{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Parallaxes from GAIA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The text.latex.preview rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The mathtext.fallback_to_cm rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: Support for setting the 'mathtext.fallback_to_cm' rcParam is deprecated since 3.3 and will be removed two minor releases later; use 'mathtext.fallback : 'cm' instead.\n",
      "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The validate_bool_maybe_none function was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The savefig.jpeg_quality rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The keymap.all_axes rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The animation.avconv_path rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /Users/holtz/anaconda3/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The animation.avconv_args rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this exercise, we will download some data from the GAIA archive on parallaxes of stars. The parallax, $p$, of a star is half the change in the angular direction of a star as seen from opposite points of the Earth's orbit, as shown here:\n",
    "\n",
    "<img src=https://pbs.twimg.com/media/Ci6iK8zXEAAdKNM.jpg>\n",
    "\n",
    "\n",
    "It can be used to determine the distance to a star: simple geometry gives \n",
    "$$tan(p) = 1 / d$$\n",
    "where $d$ is the distance in units of the earth-Sun distance, which is called an astronomical unit (and is equal to $1.496 \\times 10^{13}$ cm\n",
    "\n",
    "Since stars are very far away, the parallax is always a very small angle, so\n",
    "$$tan(p) \\approx p = 1/d$$\n",
    "where $p$ is in radians.\n",
    "Astronomers have defined a distance unit called the parsec, such that the distance in parsecs is:\n",
    "$$d({\\rm in\\ parsec}) = 1 / p ({\\rm in\\ arcsec})$$\n",
    "where 1 arcsec = 1/3600. degree. With this definition, \n",
    "$$1 parsec = 1 astronomical unit \\times 3600 arcsec/degree \\times 180 / \\pi = 3.086\\times 10^{18} cm$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The <a href=https://sci.esa.int/web/gaia> GAIA </a> mission is currently measuring parallaxes to <b> billions</b> of stars. They release data to the public through a relational database in the <a href= https://gea.esac.esa.int/archive/> GAIA archive</a>. We will download some data from the database, using a Python package called <a href=https://astroquery.readthedocs.io/en/latest/> astroquery </a>. Once astroquery has been installed in your Python distribution, we can import it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import astroquery"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many quantities are available in the GAIA archive database. These are described by the database <i> schema</i>. You can find the schema for GAIA at the <a href= https://gea.esac.esa.int/archive/> GAIA archive</a>: click on the Search link at the top, and then the Advanced (ADQL) link, and finally expand the gaia.edr3.gaia_source description on the left by clicking the +. This will show you all of the information in this database table. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will query the database using the Astronomical Data Query Language (ADQL) which is a superset of the standard Structured Query Language (SQL). The basic format of queries is relatively simple:\n",
    "\n",
    "<pre>\n",
    "SELECT selectList \n",
    "FROM fromClause \n",
    "[WHERE conditions] \n",
    "</pre>\n",
    "\n",
    "Basically, the selectList gives the quantities you want to download, the fromClause gives the table where the quantities are located, and the optional WHERE clause gives some conditions for which objects you want to download.\n",
    "\n",
    "\n",
    "ADQL is an extension of SQL, in particular, defines some useful geometric functions, e.g. CONTAINS() can be used to select objects within some distance of some point in the sky, e.g.\n",
    "<pre>\n",
    "WHERE 1=CONTAINS(POINT('ICRS', ra, dec), CIRCLE('ICRS', tablera, tabledec, radius)\n",
    "</pre>\n",
    "would select points where the database coordinate variables (tablera and tabledec, but you will need to use the appropriate column names) fall within some distance of the ra/dec specified in the query.\n",
    "\n",
    "For a little more information on ADQL/SQL see https://www.cosmos.esa.int/documents/915837/915858/ADQL_handson_slides.pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's write a query to get the parallaxes of all stars within 0.5 degree of the north Galactic pole. Look at the schema to get the column names for ra, dec, and parallax, and try to complete the following SQL query. Give it a quick try, then move on to the next cell to see a valid query:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell gives and implements the query"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SELECT ra, dec, parallax, parallax_error\n",
      "         FROM gaiaedr3.gaia_source\n",
      "         WHERE 1=CONTAINS(\n",
      "                  POINT('ICRS', 192.859478, 27.128252),\n",
      "                  CIRCLE('ICRS',ra, dec, 0.500000))\n",
      "INFO: Query finished. [astroquery.utils.tap.core]\n",
      "Returned 2052 objects\n"
     ]
    }
   ],
   "source": [
    "from astroquery.gaia import Gaia\n",
    "from astropy.coordinates import SkyCoord\n",
    "import astropy.units as u\n",
    "\n",
    "# get RA/DEC at the Galactic pole, which has l=0, b=90\n",
    "coord = SkyCoord(0, 90, unit=(u.degree, u.degree), frame='galactic')\n",
    "ra=coord.icrs.ra.value\n",
    "dec=coord.icrs.dec.value\n",
    "\n",
    "# search radius\n",
    "rad=0.5\n",
    "\n",
    "#form the SQL query\n",
    "query=\"\"\"SELECT ra, dec, parallax, parallax_error\n",
    "         FROM gaiaedr3.gaia_source\n",
    "         WHERE 1=CONTAINS(\n",
    "                  POINT('ICRS', {:f}, {:f}),\n",
    "                  CIRCLE('ICRS',ra, dec, {:f}))\"\"\".format(ra,dec,rad)\n",
    "print(query)\n",
    "\n",
    "# run the query and get the results\n",
    "job = Gaia.launch_job_async(query)\n",
    "tab = job.get_results()\n",
    "print('Returned {:d} objects'.format(len(tab)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are returned in an astropy table. You can display them in a convenient notebook interface. Individual columns can be referenced using tab['columnname'], e.g. tab['parallax']. If you are more familiar/comfortable with pandas data frame, tables can easily be converted to pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "parallax of row 100: 0.294\n"
     ]
    }
   ],
   "source": [
    "#display the results\n",
    "print('parallax of row 100: {:.3f}'.format(tab['parallax'][100]))\n",
    "tab.show_in_notebook(display_length=10)\n",
    "tab.write('gaia.fits')\n",
    "\n",
    "#if you prefer to convert to pandas, use the following\n",
    "#ptab = tab.to_pandas()\n",
    "#print(ptab['parallax'][100])\n",
    "#print(ptab)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's solve for Bayesian posterior probability distribution for distance to our stars. \n",
    "$$P(d|p) = {P(p|d)P(d)\\over P(p)}$$\n",
    "We will avoid any calculation of $P(p)$ and just normalize our posterior PDF.\n",
    "First, we need to formulate an expression for the likelihood, $P(p|d)$. For GAIA, the parallax uncertainties are expected to be distributed according to a normal distribution. For a gaussian uncertainty in measurement parallax, we then have:\n",
    "$$P(p|d) = {1\\over \\sigma_p\\sqrt{2\\pi}} \\exp{-0.5 (p-{1\\over d})^2 \\over \\sigma_p^2}$$\n",
    "Write a function that will calculate this likelihood:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood(parallax,parallax_err,distance) :\n",
    "    \"\"\" Return likelihood of a parallax, given a distance and parallax uncertainty\n",
    "        assume parallax in mas, and distance in kpc\n",
    "    \"\"\"\n",
    "    # return value of likelihood\n",
    "    return 1/np.sqrt(2*np.pi)/parallax_err*np.exp(-0.5*(parallax-1./distance)**2/parallax_err**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have to decide what to use for a prior. One could use just a positivity constraint, which would lead to an improper prior (since the integral to infinity is infinite), or one could impose a maximum distance, perhaps motivated by the faint limit of gaia (around g=20) and the absolute magnitude of the faintest stars. \n",
    "<br>\n",
    "However, these would not account for the fact that in a cone search, such as we have done above, the volume element grows as $d^2$, so that could be added to the prior.\n",
    "<br>\n",
    "In addition, one might want to incorporate the knowledge that, looking perpendicular to the Galactic plane, the density of stars is known to drop off, roughly exponentially, let's say with a scale height of 0.5 kpc.\n",
    "<br>\n",
    "<a href=https://iopscience.iop.org/article/10.3847/1538-3881/aacb21> Bailer-Jones et al 2018</a> adopt a prior\n",
    "$$P(d) = d^2 \\exp(-d/L)$$\n",
    "to account for these considerations,  where $L$ is a scale length that depends on Galactic longitude and latitude. Let's adopt this prior, with $L=0.5$ at the Galactic pole. Note that this is a proper prior, since the exponential drops off faster than the $d^2$ term.\n",
    "<br>\n",
    "Write a function to return the value of this prior:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prior(distance,scalelength) :\n",
    "    \"\"\" Return distance prior based on Bailer-Jones formulation\n",
    "    \"\"\"\n",
    "    return distance**2 *np.exp(-distance/scalelength)  # return value of prior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK, now let's construct the posterior PDF. We'll input an array of distances at which to sample the PDF. Write a function to return the posterior PDF for a single star, given the measured parallax and parallax uncertainty:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def posterior(p,perr,dist,l=0.5):\n",
    "    \"\"\" Calculate posterior PDF P(d|p,perr) for 0<d<5 kpc\n",
    "        Return the normalized PDF\n",
    "    \"\"\"\n",
    "    pdf=likelihood(p,perr,dist)*prior(dist,l)  #calculate posterior PDF at input distances\n",
    "    return pdf/pdf.sum()                       # return normalized PDF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also write a routine to return the maximum likelihood distance and the frequentist uncertainty (from propagation of errors):\n",
    "$$d = {1\\over p}$$\n",
    "$$\\sigma_d = \\left|{\\sigma_p\\over p^2}\\right|$$\n",
    "We'll also write a routine to return the distribution given a set of input distances, assuming a Gaussian with center $d$ and standard deviation $\\sigma_d$\n",
    "$$P = {1\\over \\sigma_d\\sqrt{2\\pi}} \\exp{-0.5 (dist-d)^2\\over \\sigma_d^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mle(p,perr) :\n",
    "    \"\"\" Return maximum likelihood distance and uncertainty\n",
    "    \"\"\"\n",
    "    return 1/p, np.abs(perr/p**2)   # return MLE distance and uncertaintye\n",
    "\n",
    "def mle_dist(dist,p,perr) :\n",
    "    \"\"\" Return a distribution around the MLE estimate for an input array of distances\n",
    "    \"\"\"\n",
    "    d,derr=mle(p,perr)\n",
    "    return 1/np.sqrt(2*np.pi)/derr*np.exp(-0.5*(dist-d)**2/derr**2)  # return Gaussian distribution at input dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK, now let's calculate the posterior for a few of our stars. For each star calculate and plot the posterior PDF, and also plot the MLE distribution given the MLE mean and uncertainty, under the usual approximation that the uncertainty is given by a Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/holtz/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \n"
     ]
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    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12cd09c90>"
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     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# color array so we can color Bayesian and MLE with same color, but different line type\n",
    "colors=['r','g','b','c','m','y']\n",
    "icolor=0\n",
    "dist=np.arange(0,5,0.001)   # distances at which to calculate posterior, in kpc\n",
    "\n",
    "# loop over first 10 stars\n",
    "for istar,data in enumerate(tab[0:10]) :\n",
    "  # only consider records with valid parallax\n",
    "  if np.isfinite(data['parallax']) :\n",
    "    pdf=posterior(data['parallax'],data['parallax_error'],dist)  # calculate the posterior PDF with your routine\n",
    "    \n",
    "    # plot the Bayesian posterior PDF as solid lines\n",
    "    plt.plot(dist,pdf,color=colors[icolor%6],label=str(istar))\n",
    "    \n",
    "    # plot the MLE PDF as dotted lines. Need to normalize this because our bin spacing not equal to 1\n",
    "    mle_pdf = mle_dist(dist,data['parallax'],data['parallax_error'])   # calculate the MLE distribution using your routine\n",
    "    plt.plot(dist,mle_pdf/mle_pdf.sum(),color=colors[icolor%6],ls=':')\n",
    "    \n",
    "    icolor+=1   #increment the counter for the color\n",
    "plt.legend()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Describe and discuss the posterior PDFs and how they are or are not affected by the prior. Describe how the Bayesian PDF compares to the maximum likelihood distribution.\n",
    "<br>\n",
    "<b> ANSWER HERE: </b>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now write a routine to return some statistics derived from posterior PDF: the mean, mode, median, and 90% equal tailed credible region. Note the routine <a href=https://numpy.org/doc/stable/reference/generated/numpy.cumsum.html> numpy.cumsum()</a> for converting a PDF into a cumulative distribution function (CDF). You can then find the index where the CDF equals desired percentiles (e.g., 5, 50, and 95) and then get the distance at that index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pdb\n",
    "def stats(dist,pdf) :\n",
    "    \"\"\" return some statistics of a PDF\n",
    "    \"\"\"\n",
    "    mean = (dist*pdf).sum()/pdf.sum()   # expression for mean distance\n",
    "    mode = dist[pdf.argmax()]           # exprssion for mode\n",
    "\n",
    "    cdf=np.cumsum(pdf/pdf.sum())\n",
    "    p5 = np.argmin(np.abs(cdf-0.05))    # expression for 5th percentile distance\n",
    "    p50 = np.argmin(np.abs(cdf-0.5))    # expression for 50th percentile distance\n",
    "    p95 = np.argmin(np.abs(cdf-0.95))   # expression for 95th percentile distance\n",
    "    \n",
    "    median = dist[p50]\n",
    "    credible_interval = [dist[p5],dist[p95]]\n",
    "\n",
    "    return mean, mode, median, credible_interval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a function to get the posterior PDF and its statistics for a given input record, and plot them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pdf_stats(data) :\n",
    "    \"\"\" Calculate posterior PDF statistics given a single data record that has 'parallax' and 'parallax_error'\n",
    "    \"\"\"\n",
    "\n",
    "    if np.isfinite(data['parallax']) :\n",
    "        pdf=posterior(data['parallax'],data['parallax_error'],dist)  # get posterior using your routine\n",
    "    \n",
    "        # plot the Bayesian posterior PDF as solid lines\n",
    "        plt.plot(dist,pdf,color='k')\n",
    "\n",
    "        mean, mode, median, credible_interval = stats(dist,pdf)    # get statistics from posterior using your routine\n",
    "        plt.plot([mean,mean],plt.ylim(),label='mean')\n",
    "        plt.plot([mode,mode],plt.ylim(),label='mode')\n",
    "        plt.plot([median,median],plt.ylim(),label='median')\n",
    "        plt.plot(credible_interval,[0,0],label='credible interval')\n",
    "\n",
    "        print(mean,mode,median,credible_interval)\n",
    "        \n",
    "        d,derr=mle(data['parallax'],data['parallax_error'])    # get the MLE distance and uncertainty\n",
    "        plt.plot([d,d],plt.ylim(),label='MLE distance',ls=':')\n",
    "        plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Choose some interesting individual stars from your plot above and plot the PDFs and their statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/holtz/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5858317936626336 1.087 1.424 [0.674, 3.061]\n",
      "1.6014695612247376 1.174 1.452 [0.805, 2.915]\n",
      "0.9427905871169853 0.918 0.934 [0.807, 1.107]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for star in [1,4,6] :\n",
    "    plt.figure()\n",
    "    pdf_stats(tab[star])\n",
    "    plt.title('star {:d}'.format(star))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Discuss differences between the different statistics, and what you think are the most useful descriptive statistics.\n",
    "<br>\n",
    "<b>ANSWER HERE: </b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}