_c=theta[0], \n",
    "        Omega_b=0.045, \n",
    "        h=0.67, \n",
    "        n_s=0.96, \n",
    "        sigma8=theta[1], \n",
    "        transfer_function='bbks')\n",
    "        \n",
    "    tracer1 = ccl.WeakLensingTracer(cosmo, dndz = (z, dNdz))\n",
    "    tracer2 = ccl.WeakLensingTracer(cosmo, dndz = (z, dNdz))\n",
    "    model = ccl.angular_cl(cosmo, tracer1, tracer2, ell)\n",
    "    diff = data - model\n",
    "    return -np.dot(diff, np.dot(icov, diff)) / 2.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll sample a 2-dimensional Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ndim = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Choose an initial set of positions for the walkers as a 2-d gaussian around some reasonable values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "nwalkers = 10\n",
    "p0 = [np.array([0.27,0.83]) * np.ones(ndim) + np.array([0.05 * np.random.rand(),\n",
    "      0.1 * np.random.rand()]) \n",
    "      for i in range(nwalkers)] \n",
    "p0 = np.array(p0)\n",
    "p0 = p0 - len(p0) * [[0.025,0.05]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the sampler with the chosen specs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run 50 steps as a burn-in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 12min, sys: 22.5 s, total: 12min 23s\n",
      "Wall time: 1min 54s\n"
     ]
    }
   ],
   "source": [
    "%time pos, prob, state = sampler.run_mcmc(p0, 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reset the chain to remove the burn-in samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler.reset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting from the final position in the burn-in chain, sample for 100 steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler.run_mcmc(pos, 100, rstate0 = state); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print out the mean acceptance fraction. In general, acceptance_fraction has an entry for each  walker so, in this case, it is a 10-dimensional vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean acceptance fraction: 0.67\n"
     ]
    }
   ],
   "source": [
    "print(f\"Mean acceptance fraction: {np.mean(sampler.acceptance_fraction):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the samples from the results to plot them later:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = sampler.chain[:, :, :].reshape((-1, ndim))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results as mean and $95\\%$ Confidence interval of $\\Omega_c$ and $\\sigma_8$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "mapout=map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),\n",
    "                             zip(*np.percentile(samples, [2.5, 50, 97.5],\n",
    "                                                axis=0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results as a contour plot of the two parameters $-$ $\\Omega_c$ and $\\sigma_8$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0x15d9fdf40>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.jointplot(\n",
    "    data=mapout,\n",
    "    x=samples[:,0],\n",
    "    y=samples[:,1],\n",
    "    kind='kde',\n",
    "    height=10).set_axis_labels(r\"$\\Omega_c$\", r\"$\\sigma_8$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python [conda env:ccl-dev-v3] *",
   "language": "python",
   "name": "conda-env-ccl-dev-v3-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}