Binary-fraction.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "02d68a5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "import astropy.table as at\n",
    "import numpy as np\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpyro.distributions as dist\n",
    "from numpyro_ext import distributions as distx\n",
    "\n",
    "%matplotlib inline\n",
    "jax.config.update(\"jax_enable_x64\", True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5a2bca6",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "We observe radial velocity data $v$ for a set of $N$ sources at distinct observation times $t$. Let's assume that the sources observed are the luminous star in a bunch of binary systems where the companions are nonluminous (i.e., SB1 systems). For simplicity, we enforce that the orbits are circular, the eccentricities are zero, the systemic velocities are zero, and the angles are all zero. For this simplified model, the radial velocity data for a given source is generated by the model: \n",
    "$$\n",
    "v(t) = K \\, \\cos(2\\pi t / P)\n",
    "$$\n",
    "where $K$ is the semi-amplitude and $P$ is the period of the orbit. The data are also noisy, with varied quality, but all Gaussian noise. Let's simulate some data.\n",
    "\n",
    "First, we generate the \"true\" parameters for each star:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fcbc872d",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_stars = 1024\n",
    "\n",
    "rng = np.random.default_rng(seed=12345)\n",
    "\n",
    "# number of observations per star\n",
    "n_times = np.exp(rng.uniform(np.log(3), np.log(100), size=n_stars)).astype(int)\n",
    "time_baseline = 100.0\n",
    "\n",
    "# period values per star\n",
    "max_period = 500.0\n",
    "true_periods = np.exp(rng.uniform(np.log(1.0), np.log(max_period), n_stars))\n",
    "\n",
    "# amplitudes\n",
    "true_amps = rng.choice([-1, 1], size=n_stars) * np.exp(\n",
    "    rng.uniform(-1, 1.0, size=n_stars)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54845ba8",
   "metadata": {},
   "source": [
    "We now have to define what we mean by \"binary fraction\" to get the true binary fraction of the sample. This amounts to some selection in the physical parameters. In the case of real systems, this might be a selection on periods (to get \"close-binaries\") and a selection on companion mass (i.e. to distinguish stellar-mass companions vs. others). Here, we will just define a selection on the period and semi-amplitude:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4478d1b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True binary fraction: 0.341\n"
     ]
    }
   ],
   "source": [
    "binary_max_period = time_baseline\n",
    "binary_min_amp = 1.0\n",
    "true_binary_frac = (\n",
    "    np.sum((true_periods < binary_max_period) & (np.abs(true_amps) > binary_min_amp))\n",
    "    / n_stars\n",
    ")\n",
    "print(f\"True binary fraction: {true_binary_frac:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c014dc6",
   "metadata": {},
   "source": [
    "Now we can generate the radial velocity data for each star, including noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cf0f9662",
   "metadata": {},
   "outputs": [],
   "source": [
    "rv_data = defaultdict(list)\n",
    "for i in range(n_stars):\n",
    "    # Generate random times for each star\n",
    "    rv_data[\"time\"].append(np.sort(rng.uniform(0, time_baseline, size=n_times[i])))\n",
    "\n",
    "    # Generate random radial velocities for each star\n",
    "    rv_data[\"rv_err\"].append(np.exp(rng.uniform(-1, 1.0, size=n_times[i])))\n",
    "    rv_data[\"rv\"].append(\n",
    "        true_amps[i] * np.cos(2 * np.pi * rv_data[\"time\"][i] / true_periods[i])\n",
    "        + rng.normal(scale=rv_data[\"rv_err\"][i], size=n_times[i])\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "85e2cfb7",
   "metadata": {},
   "outputs": [
    {
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SpfSIxYGsgtSYtuOOO8aNN97Y604spTTQNUqHma4aBbuSjpVDDjkkGoUAAL2tQ4qvF44++uiqBhmqcT3TWeeD9supn4Dttttum8UB5s2bt8Q6uJLSebi47qrEedlvgCZL4bjqqqvG1VdfnfXKSv/8ddZZJ9Zee+3YaaedYu+9986+FPvss0985Stfif/4j//IvhjpduCBB2ZfmjSH2oknnhhrrLFGnsUEgF6RRoJqEfgpD99hejtChcabuyL9Xy+77LIsTU+67+7/uavjpNHTxlZr7pDe6El6xJEjR5atE8uSepQ3SoeZ1C5UuHVHrQUHysF8NvREs86D2JGO0tlRn/O1peP37rvvXiR4Vkspintad9E4cg2gFdI4/s///E92EZACYq+88kqWkuJ3v/tdLFy4MFt28803Zz3w0sVeWqdwS72wlnThDQDVVo8NRTQGgZ/y8B2mVBqumqNxuvB/TiNeUofOdN+d//OSjpNGCYY0SnCgp/OJVrITiw4znVvSdVAtq8Z8NhqC61czz4PYGdfm9a9e5/R2Lm0uLa0pUlUB6SIgpXFMvehS4Kwrw4cPj7POOiv23HPPShStKRV6y3U1qTEAPUv909UcFo10/leX1NaP6c7UWkNlLauH7zCN/V1raWlpe1yhn2kNX5+kBpf9998/3nnnnXj99ddj9913z6YJ6KzBo7f/51K2T5laSklHl0a+VSIdX57HXfHnv9xyy8VVV11Vcw2e6XPuyf8jNfqlwOiSUlWWOl9KV/+Hnr5XXmm3qjH/UvHnUyx10l5zzTUXea3Wz5/VOven42jo0KFtz2fOnFkTo/vqpT6ppnKfb/JU6eOso3NDPZwD6umar31Zy1n2ntTBtfDZVbMMtfD316q86oCKBdAKpk2bFr///e/jL3/5S/YD5o033oiBAwfGSiutFJtuummW83TnnXeOPn1yHxzX1Br1ogKg2lJDUfEPhPQDoto/Yor5gdqYBH6a5ztMYzdc1dMP4nqsT5b0+fb2/1zq9s8++2xssMEGNdMQWk/HXR5SUDONNCxlvfZ1ajkD60v6P/TkvfL631bjmOksgJa+K+2/S/XWeagSAclavlasx/qkXgL9lVaN46zwnSlOL1gPdVk91b15BtB6UgdXoxNHewJotSmvOqBfVNgqq6wS3/72t7MbADSaJc1hAXlIPyZS6uta7+VfD6oxUTS1rztzVlWz4Yrq/p9L3f6OO+7IGhO7CoZIG1s5vUmPWGjMa/+/zKPBuLCvWg2CVEtH37nC/6NePpO8G4A7C74WUv/V02fVrOoh9W+1jrOOAmjkq/i3UjXqYGkTqbSKB9AAACi/1NB60003VbsYDcGPsubUVW/Wemi4ovd6+3/uzvaVDLzQtTRP6JFHHrnEEYGdzSea/lft/495jR4sdJgpHildCynbalEKNKbPqt4/m96OtCh1fqFG+KzyUAsjXephHkTHWXMp53eht3VwPauV8wtLlmuexPvuuy/P3QMAAJRF6rlcuBVLP2gfeuih3BuuUuNTV8+p/QbK7m7fUZAsBUN6EzwzqX33pWBUClp2pbsjAvNsIJbtoDSF0aLVks7hu+yyS2y33XbZfU/P6Z3VTXmMrKX8n3+5pOBBCiJ0pZpBBscZtVQH14taOb9Q5RFoX/jCF+KDDz7I8y2a0tNPPx3XXnttvP3229G3b9/stTR33Je//OW25wAAQO+V+qO2Nw1XhTlDiqW5tIxEqqze9oIuRy/q3jYQFR+vgmj1lR6xnCmx+H+uueaaqqTV7WgeqEqf0wvf/7/85S8lrW8EdX0EGWo19a+R+lSzDq70SK6OOr0Vjwyn8eQaQJs7d248//zzsd566+X5Nk3lxhtvzCYFPemkk2LUqFHZazNmzMh+KN1///3ZhVr//v2rXUwqwFBfAJqNuo9a1tOGK3PTNE4DZa03cFLb6RGrVa81ct167733xuzZsyv6nauVc3p3RzRUK/Uf9RXo7+3xk0b0F84zjXa+oTp1cApeFZ/vjj766FyDWTq9NaeW1tbW1rx23qdPn/iP//iPuOWWW/xIKFNKzNNPPz2+8Y1vxN57773IsmnTpsUBBxwQn/nMZ+LEE0+MlpaWLvc1cuTI7P6RRx7Jtczkp/h/nOPXGGiw72c5z//qEiqtlr9bNO7xVfz6GWecUdaGq/SjP/3oXtKIpVqc46je6pP0WQ8dOrTt+cyZMzttYOlo9Eh3/s/d2b7977bentt6cp50bu3955Eagosb8PL+HEstYynr1csxU/yeP/zhD+PHP/5xLFiwYInbpQ7IlRqFlsc5vSefdfvzXXrPWq5nark+qcXzYwoKF9df6f9d7WuEUo/94uXl/jzrrTNALR5btVDW7rxXb6/XytVBovh3Qnfet6efaz0dO5WW12+KXOdAS9KoqHXWWSe7wHn88cfzfruGlU4GP/nJT7Ivxs4777zY8lVWWSU222yzrIfVnXfeWZUyAgBAI0s/ilMjY7nmrDJnSGWkBo/UsFcsPU+vd/V/Tg3vqTEk3Xfn/1zu46QWmFuta+lzSSkYC7d6Ua9zL5511lnx+c9/vuZSxtXCOb2j813KDtUVI2PrSy3Og1jqPFZ5Uk81l0Iwq/05tzDat7NrvJ5K9WP7kWftpeUpwE3jyTWFY7LiiivG9ttvHw888EBccMEFMXz48PjqV78ae+21V2y88cZ5v33DuP766+Odd96JtdZaa5GeRMU22WSTLMJ69dVXZ3OimQ8NAABqt+HKnCG1m04t/V97M2qlFhs4a2VutXobJVCqWvtbljRHS0dpqFZeeeUsi9DnPve5mvt72vva175WUufhSqYmTHOuVfOc3tn5bt68edl9mu6jOJhWC6n/6JlaDNSXkmKyq9E7NIZK1PGlBrNSSshyXX91p4NENebepI4DaGlI4YMPPhgf+9jHsucpAHTTTTfF7373uzjvvPNi7bXXzoJpe+65Z3ziE5/Isyh179Zbb83uUwCtM+nzTF5//fV47LHH2oYtAlBZtfiDBoDaU2rDrrlp6qeBpREtKRBTzWAcPZujpatAy913353dav1/M3r06DjyyCOXmDIurVcJ6TMtNRtQHuf0Us53/fr1WySAVovpgRv53FdOtfr9rPZcklRXpeYjq0YwS6e35pZrCsfUu6UQPEuWW2652G+//bIgWpqz69hjj41HH300C/RstNFGcdppp8Vzzz2XZ5Hq0uTJk2PGjBnZ41VXXbWki7CHH364ImUDYHHSRwBQSh2RGnZTA29XKtkA3GhqIZ1as6W/bISUgbWYirE715ZLSmuV5kxfUqAlqZU0VOkY+eIXv7jYa6WmjKtEw30pwau8z+mlnO/ee++92GWXXdqOb0GNyp37mkmjjcDOQz3Uhd0tayW/M9UIZun01txyHYHWVeWdTqAHHHBAdktfvhtuuCEbmfajH/0o1l133SzFYxqZNmLEiGh2Tz75ZNvjztI3tl/21FNPLXG/kyZNih122KHH5brjjjt6vC0APdebc3c695ezblWXAPRu9E1q4O0qpVGeDcCNXp/oLVyd9Jc9HRVVK2qxA1T780Znwb1SAjnnnHPOEufESmohDVU6ZtLfXkhBWPCRj3wkTjrppLbjpv1xWunUhKUEr/I+p5d6HvvUpz6Vy+fSSPVJml+vnOc+qMe6sDtlLef1QimdV6oRzKq1Uc+NbIcaqk8qEkDr06e0AW6p59CBBx6YBcz++7//O/typYuhdEvzeqXX855sspYVRp8lyyyzTKfrDRw4sMNtAACA2lTKnCHUZ2/hUhqB0jr33HNPW6NtrcxJUu70l+UOxjW7zv6HpQRySgmeFTLhdOe9y62zY6bwNxQfN+3Xq3TKuFKDV1/4whdyO86rfb5rFPPnz5f6l9zUU11YalnLfb1QSh1TjWBWYdRzuTq91XKKWBbX0tra2hpV9swzz8Qll1wSV111VVuagEKxUlAoTQ77q1/9KprVBRdc0DYH2ve+973YeeedO1xv4cKFsdNOO2WPl1pqqbjttts63WdhfrRHHnkklzKTvzTHYEENfI2BOlHO87+6hEpT91GN46uj13tzLHa2bfodVPzDOf2QruXGuXqoT9JnmHpKL6mBpZHmZ+nOcdzVsssuuywOOeSQJb5fWm9Jo5Sa8f9QbqWec84444wsRWM5DBgwINtX+8bc4rIsqTzdVWg4/eCDD+JnP/tZlnKwK4Xjpn2jY57XCB0Fo3vyfSk1qN3Z/z59r/bff/949913Y9lll42LLrooNtxww7r8ntVSfVLOc18z6+z4buZr+XqqC7tT1pRNrhrfma46WRTqwzyCkYVReb3p9NbbfTTz96havylyHYF25ZVXZikaO5KG4KfeUSlwdt999y32T19vvfXisMMOy0amNXsENl24FgfJOlO8bOmll869XAAAQHmYM6T8yt1buF71pJdzOdNfdmcuOg3SvVPq6KLUxvDhhx92uU5aXsqIiHL1mk/7KU5VWYpqzGHYPp1mT0dDdLSfUnXU+HrXXXfF1ltvHRMnTmzq811vVSL1byH4OXPmzPjHP/6RTWOTpmRJgwoapf2zFlPhVls91YXdKWtvvjPdHR1fCxkc0n7TaLri72p3gp71NAqRfystx2IPHXrooR2mATj22GNj9dVXj/322y8LnqXAWbr169cv9thjj6zCf/bZZ7MLkEapPHpj+eWXb3vcPvd3Z6kYuporDQAAoBmkRojUCzk1qBRLz/PqnVxLgbLUUJN6kRdLz9PrlUoHZy66ykkBmvbHentp+THHHFPyPlPjZCFTUEfHTSnH05J0dJyWqhaOm0KwvivlCl4VGl/bN26n56ktLaWJbIbzXV7yToVZONb/8Ic/xL333hvTpk3L7tPzcnyX6q2Oaib1VBd2p6w9/c4UOk0Ubj05HtI5LQWvdtlll9h2222z+/Q8vZ4CcoVbrXR6KzXdZaHO7Sr9d+FGAwTQUo+lFCB744034oYbbogvfvGL2URu5557bkyfPr0tcJYqiXRAv/zyy9nQz+222y7PYtWdFGws6OpLVLxsjTXWyL1cVE+zX3gAANTjNZdruOooNLAUKzSwVEP6v6dGnvS7N92X4zjoKACx8sord9rQnl7vqqG21EBMKfOLmJspKnbeKDWQc/rpp5f8/oVRBkvqNd/Thv/OAkKlqpXjphLB+lIaXx988MF47rnnauZ8V2/Kee7r7rHe2+9SLetpZ45GUk91YXfK2pPvTDmPhxS8uummm7JRuOm+EMwqDs7Viu6M7OtKnsFBqhBAS7bZZpu2L9Sf//znLM1gIVXj9ttvH7///e/jpZdeipNOOqkmThK1aLPNNou+fftmj2fMmNHpesXLCjk/aTwuPABoRgIP1Ps1l2u4+k2RWc6GiuLRB3fffXdZRh101ijbVfaS4l7OHfVkLueImlIa19Ic3j1pkG50PTlvlBLI6W4dmjIJlaPXfE8CQj0JZFSrUbHUYH1Pr2lKbXxNbW/F32tpG6s/mrA7x3pPvku1rKtRk40aMKx0cLaaZe3ud6aZj4d6GoVIO605amlpae3Tp092X7itsMIKrUcffXTrP/7xjzzfuuH84Ac/aP3CF77Q+v3vf7/Tdf74xz9m6+y4446t06ZN63J/m2++eXajvpxxxhkp+tzpLS0Has/JJ5/cdqu2cp7/1SVUSqrfBg0atEidl56r9yin9tdUXV1zFd/KeQ3X3f1WUz3WJz35fGfOnLnIdul5LV3Lp/K0Pz9253bZZZdV5PxbyneK8h4vs2bNWmT99Lyw3+4eMwceeGBZjqf2Lr300h4fu52dO/M+nkp5j66u/bv7nSpe7/TTT+/W51IvarE+Kfe1Z3eP9e5+l3pSd3z5y19u3XbbbbP73tRtS3qfJZ1v0vJjjz22Zn4v56me2vS6W9ZSvjOlHg+F+qo38q4PerL/Us8DeX7/a6ltKg95/aaoWABt1KhRrb/+9a9b33///TzfsmE99thjWXBs1113bV2wYEGH65x//vnZOueee+4S96fRs/5UsqIByqecDW+N+gMVGuWHJvWt/TVVqY1c5byGq0TjbzPXJ939fMvZgJrXtXy5AhA9CcR015ICN5T/eGn/+Xanc0Dx+5xwwgllO56KlRoQan/r37//Iu9VyeOpo/dI/6/0XUx/T7rv7Hq/J9c0xctrofG1meqTcp37enKs53l9W8mOaT2poxpdPXUM7G5Zl/SdqeQ5LO9jqif7r3a7bq21TeUhr98Uuadw3HzzzeP++++Phx56KL7xjW/E0ksvnfdbNqRPfvKTsdVWW2VDWp988snFli9YsCD7jNMQ2v32268qZaQ+cuUClSNdF/ROuSZahu7q6Vw8vb2GMyl47Sh3iqG8ruV7m+anlGkUepP+cknp7ajc8dLTdIkp9dbw4cNLWre703KUuv7GG2+8yPM333xziXN6VSrVc+F6/5BDDokTTzwxu+/oer8c1zT1lAKuEZTr3Jfnd6O7Kp0+Tyq62p+XtZxlTd+RrtLHNlIKw55cs+eVIrYU2qZ6p1/kqKWlJW655ZZYZZVV8nybpnHsscfGUUcdFVdddVVstNFGbfOiJbfddlu8/fbb2YG/6qqrVrWc5KORKhpoBkuaaD2pxYtkqNcGxIMOOqhi5YK8ruFMBl4bSm3oHjt2bMmNHHldy/emkbU7De3lCuqaiymqdryUUqe2Pz5SQ15hzrQjjzyyy+17ErhJ65ey3/vuuy9reOzOcZQaBgvlr4Xr/Z5c03QUBEx/U0fvWbzc96z2lHKs5x0EzaNuq1YgsN6VMzhba2Xt6lq21OOhHo6bnl6zF+qE9F0rPh8U17nlpm2q93Idgda/f3/BszJKX6azzz47+vXrF8ccc0zceeed8eCDD8bPf/7zuO666+K0007LRvzRmBqpooFGZ9QMlIfOI9SyXXbZpaSggmu4+ustnMfon7yOg1JGpJSjoT01FBVuPdHb7ZtNHsdLd+vK4lEGefWaL8d+O+s9n9eImmLdud7v7jVNZ6MFkjPOOGOx7316nl7XCFqbSjnW8w6CViOrUamjJmkOlRpF277zQRqQUkvXH5UchZj+9lNPPbXLdbRNVTmAdtddd+W5+6a0wgorxFlnnRWHHXZYdkJ4+eWXY9NNN43LLrssRo0aVe3ikSPpGqB+SLkK5SHwQKW0/6FdyjVXygpRyo9x13C1o9QgTh7B+7yOg1IaZVPH1mo3tKfGm8JNqtLqHC/drSvbN+Cn4yUdNx2VozfHU2G/PQkIVbrTWvu6ojvX+925pllSmr2kXlLAseRjvVLn5mp0TCs1SE5zqEQKw446H6TBKEsKIjXqKMT0t8+bN6/LdbRNVTmAtvXWW+e5+6a27rrrxu677x577713fPrTn17sRxGNp5q5coHuMWoGykPggUro6If23Llzy3bN5Rqu/uQRvM/zOFhSACLNF1XNhvb2QYejjz7aaLQqHC+9Ga1YcMQRRyz2WjmOp572xq9kp7WO6oruXO+Xek2zww47lBQUTLqaa4jaVDjW0yj2z372s1nWrs997nPZ87zPzdXqmNabIDmNJ8/jobPOB8XL6Zi2qSVopSltvvnm2Y36c8YZZ7QOGjSoNX19C7f0PL0O1IZLL710ke9oZ7fLLrusrs//6hIqIdVvXX2P1H/keXz1799/kedLLbVU67bbbtvj92qka7hGrk9mzpy52P+q/S0tnzVrVk0dB6k8xfstLl/x65W0pL+3WuWqF709Xoq3O/nkk7PzVynXqB39PzoqS7nr4a7ev6Nlp59+ekl/S2/LuKS6otTr/VKuaWr5d0Qz1ieNdI7Ks26r1zqqmurpb86jrF0dD/V4fNfqMdCTuqqebZ7Tb4p+SwqwAbUl9cZIk7oWT6KceirpcQa1o9QJ0Y2agdqcaJnmUErqrzT3cPFotJQC5e677862Lb4WK4VruPob/dPRhOvlGC2WjoP9998/3nnnnVhuueWydKDlOA66SgdUjXSJpUxaT+XOG4X0VamHf2d1amdpnjr7XyaF18tRH3f3OK3EiJpS6opSr/dLuabpKE1mR4wWqIxGSjWbZ91WSynralU6l6TRsOm7K/38//v/F3+/ens8dGdE8kEHHdSr92o02qaWTAAN6lCzX3hArav2jxNoNAIP5KGUH9rvvfdeh6+nNF49CeC6hqsfeQbv0//9pptuikqqdLrEUuemqtTfXM/pIntz3kiNkx988EE2B0pxGsbu1Kml/i/TPnt7Tuvu/6kSndZKqSu6c72/pGsa87/Wlno+d3REx7TqSJ0Q2n/mlPf7ZRqNntM2VeU50ACaWakT1dOY5HqH8hJ4oNx68wO6MILGXAqNrafzMlF6T/A8pRFXhVuzWmqppeKiiy5arAPAz372s5Lr1ErOM9ZdlZhjsid1xZKu97u6pjH/K5Wch23bbbetyPxrzWxJ83JRHjofLJm2qZ4zAg0gJ8U/1gXRmpNRMwC1qxw/oMs16oLaJXjfM3p4V1+5UmjWeq/+vEfUlFpXbLrpprH88sv3Oi2rTBZUQjVGQjejUlPAzp49uyrf6VS+lFL63XffjWWXXTY7d3U3RXmtKGVE8sCBA5u680Fqi8ojhXgzEEADgDrK7Q1A5X5oL4m5FJpDI82BUynN3MO7Xhpt0+i0733vezFgwIC679WfZ6e1UtNE/u///m/ZrvOl2YPGUGoK2GpcS3aUVrKnKcprQSmdD+bPn5+NwK7Hv68cBM57TgANAHJmBCJAff7QLoWRNo1PPZ5f0EFKq+o12s6bNy9GjBixxEbbSswzVsujRfMaEbakwLxMFlD/anUEbykjlOsxyFQoc8oGleq49ubOnVvXfx/VYw40AACgKXU1X+Vuu+1W0j6MtIGez01F7TfaVmKesXJJQanCrdbnNi5lvmwpZKG+1eII3lJGKKflKa1kPTriiCOif//+Dfv3UR1GoAEAAE2rs17+ra2tWSqbco+6kA6QZlFKGrrejgBtFt09b5S70baz/2XS0wBSvY0WNSIMyCtdeCVH8JYyQrmeU5TX09/nN0H9EEADAACaWme9/PNI2yUdIM1E0KE8unveyCPtYkf/y8LrzcKIMCCPdOGVPJfUalrJZvz7/CaoHwJoADkNi2//vP2PTQCgtnU2QqZ4BA0QS2wYLO5lXWgodL2cn7zm7RIwAnqjGUfcdDWCtxp6MkK5nv5vtZg2k/rX0ppyk9S4UaNGxd///vdqF6OhjBw5Mrt/5JFHql0UeqilpaXtcR18jZtKmpC1q1Q10Cjnf3UJlabuoxrHV/HrxQ39zd6QrD6pTfVynqzE9XK9fBb19jm3PydW6rOtlf9npctRK393ntQnNMNxnubc2n///eOdd96J5ZZbLm6++eaq/M3pGraUFOX1Olq80f++7mqG71Yl6oC6GIH29NNPV7sIACX/SO2op2eqvAuvC6IBQH1rhh/c1Kd66CXuerlyGimFZj0c2wCdSefdm266qerp+/IaoVwrGv3vozpqfgTae++9lx388+bNq3ZRGopeOfWvuLKVN7c26OlCPdDDk3rWbD3oqL0RaIUGXNde6hNq/3pZnZHPZ1GtEWi1wgi08lOfNLdULwwdOrTt+cyZM6XzrYBGz5zUUQaJRvr7StGM362RtTQCbZ111olK/rMXLlxYsfeDeqHhpvZMmDBhiTmt0/K03kEHHVSxcgEA5Rn14PoLesf1MgDtgzjFUieLZgpyVHuEcqpvp06dms0JNnr06Ibu7N1Mndl9t6L6AbSXXnqpw0huHlIPm0q9F0BvpIuOcq4HwKKkb6IaBM2gfFwvN1b9qV4Geko63+pLwaRG7axSqJ9OPfXUtteaKXjmuxW1MQdaow4dB+ip1GOnnOsBsCiBDID65nq5sepP9TLQ02xj7UfHtJeWpxFSzRL0IJ/6qTiA1gx8t/LRpycbpRFhr7/+epZaMe/bq6++agQaUBfScPeUU7kraXlaDwAAmk2lrpdTA1JXz6E3oxoKNyD/dL5A6Xy3aiiANmDAgIr1CEv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",
      "text/plain": [
       "<Figure size 864x576 with 16 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 584,
       "width": 872
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(\n",
    "    4, 4, figsize=(12, 8), sharex=True, sharey=True, layout=\"constrained\"\n",
    ")\n",
    "\n",
    "for i, ax in enumerate(axes.flatten()):\n",
    "    ax.errorbar(\n",
    "        rv_data[\"time\"][i], rv_data[\"rv\"][i], yerr=rv_data[\"rv_err\"][i], fmt=\"o\"\n",
    "    )\n",
    "\n",
    "for ax in axes[:, 0]:\n",
    "    ax.set_ylabel(\"radial velocity\")\n",
    "for ax in axes[-1, :]:\n",
    "    ax.set_xlabel(\"time\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f1f4e21",
   "metadata": {},
   "source": [
    "## The Joker-style rejection sampler\n",
    "\n",
    "We'll implement a rejection sampler that:\n",
    "1. Samples periods from a prior\n",
    "2. Analytically marginalizes over the amplitude (linear parameter)\n",
    "3. Uses rejection sampling based on the marginalized likelihood\n",
    "4. Samples amplitudes from their conditional distribution for accepted samples\n",
    "\n",
    "The key trick: for a linear parameter $K$, the likelihood is Gaussian in $K$, so we can analytically compute the marginal likelihood and then sample $K$ from its posterior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f09e8839",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max observations: 99\n",
      "Padded shapes: t=(1024, 99), rv=(1024, 99), rv_err=(1024, 99)\n"
     ]
    }
   ],
   "source": [
    "# Pad all data to the same length (max number of observations)\n",
    "# This is a hack so that JIT doesn't recompile for each star of different n_obs...\n",
    "max_n_obs = np.max(n_times)\n",
    "print(f\"Max observations: {max_n_obs}\")\n",
    "\n",
    "\n",
    "def pad_to_length(arr, length, pad_value):\n",
    "    \"\"\"Pad array to specified length.\"\"\"\n",
    "    padded = np.full(length, pad_value)\n",
    "    padded[: len(arr)] = arr\n",
    "    return padded\n",
    "\n",
    "\n",
    "# Create padded arrays for all stars\n",
    "t_padded = jnp.array([pad_to_length(t, max_n_obs, 0.0) for t in rv_data[\"time\"]])\n",
    "rv_padded = jnp.array([pad_to_length(rv, max_n_obs, 0.0) for rv in rv_data[\"rv\"]])\n",
    "rv_err_padded = jnp.array(\n",
    "    [pad_to_length(err, max_n_obs, jnp.inf) for err in rv_data[\"rv_err\"]]\n",
    ")\n",
    "\n",
    "print(\n",
    "    f\"Padded shapes: t={t_padded.shape}, rv={rv_padded.shape}, rv_err={rv_err_padded.shape}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1bd0f97f",
   "metadata": {},
   "outputs": [],
   "source": [
    "linear_prior_scale = 100.0\n",
    "\n",
    "\n",
    "@jax.jit\n",
    "def compute_all_log_likelihoods(periods, t_all, rv_all, rv_err_all):\n",
    "    \"\"\"Compute log likelihoods for all periods and all stars using scan.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    periods : array (n_periods,)\n",
    "    t_all : array (n_stars, max_n_obs)\n",
    "    rv_all : array (n_stars, max_n_obs)\n",
    "    rv_err_all : array (n_stars, max_n_obs)\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    lnL : array (n_stars, n_periods)\n",
    "    \"\"\"\n",
    "\n",
    "    def compute_star_likelihoods(t, rv, rv_err):\n",
    "        \"\"\"Compute likelihoods for one star, all periods.\"\"\"\n",
    "        # Create mask for valid (non-padded) points\n",
    "        # Padded points have rv_err = inf\n",
    "        valid_mask = jnp.isfinite(rv_err)\n",
    "\n",
    "        # Replace padded points with valid values (won't affect likelihood)\n",
    "        # Set padded values to 0 error so they contribute nothing\n",
    "        rv_err_safe = jnp.where(valid_mask, rv_err, 1e10)\n",
    "\n",
    "        def single_period_likelihood(period):\n",
    "            design_matrix = jnp.cos(2 * jnp.pi * t / period)[:, None]\n",
    "            linear_prior = dist.Normal(0.0, 1000.0)\n",
    "            marginalized = distx.MarginalizedLinear(\n",
    "                design_matrix,\n",
    "                linear_prior,\n",
    "                dist.Normal(jnp.zeros(len(rv)), rv_err_safe),\n",
    "            )\n",
    "            return marginalized.log_prob(rv)\n",
    "\n",
    "        return jax.vmap(single_period_likelihood)(periods)\n",
    "\n",
    "    # use scan to loop over stars without vmapping (because memory)\n",
    "    def scan_fn(carry, x):\n",
    "        t, rv, rv_err = x\n",
    "        lnL = compute_star_likelihoods(t, rv, rv_err)\n",
    "        return carry, lnL\n",
    "\n",
    "    _, lnL_all = jax.lax.scan(scan_fn, None, (t_all, rv_all, rv_err_all))\n",
    "\n",
    "    return lnL_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e8eae702",
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def rejection_step(key, lnL_all):\n",
    "    \"\"\"Perform rejection sampling for all stars\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    key : PRNGKey\n",
    "    lnL_all : array (n_stars, n_periods)\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    weights : array (n_stars, n_periods)\n",
    "    accepted : array (n_stars, n_periods) boolean\n",
    "    \"\"\"\n",
    "    # Normalize weights per star\n",
    "    lnL_max = jnp.max(lnL_all, axis=1, keepdims=True)\n",
    "    weights = jnp.exp(lnL_all - lnL_max)\n",
    "\n",
    "    # Rejection sampling\n",
    "    uniform_draws = jax.random.uniform(key, shape=lnL_all.shape)\n",
    "    accepted = uniform_draws < weights\n",
    "\n",
    "    return weights, accepted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "feeabace",
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def sample_K_given_period(key, periods, t, rv, rv_err):\n",
    "    \"\"\"Sample amplitude K given period from the conditional posterior.\"\"\"\n",
    "\n",
    "    def sample_single_K(period, subkey):\n",
    "        # Design matrix for this period\n",
    "        design_matrix = jnp.cos(2 * jnp.pi * t / period)[:, None]\n",
    "\n",
    "        # Linear prior on K\n",
    "        linear_prior = dist.Normal(0.0, 1000.0)\n",
    "\n",
    "        # Create the marginalized distribution\n",
    "        marginalized = distx.MarginalizedLinear(\n",
    "            design_matrix,\n",
    "            linear_prior,\n",
    "            dist.Normal(jnp.zeros(len(rv)), rv_err),\n",
    "        )\n",
    "\n",
    "        # Sample K from the conditional posterior\n",
    "        K_sample = marginalized.conditional(rv).sample(subkey)\n",
    "\n",
    "        return K_sample[0]  # Return scalar (remove the [0] dimension)\n",
    "\n",
    "    # Generate keys for each period\n",
    "    keys = jax.random.split(key, len(periods))\n",
    "\n",
    "    # Sample K for each period\n",
    "    K_samples = jax.vmap(sample_single_K)(periods, keys)\n",
    "\n",
    "    return K_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7ab672de",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_batched_rejection_sampler(\n",
    "    key,\n",
    "    t_padded,\n",
    "    rv_padded,\n",
    "    rv_err_padded,\n",
    "    n_prior_samples=100_000,\n",
    "    n_posterior_samples=256,\n",
    "    period_min=1.0,\n",
    "    period_max=500.0,\n",
    "):\n",
    "    \"\"\"\n",
    "    Run rejection sampler on all stars in a single batched computation.\n",
    "    \"\"\"\n",
    "    key1, key2, key3 = jax.random.split(key, 3)\n",
    "\n",
    "    # Generate shared period samples\n",
    "    lnP_samples = jax.random.uniform(\n",
    "        key1,\n",
    "        shape=(n_prior_samples,),\n",
    "        minval=jnp.log(period_min),\n",
    "        maxval=jnp.log(period_max),\n",
    "    )\n",
    "    P_samples = jnp.exp(lnP_samples)\n",
    "\n",
    "    # Compute all likelihoods at once (n_stars, n_periods)\n",
    "    print(\"Computing likelihoods for all stars...\")\n",
    "    lnL_all_stars = compute_all_log_likelihoods(\n",
    "        P_samples, t_padded, rv_padded, rv_err_padded\n",
    "    )\n",
    "\n",
    "    # Rejection step for all stars\n",
    "    print(\"Running rejection step...\")\n",
    "    weights, accepted_mask = rejection_step(key2, lnL_all_stars)\n",
    "\n",
    "    # Extract accepted samples for each star\n",
    "    print(\"Extracting accepted samples...\")\n",
    "    n_stars = t_padded.shape[0]\n",
    "    results = {}\n",
    "\n",
    "    keys = jax.random.split(key3, n_stars)\n",
    "    for n in range(n_stars):\n",
    "        k1, k2 = jax.random.split(keys[n], 2)\n",
    "        tmp = P_samples[accepted_mask[n]]\n",
    "        accepted_periods_n = jax.random.choice(\n",
    "            k1,\n",
    "            tmp,\n",
    "            shape=(jnp.minimum(tmp.shape[0], n_posterior_samples),),\n",
    "            replace=False,\n",
    "        )\n",
    "\n",
    "        _mask = jnp.isfinite(rv_err_padded[n])\n",
    "        t_orig = t_padded[n][_mask]\n",
    "        rv_orig = rv_padded[n][_mask]\n",
    "        rv_err_orig = rv_err_padded[n][_mask]\n",
    "\n",
    "        amplitudes = sample_K_given_period(\n",
    "            k2,\n",
    "            accepted_periods_n,\n",
    "            t_orig,\n",
    "            rv_orig,\n",
    "            rv_err_orig,\n",
    "        )\n",
    "\n",
    "        results[n] = {\n",
    "            \"periods\": accepted_periods_n,\n",
    "            \"amplitudes\": amplitudes,\n",
    "        }\n",
    "\n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b7e2cb03",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing likelihoods for all stars...\n",
      "Running rejection step...\n",
      "Extracting accepted samples...\n"
     ]
    }
   ],
   "source": [
    "results = run_batched_rejection_sampler(\n",
    "    jax.random.PRNGKey(74),\n",
    "    t_padded,\n",
    "    rv_padded,\n",
    "    rv_err_padded,\n",
    "    n_prior_samples=1_000_000,\n",
    "    n_posterior_samples=256,\n",
    "    period_min=1.0,\n",
    "    period_max=max_period,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "0018d3fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.int64(69)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_posterior_samples_returned = np.array(\n",
    "    [results[n][\"periods\"].shape[0] for n in range(n_stars)]\n",
    ")\n",
    "n_posterior_samples_returned.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6e9e9555",
   "metadata": {},
   "outputs": [
    {
     "data": {