{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# False Alarm Probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from astropy.timeseries import LombScargle\n",
    "\n",
    "plt.style.use('seaborn-whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_data(N, T=100, period=0.6, amp=(1, 0.6, 0.3), err=0.1,\n",
    "              err_range=0.0, alias_period=1, alias_level=0,\n",
    "              return_model=False, rseed=None):\n",
    "    rng = np.random.RandomState(rseed)\n",
    "    t = T * rng.rand(N)\n",
    "    t -= (t % alias_period) * alias_level\n",
    "    phase = rng.rand(len(amp))[:, None]\n",
    "    def model(t, amp=amp, phase=phase, period=period):\n",
    "        k = np.arange(1, len(amp) + 1)[:, None]\n",
    "        return np.dot(amp, np.sin(2 * np.pi * k * (t - phase) / period))\n",
    "    dy = err + err_range * np.random.rand(N)\n",
    "    y = model(t) + dy * rng.randn(N)\n",
    "    if return_model:\n",
    "        return t, y, dy, model\n",
    "    else:\n",
    "        return t, y, dy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Baluev Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.special import gammaln\n",
    "\n",
    "\n",
    "def weighted_sum(val, dy):\n",
    "    return (val / dy ** 2).sum()\n",
    "\n",
    "\n",
    "def weighted_mean(val, dy):\n",
    "    return weighted_sum(val, dy) / weighted_sum(np.ones_like(val), dy)\n",
    "\n",
    "\n",
    "def weighted_var(val, dy):\n",
    "    return weighted_mean(val ** 2, dy) - weighted_mean(val, dy) ** 2\n",
    "\n",
    "\n",
    "def gamma(N):\n",
    "    # Note: this is closely approximated by (1 - 1 / N) for large N\n",
    "    return np.sqrt(2 / N) * np.exp(gammaln(N / 2) - gammaln((N - 1) / 2))\n",
    "\n",
    "\n",
    "def FAP_single(Z, N, normalization='standard'):\n",
    "    \"\"\"False Alarm Probability for a single observation\"\"\"\n",
    "    NH = N - 1  # DOF for null hypothesis\n",
    "    NK = N - 3  # DOF for periodic hypothesis\n",
    "    if normalization == 'psd':\n",
    "        return np.exp(-Z)\n",
    "    elif normalization == 'standard':\n",
    "        # Note: astropy's standard normalization is Z = 2/NH * z_1 in Baluev's terms\n",
    "        return (1 - Z) ** (NK / 2)\n",
    "    elif normalization == 'model':\n",
    "        # Note: astropy's model normalization is Z = 2/NK * z_2 in Baluev's terms\n",
    "        return (1 + Z) ** -(NK / 2)\n",
    "    elif normalization == 'log':\n",
    "        # Note: astropy's log normalization is Z = 2/NK * z_3 in Baluev's terms\n",
    "        return np.exp(-0.5 * NK * Z)\n",
    "    else:\n",
    "        raise NotImplementedError(\"normalization={0}\".format(normalization))\n",
    "        \n",
    "\n",
    "def P_single(Z, N, normalization='standard'):\n",
    "    \"\"\"Cumulative Probability for a single observation\"\"\"\n",
    "    return 1 - FAP_single(Z, N, normalization=normalization)\n",
    "        \n",
    "    \n",
    "def FAP_estimated(Z, N, fmax, t, normalization='standard'):\n",
    "    \"\"\"False Alarm Probability based on estimated number of indep frequencies\"\"\"\n",
    "    T = max(t) - min(t)\n",
    "    N_eff = fmax * T\n",
    "    return 1 - P_single(Z, N, normalization=normalization) ** N_eff\n",
    "\n",
    "\n",
    "def tau_davies(Z, N, fmax, t, y, dy, normalization='standard'):\n",
    "    \"\"\"tau factor for estimating Davies bound (see Baluev 2008, Table 1)\"\"\"\n",
    "    # Variable names follow the discussion in Baluev 2008\n",
    "    NH = N - 1  # DOF for null hypothesis\n",
    "    NK = N - 3  # DOF for periodic hypothesis\n",
    "    Dt = weighted_var(t, dy)\n",
    "    Teff = np.sqrt(4 * np.pi * Dt)\n",
    "    W = fmax * Teff\n",
    "    if normalization == 'psd':\n",
    "        return W * np.exp(-Z) * np.sqrt(Z)\n",
    "    elif normalization == 'standard':\n",
    "        # Note: astropy's standard normalization is Z = 2/NH * z_1 in Baluev's terms\n",
    "        return gamma(NH) * W * (1 - Z) ** (0.5 * (NK - 1)) * np.sqrt(NH * Z / 2)\n",
    "    elif normalization == 'model':\n",
    "        # Note: astropy's model normalization is Z = 2/NK * z_2 in Baluev's terms\n",
    "        return gamma(NK) * W * (1 + Z) ** (- 0.5 * NK) * np.sqrt(NK * Z / 2)\n",
    "    elif normalization == 'log':\n",
    "        # Note: astropy's log normalization is Z = 2/NK * z_3 in Baluev's terms\n",
    "        return gamma(NK) * W * np.exp(-0.5 * Z * (NK - 0.5)) * np.sqrt(NK * np.sinh(0.5 * Z))\n",
    "    else:\n",
    "        raise NotImplementedError(\"normalization={0}\".format(normalization))\n",
    "\n",
    "    \n",
    "def FAP_davies(Z, N, fmax, t, y, dy, normalization='standard'):\n",
    "    \"\"\"Davies bound (Eqn 5 of Baluev 2008)\"\"\"\n",
    "    FAP_s = FAP_single(Z, N, normalization=normalization)\n",
    "    tau = tau_davies(Z, N, fmax, t, y, dy, normalization=normalization)\n",
    "    return FAP_s + tau\n",
    "\n",
    "\n",
    "def FAP_aliasfree(Z, N, fmax, t, y, dy, normalization='standard'):\n",
    "    \"\"\"Alias-free approximation to FAP (Eqn 6 of Baluev 2008)\"\"\"\n",
    "    P_s = P_single(Z, N, normalization=normalization)\n",
    "    tau = tau_davies(Z, N, fmax, t, y, dy, normalization=normalization)\n",
    "    return 1 - P_s * np.exp(-tau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def FAP_bootstrap(Z, t, y, dy, fmax, n_bootstraps=1000,\n",
    "                  random_seed=None, normalization='standard'):\n",
    "    rng = np.random.RandomState(random_seed)\n",
    "    \n",
    "    def bootstrapped_power():\n",
    "        resample = rng.randint(0, len(y), len(y))  # sample with replacement\n",
    "        ls_boot = LombScargle(t, y[resample], dy[resample])\n",
    "        freq, power = ls_boot.autopower(normalization=normalization,\n",
    "                                        maximum_frequency=fmax)\n",
    "        return power.max()\n",
    "    \n",
    "    pmax = np.array([bootstrapped_power() for i in range(n_bootstraps)])\n",
    "    pmax.sort()\n",
    "    \n",
    "    return 1 - np.searchsorted(pmax, Z) / len(pmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "def cached(filename, overwrite=False):\n",
    "    def decorator(func):\n",
    "        def new_func(*args, **kwargs):\n",
    "            if overwrite or not os.path.exists(filename):\n",
    "                np.save(filename, func(*args, **kwargs))\n",
    "            return np.load(filename)\n",
    "        return new_func\n",
    "    return decorator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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YP348vXv35tKlS/j5+fH1119Lt/fLU+Z5jRs3pmfPnixfvpyMjAxatGhBZGQkK1aswMnJ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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ca4eba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = np.linspace(0, 0.3, 100)\n",
    "fmax = 10\n",
    "T = 5\n",
    "N = 100\n",
    "normalization='standard'\n",
    "\n",
    "t, y, dy = make_data(N=N, T=T, amp=[0], err=1.0, rseed=1324)\n",
    "FAP_bootstrap_cached = cached('FAP-cache.npy', overwrite=False)(FAP_bootstrap)\n",
    "FAP_boot = FAP_bootstrap_cached(Z, t, y, dy, fmax=fmax, normalization=normalization,\n",
    "                                n_bootstraps=10000, random_seed=1324)\n",
    "\n",
    "t, y, dy = make_data(N=N, T=T, amp=[0], err=1.0, alias_level=0.8, rseed=1324)\n",
    "FAP_bootstrap_cached = cached('FAP-alias-cache.npy', overwrite=False)(FAP_bootstrap)\n",
    "FAP_boot_alias = FAP_bootstrap_cached(Z, t, y, dy, fmax=fmax, normalization=normalization,\n",
    "                                      n_bootstraps=10000, random_seed=1324)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "ax.semilogy(Z, FAP_boot, '-', color='black',\n",
    "            label='Bootstrap, unstructured window')\n",
    "ax.semilogy(Z, FAP_boot_alias, '-', color='gray',\n",
    "            label='Bootstrap, structured window')\n",
    "ax.semilogy(Z, FAP_aliasfree(Z, N, fmax, t, y, dy, normalization=normalization),\n",
    "            '--k', label='Baluev method')\n",
    "ax.semilogy(Z, FAP_estimated(Z, N, fmax, t, normalization=normalization),\n",
    "            ':k', label='approx. $N_{eff}$ method')\n",
    "\n",
    "ax.legend()\n",
    "\n",
    "ax.set(xlim=(Z.min(), Z.max()), ylim=(1E-3, 2),\n",
    "       xlabel='Observed Maximum Peak Value',\n",
    "       ylabel='False Alarm Probability',\n",
    "       title=r'100 observations over 5 days; $f_{max} = 10$ days$^{-1}$');\n",
    "\n",
    "fig.savefig('fig27_FAP_bootstrap.pdf')"
   ]
  }
 ],
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