single-source/tutorial/Distance_inference-single_source.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coryn Bailer-Jones, MPIA Heidelberg (https://mpia.de/homes/calj)\n",
    "\n",
    "The main reference for this tutorial is [Bailer-Jones 2015](http://adsabs.harvard.edu/abs/2015PASP..127..994B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3d0f87d2-479b-49c5-9219-35dd71c8ae54"
    }
   },
   "source": [
    "# Global settings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Relative to the root directory, ensure that the R codes (*.R) are \"Rcode/\" and the data files (*.csv) are in \"data/\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nbpresent": {
     "id": "ba432e7c-ac3d-4650-a06d-4ea0d7127f20"
    }
   },
   "outputs": [],
   "source": [
    "rootDir <- \"./\" # directory containing Rcode/ and data/ directories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "nbpresent": {
     "id": "082aeada-6ebe-46da-bfa7-b1864f78dd20"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: spam\n",
      "Loading required package: dotCall64\n",
      "Loading required package: grid\n",
      "Spam version 2.2-0 (2018-06-19) is loaded.\n",
      "Type 'help( Spam)' or 'demo( spam)' for a short introduction \n",
      "and overview of this package.\n",
      "Help for individual functions is also obtained by adding the\n",
      "suffix '.spam' to the function name, e.g. 'help( chol.spam)'.\n",
      "\n",
      "Attaching package: ‘spam’\n",
      "\n",
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    backsolve, forwardsolve\n",
      "\n",
      "Loading required package: maps\n",
      "See www.image.ucar.edu/~nychka/Fields for\n",
      " a vignette and other supplements. \n"
     ]
    }
   ],
   "source": [
    "setwd(paste(rootDir, \"Rcode\", sep=\"\"))\n",
    "conv <- pi/180 \n",
    "source(\"general_functions.R\")\n",
    "source(\"distance_functions.R\")\n",
    "setwd(\"../\")\n",
    "library(MASS) # for truehist\n",
    "library(fields) # for image.plot\n",
    "library(RColorBrewer) # for colorRampPalette\n",
    "mypalette <- colorRampPalette(brewer.pal(9, \"Greys\"), space=\"rgb\", interpolate=\"linear\", bias=2.5)\n",
    "mycols <- mypalette(64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "3a87d403-95c2-426b-8ee6-f98cc9e56b54"
    }
   },
   "source": [
    "# Draw from distance priors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "nbpresent": {
     "id": "3b870828-d7e7-4705-97f3-01f086323881"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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87s3bs3ODjY1dV17dq1bCcCANAYhmGy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\nvhBGv7MwAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the priors to get feel for what they look like.\n",
    "# To check the code, we draw from distance priors and plot the samples as a histogram. \n",
    "# 1,2,3 are uniform in distance, uniform space density, and exponentially decreasing space density, respectively.\n",
    "par(mfrow=c(2,2), mar=c(5,5,0.5,1), oma=c(0.1,0.1,0.5,0.1), mgp=c(2.2,0.8,0), cex=1.0) \n",
    "truehist(r.distprior1(Nsamp=1e5, rmax=1e3), h=20)\n",
    "truehist(r.distprior2(Nsamp=1e5, rmax=1e3), h=20)\n",
    "truehist(r.distprior3(Nsamp=1e5, rlen=1e3), h=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Posterior for a simulated parallax using the exponentially decreasing distance prior\n",
    "\n",
    "I won't consider further the uniform distance or uniform space density priors. They are not recommended. But you can easily plot these and compute estimates from them as described in [Bailer-Jones 2015](http://adsabs.harvard.edu/abs/2015PASP..127..994B). See also [Astraatmadja & Bailer-Jones 2016a](http://adsabs.harvard.edu/abs/2016ApJ...832..137A)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "nbpresent": {
     "id": "d8154560-bacb-4cd1-8b58-693ea84cc9cc"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>mode</dt>\n",
       "\t\t<dd>1097.86125034192</dd>\n",
       "\t<dt>lo</dt>\n",
       "\t\t<dd>790.894722005958</dd>\n",
       "\t<dt>hi</dt>\n",
       "\t\t<dd>1748.04964710417</dd>\n",
       "\t<dt>5%</dt>\n",
       "\t\t<dd>813.041734370808</dd>\n",
       "\t<dt>50%</dt>\n",
       "\t\t<dd>1419.88248491656</dd>\n",
       "\t<dt>95%</dt>\n",
       "\t\t<dd>3440.21003730251</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[mode] 1097.86125034192\n",
       "\\item[lo] 790.894722005958\n",
       "\\item[hi] 1748.04964710417\n",
       "\\item[5\\textbackslash{}\\%] 813.041734370808\n",
       "\\item[50\\textbackslash{}\\%] 1419.88248491656\n",
       "\\item[95\\textbackslash{}\\%] 3440.21003730251\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "mode\n",
       ":   1097.86125034192lo\n",
       ":   790.894722005958hi\n",
       ":   1748.049647104175%\n",
       ":   813.04173437080850%\n",
       ":   1419.8824849165695%\n",
       ":   3440.21003730251\n",
       "\n"
      ],
      "text/plain": [
       "     mode        lo        hi        5%       50%       95% \n",
       "1097.8613  790.8947 1748.0496  813.0417 1419.8825 3440.2100 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ebo6Ghl85Q1a9Y07TcDAHBLNFPs5s2b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\nYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulate parallax (w) and its uncertainty (wsd) (in as). You should experiment with changing these.\n",
    "w    <- 1e-3\n",
    "wsd  <- 3e-4\n",
    "# Set length scale of the prior (in pc)\n",
    "rlen <- 1e3\n",
    "# Plot unnormalized posterior, P*(r|w,wsd,rlen).\n",
    "# Compute and overplot the mode and FWHM (red) and the three quantiles 5%, 50% (median), 95% (blue).\n",
    "# Note: The quantiles are computed via MCMC sampling, which is slow and sometimes inaccurate.\n",
    "# Note: computation of the FWHM uses a root finding algorithm which may return warnings.\n",
    "# Compute and overplot the distance from a naive parallax inversion and the uncertainty on this \n",
    "# from a first order uncertainty propagation (green).\n",
    "r <- seq(from=0, to=5e3, length.out=1e3) # May need to change limits depending on values of simulated data.\n",
    "plot(r, ud.distpost3(r, w, wsd, rlen), type=\"l\", lwd=2, xlab=\"distance r [pc]\", ylab=\"P*(r|w,wsd,rlen)\")\n",
    "rMode  <- mode.distpost3(w, wsd, rlen)\n",
    "rFWHM  <- fwhm.distpost3(w, wsd, rMode=rMode, rlen, rmax=1e6) \n",
    "rQuant <- quantiles.distpost3(w, wsd, rlen, probs=c(0.05, 0.5, 0.95), Nsamp=1e5)\n",
    "c(mode=rMode, rFWHM, rQuant) # FWHM given as \"lo, hi\", quantiles given as \"5%, 50%, 95%\"\n",
    "abline(v=c(rMode, rQuant), col=c(\"red\", rep.int(\"blue\", length(rQuant))))\n",
    "M <- ud.distpost3(r=rMode, w, wsd, rlen)\n",
    "lines(x=c(rFWHM), y=c(M,M)/2, col=\"red\")\n",
    "abline(v=c(1/w, (1/w)+c(+1,-1)*wsd/w^2), col=\"green\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distance inference for multiple stars from GDR1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "e661fab7-5570-425f-ae9a-4614d98459e9"
    }
   },
   "source": [
    "## Read and check GDR1 data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following Gaia archive query was used to creates gdr1set01.csv (6909 sources):\n",
    "```\n",
    "select\n",
    "parallax, parallax_error, l, b\n",
    "from gaiadr1.tgas_source\n",
    "where l > 175 and l < 185 and b > -5 and b < +5\n",
    "```\n",
    "Note the unfortunate choice of the field name \"parallax_error\". This is not the \"error\" in the parallax, but its uncertainty (defined as the standard deviation of the Gaussian likelihood)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note that parallaxes are in mas, angles in degrees\n",
    "dat <- read.csv(paste(rootDir, \"data/gdr1set01.csv\", sep=\"\"), sep=\",\")\n",
    "# convert parallaxes to arcsec so that distances come out as pc\n",
    "dat$parallax <- 1e-3*dat$parallax\n",
    "dat$parallax_error <- 1e-3*dat$parallax_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "nbpresent": {
     "id": "f75b19d4-ad2f-47c5-bc2d-caa5c7a0c72f"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>parallax</th><th scope=col>parallax_error</th><th scope=col>l</th><th scope=col>b</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.0003544360</td><td>0.0009808290</td><td>175.2932    </td><td>-4.994473   </td></tr>\n",
       "\t<tr><td>0.0017235501</td><td>0.0002843546</td><td>175.1683    </td><td>-4.150353   </td></tr>\n",
       "\t<tr><td>0.0004696314</td><td>0.0003569680</td><td>175.1830    </td><td>-4.193350   </td></tr>\n",
       "\t<tr><td>0.0013279830</td><td>0.0004677145</td><td>175.1697    </td><td>-4.573416   </td></tr>\n",
       "\t<tr><td>0.0016021144</td><td>0.0002714283</td><td>175.0998    </td><td>-4.030721   </td></tr>\n",
       "\t<tr><td>0.0038513590</td><td>0.0002324245</td><td>175.0159    </td><td>-3.711086   </td></tr>\n",
       "\t<tr><td>0.0011199443</td><td>0.0003135849</td><td>175.1362    </td><td>-4.367051   </td></tr>\n",
       "\t<tr><td>0.0003205481</td><td>0.0002506443</td><td>175.0811    </td><td>-4.690289   </td></tr>\n",
       "\t<tr><td>0.0016388455</td><td>0.0003956992</td><td>175.0806    </td><td>-4.610517   </td></tr>\n",
       "\t<tr><td>0.0013188627</td><td>0.0002670727</td><td>175.1550    </td><td>-4.655140   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " parallax & parallax\\_error & l & b\\\\\n",
       "\\hline\n",
       "\t 0.0003544360 & 0.0009808290 & 175.2932     & -4.994473   \\\\\n",
       "\t 0.0017235501 & 0.0002843546 & 175.1683     & -4.150353   \\\\\n",
       "\t 0.0004696314 & 0.0003569680 & 175.1830     & -4.193350   \\\\\n",
       "\t 0.0013279830 & 0.0004677145 & 175.1697     & -4.573416   \\\\\n",
       "\t 0.0016021144 & 0.0002714283 & 175.0998     & -4.030721   \\\\\n",
       "\t 0.0038513590 & 0.0002324245 & 175.0159     & -3.711086   \\\\\n",
       "\t 0.0011199443 & 0.0003135849 & 175.1362     & -4.367051   \\\\\n",
       "\t 0.0003205481 & 0.0002506443 & 175.0811     & -4.690289   \\\\\n",
       "\t 0.0016388455 & 0.0003956992 & 175.0806     & -4.610517   \\\\\n",
       "\t 0.0013188627 & 0.0002670727 & 175.1550     & -4.655140   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "parallax | parallax_error | l | b | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0.0003544360 | 0.0009808290 | 175.2932     | -4.994473    | \n",
       "| 0.0017235501 | 0.0002843546 | 175.1683     | -4.150353    | \n",
       "| 0.0004696314 | 0.0003569680 | 175.1830     | -4.193350    | \n",
       "| 0.0013279830 | 0.0004677145 | 175.1697     | -4.573416    | \n",
       "| 0.0016021144 | 0.0002714283 | 175.0998     | -4.030721    | \n",
       "| 0.0038513590 | 0.0002324245 | 175.0159     | -3.711086    | \n",
       "| 0.0011199443 | 0.0003135849 | 175.1362     | -4.367051    | \n",
       "| 0.0003205481 | 0.0002506443 | 175.0811     | -4.690289    | \n",
       "| 0.0016388455 | 0.0003956992 | 175.0806     | -4.610517    | \n",
       "| 0.0013188627 | 0.0002670727 | 175.1550     | -4.655140    | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   parallax     parallax_error l        b        \n",
       "1  0.0003544360 0.0009808290   175.2932 -4.994473\n",
       "2  0.0017235501 0.0002843546   175.1683 -4.150353\n",
       "3  0.0004696314 0.0003569680   175.1830 -4.193350\n",
       "4  0.0013279830 0.0004677145   175.1697 -4.573416\n",
       "5  0.0016021144 0.0002714283   175.0998 -4.030721\n",
       "6  0.0038513590 0.0002324245   175.0159 -3.711086\n",
       "7  0.0011199443 0.0003135849   175.1362 -4.367051\n",
       "8  0.0003205481 0.0002506443   175.0811 -4.690289\n",
       "9  0.0016388455 0.0003956992   175.0806 -4.610517\n",
       "10 0.0013188627 0.0002670727   175.1550 -4.655140"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Reduce the size of the data set for testing purposes\n",
    "dat <- dat[1:10,]\n",
    "dat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "2ecbc24b-e297-41c5-9ac3-4fb41db8c880"
    }
   },
   "source": [
    "## Compute mode and FWHM of posterior\n",
    "Now compute distance posterior for each star. Rather than plotting every posterior, I compute the mode and FWHM for each (and after than the quantiles). Note the following things about R:\n",
    "1. I use the R function Vectorize to create an in-place version of the function mode.distpost3 to accept both w and wsd as vector arguments, which induces it to return a vector, namely the mode for each star.\n",
    "2. Recall what was written above about the code for computing the FWHM possibly returning warnings.\n",
    "3. I don't compute the mean and standard deviation. However, as my function to compute the quantiles draws samples (via MCMC), these samples could also be used to compute the mean (and higher moments)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "nbpresent": {
     "id": "9e46689d-a6a7-465d-a724-fff969dee022"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>rMode</th><th scope=col>lo</th><th scope=col>hi</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>2065.3055</td><td> 944.4383</td><td>4161.7413</td></tr>\n",
       "\t<tr><td> 604.0960</td><td> 501.5076</td><td> 759.5778</td></tr>\n",
       "\t<tr><td>2060.1100</td><td>1217.7406</td><td>3819.4863</td></tr>\n",
       "\t<tr><td> 899.7459</td><td> 595.9186</td><td>1722.0357</td></tr>\n",
       "\t<tr><td> 650.4302</td><td> 537.4952</td><td> 823.4606</td></tr>\n",
       "\t<tr><td> 261.3139</td><td> 243.8314</td><td> 281.5017</td></tr>\n",
       "\t<tr><td> 978.8059</td><td> 717.3162</td><td>1517.5688</td></tr>\n",
       "\t<tr><td>2502.6507</td><td>1593.9393</td><td>4244.6950</td></tr>\n",
       "\t<tr><td> 666.8227</td><td> 505.9770</td><td> 976.9305</td></tr>\n",
       "\t<tr><td> 799.7472</td><td> 637.7348</td><td>1070.7340</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       " rMode & lo & hi\\\\\n",
       "\\hline\n",
       "\t 2065.3055 &  944.4383 & 4161.7413\\\\\n",
       "\t  604.0960 &  501.5076 &  759.5778\\\\\n",
       "\t 2060.1100 & 1217.7406 & 3819.4863\\\\\n",
       "\t  899.7459 &  595.9186 & 1722.0357\\\\\n",
       "\t  650.4302 &  537.4952 &  823.4606\\\\\n",
       "\t  261.3139 &  243.8314 &  281.5017\\\\\n",
       "\t  978.8059 &  717.3162 & 1517.5688\\\\\n",
       "\t 2502.6507 & 1593.9393 & 4244.6950\\\\\n",
       "\t  666.8227 &  505.9770 &  976.9305\\\\\n",
       "\t  799.7472 &  637.7348 & 1070.7340\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "rMode | lo | hi | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 2065.3055 |  944.4383 | 4161.7413 | \n",
       "|  604.0960 |  501.5076 |  759.5778 | \n",
       "| 2060.1100 | 1217.7406 | 3819.4863 | \n",
       "|  899.7459 |  595.9186 | 1722.0357 | \n",
       "|  650.4302 |  537.4952 |  823.4606 | \n",
       "|  261.3139 |  243.8314 |  281.5017 | \n",
       "|  978.8059 |  717.3162 | 1517.5688 | \n",
       "| 2502.6507 | 1593.9393 | 4244.6950 | \n",
       "|  666.8227 |  505.9770 |  976.9305 | \n",
       "|  799.7472 |  637.7348 | 1070.7340 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      rMode     lo        hi       \n",
       " [1,] 2065.3055  944.4383 4161.7413\n",
       " [2,]  604.0960  501.5076  759.5778\n",
       " [3,] 2060.1100 1217.7406 3819.4863\n",
       " [4,]  899.7459  595.9186 1722.0357\n",
       " [5,]  650.4302  537.4952  823.4606\n",
       " [6,]  261.3139  243.8314  281.5017\n",
       " [7,]  978.8059  717.3162 1517.5688\n",
       " [8,] 2502.6507 1593.9393 4244.6950\n",
       " [9,]  666.8227  505.9770  976.9305\n",
       "[10,]  799.7472  637.7348 1070.7340"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rMode <- Vectorize(mode.distpost3, c(\"w\", \"wsd\"))(w=dat$parallax, wsd=dat$parallax_error, rlen)\n",
    "rFWHM <- Vectorize(fwhm.distpost3, c(\"w\", \"wsd\", \"rMode\"))(w=dat$parallax, wsd=dat$parallax_error, rMode=rMode, rlen=rlen, rmax=1e6)\n",
    "rFWHM <- t(rFWHM)\n",
    "cbind(rMode, rFWHM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "nbpresent": {
     "id": "00284cd3-4854-4854-be65-9a38b5d79423"
    }
   },
   "outputs": [],
   "source": [
    "# Now compute the quantiles. As noted above, this uses MCMC, which is very slow.\n",
    "# A grid would be faster, but its size/spacing would generally need to be optimized for every source separately.\n",
    "rQuant <- Vectorize(quantiles.distpost3, c(\"w\", \"wsd\"))(w=dat$parallax, wsd=dat$parallax_error, rlen, probs=c(0.05, 0.5, 0.95), Nsamp=1e5)\n",
    "rQuant <- t(rQuant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "nbpresent": {
     "id": "96c2bec1-39e3-4afa-a45a-4c0c25820a2b"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>w</th><th scope=col>fobs</th><th scope=col>rMode</th><th scope=col>lo</th><th scope=col>hi</th><th scope=col>5%</th><th scope=col>50%</th><th scope=col>95%</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.0003544360</td><td>2.76729539  </td><td>2065.3055   </td><td> 944.4383   </td><td>4161.7413   </td><td>1031.6468   </td><td>2806.7445   </td><td>6371.9319   </td></tr>\n",
       "\t<tr><td>0.0017235501</td><td>0.16498195  </td><td> 604.0960   </td><td> 501.5076   </td><td> 759.5778   </td><td> 491.5037   </td><td> 644.1648   </td><td> 952.6583   </td></tr>\n",
       "\t<tr><td>0.0004696314</td><td>0.76010247  </td><td>2060.1100   </td><td>1217.7406   </td><td>3819.4863   </td><td>1292.5082   </td><td>2754.4071   </td><td>6098.8117   </td></tr>\n",
       "\t<tr><td>0.0013279830</td><td>0.35219917  </td><td> 899.7459   </td><td> 595.9186   </td><td>1722.0357   </td><td> 655.5512   </td><td>1423.0317   </td><td>4247.1842   </td></tr>\n",
       "\t<tr><td>0.0016021144</td><td>0.16941877  </td><td> 650.4302   </td><td> 537.4952   </td><td> 823.4606   </td><td> 529.2350   </td><td> 699.3693   </td><td>1041.6373   </td></tr>\n",
       "\t<tr><td>0.0038513590</td><td>0.06034871  </td><td> 261.3139   </td><td> 243.8314   </td><td> 281.5017   </td><td> 238.8982   </td><td> 263.0258   </td><td> 292.7080   </td></tr>\n",
       "\t<tr><td>0.0011199443</td><td>0.28000044  </td><td> 978.8059   </td><td> 717.3162   </td><td>1517.5688   </td><td> 734.2660   </td><td>1253.0884   </td><td>3021.4597   </td></tr>\n",
       "\t<tr><td>0.0003205481</td><td>0.78192412  </td><td>2502.6507   </td><td>1593.9393   </td><td>4244.6950   </td><td>1629.8216   </td><td>3127.5113   </td><td>6331.3886   </td></tr>\n",
       "\t<tr><td>0.0016388455</td><td>0.24144996  </td><td> 666.8227   </td><td> 505.9770   </td><td> 976.9305   </td><td> 515.6021   </td><td> 817.1844   </td><td>1956.3907   </td></tr>\n",
       "\t<tr><td>0.0013188627</td><td>0.20250230  </td><td> 799.7472   </td><td> 637.7348   </td><td>1070.7340   </td><td> 632.2614   </td><td> 897.8218   </td><td>1558.7822   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllll}\n",
       " w & fobs & rMode & lo & hi & 5\\% & 50\\% & 95\\%\\\\\n",
       "\\hline\n",
       "\t 0.0003544360 & 2.76729539   & 2065.3055    &  944.4383    & 4161.7413    & 1031.6468    & 2806.7445    & 6371.9319   \\\\\n",
       "\t 0.0017235501 & 0.16498195   &  604.0960    &  501.5076    &  759.5778    &  491.5037    &  644.1648    &  952.6583   \\\\\n",
       "\t 0.0004696314 & 0.76010247   & 2060.1100    & 1217.7406    & 3819.4863    & 1292.5082    & 2754.4071    & 6098.8117   \\\\\n",
       "\t 0.0013279830 & 0.35219917   &  899.7459    &  595.9186    & 1722.0357    &  655.5512    & 1423.0317    & 4247.1842   \\\\\n",
       "\t 0.0016021144 & 0.16941877   &  650.4302    &  537.4952    &  823.4606    &  529.2350    &  699.3693    & 1041.6373   \\\\\n",
       "\t 0.0038513590 & 0.06034871   &  261.3139    &  243.8314    &  281.5017    &  238.8982    &  263.0258    &  292.7080   \\\\\n",
       "\t 0.0011199443 & 0.28000044   &  978.8059    &  717.3162    & 1517.5688    &  734.2660    & 1253.0884    & 3021.4597   \\\\\n",
       "\t 0.0003205481 & 0.78192412   & 2502.6507    & 1593.9393    & 4244.6950    & 1629.8216    & 3127.5113    & 6331.3886   \\\\\n",
       "\t 0.0016388455 & 0.24144996   &  666.8227    &  505.9770    &  976.9305    &  515.6021    &  817.1844    & 1956.3907   \\\\\n",
       "\t 0.0013188627 & 0.20250230   &  799.7472    &  637.7348    & 1070.7340    &  632.2614    &  897.8218    & 1558.7822   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "w | fobs | rMode | lo | hi | 5% | 50% | 95% | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0.0003544360 | 2.76729539   | 2065.3055    |  944.4383    | 4161.7413    | 1031.6468    | 2806.7445    | 6371.9319    | \n",
       "| 0.0017235501 | 0.16498195   |  604.0960    |  501.5076    |  759.5778    |  491.5037    |  644.1648    |  952.6583    | \n",
       "| 0.0004696314 | 0.76010247   | 2060.1100    | 1217.7406    | 3819.4863    | 1292.5082    | 2754.4071    | 6098.8117    | \n",
       "| 0.0013279830 | 0.35219917   |  899.7459    |  595.9186    | 1722.0357    |  655.5512    | 1423.0317    | 4247.1842    | \n",
       "| 0.0016021144 | 0.16941877   |  650.4302    |  537.4952    |  823.4606    |  529.2350    |  699.3693    | 1041.6373    | \n",
       "| 0.0038513590 | 0.06034871   |  261.3139    |  243.8314    |  281.5017    |  238.8982    |  263.0258    |  292.7080    | \n",
       "| 0.0011199443 | 0.28000044   |  978.8059    |  717.3162    | 1517.5688    |  734.2660    | 1253.0884    | 3021.4597    | \n",
       "| 0.0003205481 | 0.78192412   | 2502.6507    | 1593.9393    | 4244.6950    | 1629.8216    | 3127.5113    | 6331.3886    | \n",
       "| 0.0016388455 | 0.24144996   |  666.8227    |  505.9770    |  976.9305    |  515.6021    |  817.1844    | 1956.3907    | \n",
       "| 0.0013188627 | 0.20250230   |  799.7472    |  637.7348    | 1070.7340    |  632.2614    |  897.8218    | 1558.7822    | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      w            fobs       rMode     lo        hi        5%        50%      \n",
       " [1,] 0.0003544360 2.76729539 2065.3055  944.4383 4161.7413 1031.6468 2806.7445\n",
       " [2,] 0.0017235501 0.16498195  604.0960  501.5076  759.5778  491.5037  644.1648\n",
       " [3,] 0.0004696314 0.76010247 2060.1100 1217.7406 3819.4863 1292.5082 2754.4071\n",
       " [4,] 0.0013279830 0.35219917  899.7459  595.9186 1722.0357  655.5512 1423.0317\n",
       " [5,] 0.0016021144 0.16941877  650.4302  537.4952  823.4606  529.2350  699.3693\n",
       " [6,] 0.0038513590 0.06034871  261.3139  243.8314  281.5017  238.8982  263.0258\n",
       " [7,] 0.0011199443 0.28000044  978.8059  717.3162 1517.5688  734.2660 1253.0884\n",
       " [8,] 0.0003205481 0.78192412 2502.6507 1593.9393 4244.6950 1629.8216 3127.5113\n",
       " [9,] 0.0016388455 0.24144996  666.8227  505.9770  976.9305  515.6021  817.1844\n",
       "[10,] 0.0013188627 0.20250230  799.7472  637.7348 1070.7340  632.2614  897.8218\n",
       "      95%      \n",
       " [1,] 6371.9319\n",
       " [2,]  952.6583\n",
       " [3,] 6098.8117\n",
       " [4,] 4247.1842\n",
       " [5,] 1041.6373\n",
       " [6,]  292.7080\n",
       " [7,] 3021.4597\n",
       " [8,] 6331.3886\n",
       " [9,] 1956.3907\n",
       "[10,] 1558.7822"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Tabulate all results and compare. fobs is the observed fractional parallax uncertainty.\n",
    "cbind(w=dat$parallax, fobs=dat$parallax_error/dat$parallax, rMode, rFWHM, rQuant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "nbpresent": {
     "id": "36c04833-9f81-467f-b96f-96215de98c16"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2gxqotkfqG+vFhucXBOIlW2c61ecmZkbESILVfBZmkgUFFdpISJ9WWb3M9OeU02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\nQCQAKPD/AdVf+d8NTeXnAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visually the mode of the posterior with the median and also the naive inverse parallax estimate\n",
    "par(mfrow=c(2,1), mar=c(5,5,0.5,1), oma=c(0.1,0.1,0.5,0.1), mgp=c(2.2,0.8,0), cex=1.0) \n",
    "plot(rMode, rQuant[,2], xlab=\"mode distance [pc]\", ylab=\"median distance [pc]\")\n",
    "abline(a=0, b=1)\n",
    "plot(1/dat$parallax, rMode, xlab=\"inverse parallax [pc]\", ylab=\"mode distance [pc]\")\n",
    "abline(a=0, b=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "9f848f01-1f5e-4789-a0d6-b94e07c04d6f"
    }
   },
   "source": [
    "# Distance posterior with a hierarchical model for simulated data\n",
    "\n",
    "Instead of fixing the length scale, $L$, in the exponential decreasing space density prior - as has been done so far - we can instead put a prior on $L$ and marginalize over all values of $L$. This is a simple example of a hierarchical model. I'll call the prior on $L$ the hyperprior, with parameters, $\\phi$, and denote it $P(L, \\phi)$. The posterior we now want is $P(r|\\varpi,\\phi)$, i.e. without any dependence on $L$. We need to relate this to the quantities we already know, namely the prior, $P(r|L)$, and the likelihood $P(\\varpi|r)$, as well as the hyperprior. (For brevity I don't include the dependence on $\\sigma_{\\varpi}$ in my notation.) It follows from the basic rules of probability that\n",
    "we can write\n",
    "\n",
    "\\begin{alignat}{2}\n",
    "P(r|\\varpi,\\phi) &= \\int P(r,L|\\varpi,\\phi) \\ dL\\\\\n",
    "                 &= \\int P(r|\\varpi,L) \\ P(L|\\varpi,\\phi) \\ dL\\\\ \n",
    "                 &= \\int \\frac{P(\\varpi|r) \\ P(r|L)}{P(\\varpi|L)} \\ \\frac{P(\\varpi|L)\\ P(L|\\phi)}{P(\\varpi|\\phi)} \\ dL \\\\\n",
    "                 &= \\frac{1}{P(\\varpi|\\phi)} \\int P(\\varpi|r) \\ P(r|L) \\ P(L|\\phi) \\ dL \\\\\n",
    "\\end{alignat}\n",
    "\n",
    "Line 2 shows that the new posterior is the non-hierarchical posterior averaged over the hyperprior. In going from line 2 to line 3 I have used Bayes theorem to rewrite both terms, then I have cancelled $P(\\varpi|L)$. I have also used conditional independence in several places to remove dependencies. As $P(\\varpi|\\phi)$ is independent of r it is just a normalization constant, so if we only need the unnormalized posterior (which is the case below), we can ignore it. We can of course take the likelihood - $P(\\varpi|r)$ - out of the integral. When we do that we see that the posterior is just proportional to the likelihood multipled by the hyperior-averaged prior. (The code below keeps this inside the integral.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "nbpresent": {
     "id": "278b659b-d229-4f14-a88b-122e4984709a"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.00830777761176901"
      ],
      "text/latex": [
       "0.00830777761176901"
      ],
      "text/markdown": [
       "0.00830777761176901"
      ],
      "text/plain": [
       "[1] 0.008307778"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The function ud.distpost3hierIntegrand returns the quantity under the integral on the last line above\n",
    "# (i.e. the product of three probability densities) for given w, L, phi, and r. \n",
    "# Here I adopt a scaled and shifted beta function hyperior, specified by the function d.betagen (which is\n",
    "# defined in the file general_functions.R). The hyperparameters phi are the two shape parameters. \n",
    "# As it's based on a beta function, this hyperprior is only non-zero over the range rlenRange.\n",
    "# The lower limit - min(rlenRange) - must be >0, otherwise the prior P(r|L) evaluates to NaN (prior undefined).\n",
    "ud.distpost3hierIntegrand <- function(rlen, r, w, wsd, rlenRange) {\n",
    "  d.like(w=w, r=r, wsd=wsd)*d.distprior3(r=r, rlen=rlen)*d.betagen(x=rlen, xrange=rlenRange, shape1=1, shape2=1) \n",
    "}\n",
    "# Simulate the parallax (w) and its uncertainty (wsd) (in as). You should experiment with changing these.\n",
    "w   <- 5e-3\n",
    "wsd <- 1e-3\n",
    "# I will do the integration using Gaussian quadrature (with my function integrate.func, which is just a\n",
    "# wrapper to \"integrate\" in R's stats package). Let's first test that for some value of r.\n",
    "r <- 4e2\n",
    "rlenRange <- c(1e1, 1e3)\n",
    "integrate.func(f=ud.distpost3hierIntegrand, lower=rlenRange[1], upper=rlenRange[2], r=r, w=w, wsd=wsd, \n",
    "               rlenRange=rlenRange, subdivisions=1e3, rel.tol=1e-6, abs.tol=1e-6) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "nbpresent": {
     "id": "66ef27a9-d9c3-480f-a76b-336d0580d093"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posterior mean, SD for r = 234.685 69.65924 kpc\n"
     ]
    },
    {
     "data": {
      "image/png": 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fqrgAA5dEgeffSCD81mc11dXWFhYce2AwBAHYIdlKmqEptNKirU7WC1Wn8Idh06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Dt2zZIsho7u54+23Y2goyGBERmQSDHQnE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\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute P*(r|w,phi) on a grid of r spanning (0,max(rlenRange)).\n",
    "r <- seq(from=0, to=1e3, length.out=1e3)\n",
    "udDistpost3hier <- double(length=length(r))\n",
    "for(i in 1:length(r)) {\n",
    "    udDistpost3hier[i] <- integrate.func(f=ud.distpost3hierIntegrand, lower=rlenRange[1], upper=rlenRange[2], \n",
    "                                         r=r[i], w=w, wsd=wsd, rlenRange=rlenRange, \n",
    "                                         subdivisions=1e3, rel.tol=1e-6, abs.tol=1e-6) \n",
    "}\n",
    "# Note: Some integral may not converge, in which case integrate.func returns NA.\n",
    "# I set these to zero for this demonstration (but really we should improve the integration routine!).\n",
    "udDistpost3hier[is.na(udDistpost3hier)] <- 0\n",
    "# Normalize the posterior, then plot (in black).\n",
    "# Overplot the normalized posteriors we get with two different fixed values of rlen (in red and blue)\n",
    "# Note 1: The function pdfmom normalizes a tabulated posterior on a grid, so it's important that the tabulated posterior\n",
    "# includes all or nearly all of the probability mass. That is, the posteriors plotted should drop to zero for\n",
    "# the largest values of r (= max(rlenRange)) plotted.\n",
    "# Note 2: pdfmom computes the normalization constant numerically. It also computes the mean and variance. \n",
    "# We compute these from a *tabulated* posterior in a different way than from a *sampled* posterior. \n",
    "# See the code for pdfmom in general_functions.R, and sections 5.1.1 and 8.4 of Bailer-Jones 2015\n",
    "mom <- pdfmom(udDistpost3hier, r)\n",
    "cat(\"Posterior mean, SD for r =\", mom$mean, mom$sd, \"kpc\\n\")\n",
    "udDistpost3hier <- udDistpost3hier/mom$Z # is now normalized\n",
    "plot(r, udDistpost3hier, type=\"l\", xlab=\"distance r [pc]\", ylab=\"P(r|w,wsd)\")\n",
    "udDistpost3 <- ud.distpost3(r, w, wsd, rlen=min(rlenRange))\n",
    "lines(r, udDistpost3/pdfmom(udDistpost3, r)$Z, lty=2, col=\"red\") # posterior with rlen fixed to minimum of hyperprior range\n",
    "udDistpost3 <- ud.distpost3(r, w, wsd, rlen=max(rlenRange))\n",
    "lines(r, udDistpost3/pdfmom(udDistpost3, r)$Z, lty=2, col=\"blue\") # posterior with rlen fixed to maximum of hyperprior range"
   ]
  }
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