Power of Prediction.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib.pyplot import *\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "matplotlib.rc('image', cmap='gray_r')\n",
    "#matplotlib.rc('image', cmap='RdBu_r')\n",
    "matplotlib.rc('axes', titlesize=24)\n",
    "matplotlib.rc('text.latex', preamble=r'\\usepackage{amsmath}')\n",
    "\n",
    "rtitle = lambda t: matplotlib.pyplot.title(t, y=1.2)\n",
    "def matshow_symm(data, *args, **kwargs):\n",
    "    maxabs = np.abs(data[~np.isnan(data)]).max()\n",
    "    matshow(data, *args, vmin=-maxabs, vmax=maxabs, **kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## Demean -- remove the mean from each column\n",
    "demean = dm = lambda v: v-v.mean(0)\n",
    "\n",
    "## Z-score -- z-score each column\n",
    "zscore = zs = lambda v: (v-v.mean(0))/v.std(0)\n",
    "\n",
    "## Rescale -- make each column have unit variance\n",
    "rescale = rs = lambda v: v/v.std(0)\n",
    "\n",
    "## Matrix corr -- find correlation between each column of c1 and the corresponding column of c2\n",
    "mcorr = lambda c1,c2: (zs(c1)*zs(c2)).mean(0)\n",
    "\n",
    "## Cross corr -- find corr. between each row of c1 and EACH row of c2\n",
    "xcorr = lambda c1,c2: np.dot(zs(c1.T).T,zs(c2.T)) / (c1.shape[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate data\n",
    "To test things out, I'm creating a fake dataset of $M=10,000$ voxels, each with $T=1,000$ samples. Our model has $N=200$ features. Of the $M$ voxels, $M*Mfrac$ actually respond to the stimulus (i.e. their true beta weights are nonzero), and the other $M*(1-Mfrac)$ do not respond to the stimulus. For the responsive voxels, the true feature weights are gaussian with standard deviation `beta_sd`. For non-responsive voxels the true feature weights are all zero. The feature values, $X \\in R^{T,N}$, are independent standard normal.\n",
    "\n",
    "Responses are simulated by multiplying the features by their weights and adding noise: $Y=X \\beta + \\epsilon$. The standard deviation of the noise is `noise_sd`.\n",
    "\n",
    "Feature values and responses are split into regression and prediction sets so that there are $T_R=710$ time points in the regression set, and $T_P=290$ time points in the prediction set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "T = 1000 # number of samples\n",
    "N = 200 # number of features\n",
    "M = 10000 # number of responses (i.e. voxels)\n",
    "Mfrac = 0.1 # fraction of responses w/ non-zero weights\n",
    "noise_sd = 3.0 # noise level\n",
    "beta_sd = 1.0 / np.sqrt(N) # signal level (effect size?)\n",
    "trnfrac = 0.71 # fraction of data used for training\n",
    "\n",
    "Mreal = int(M*Mfrac)\n",
    "\n",
    "# Generate weights, features, and responses\n",
    "def generate_data(T, N, M, Mfrac, noise_sd, beta_sd, trnfrac):\n",
    "    beta_real = np.hstack([np.random.randn(N, M*Mfrac) * beta_sd, np.zeros((N, M*(1-Mfrac)))])\n",
    "    X = np.random.randn(T, N)\n",
    "    Y = np.dot(X, beta_real) + noise_sd * np.random.randn(T, M)\n",
    "    \n",
    "    # Split data into regression and prediction sets\n",
    "    Xr = X[:T*trnfrac]\n",
    "    Xp = X[T*trnfrac:]\n",
    "    Yr = Y[:T*trnfrac]\n",
    "    Yp = Y[T*trnfrac:]\n",
    "\n",
    "    return beta_real, X, Y, Xr, Xp, Yr, Yp\n",
    "\n",
    "beta_real, X, Y, Xr, Xp, Yr, Yp = generate_data(T, N, M, Mfrac, noise_sd, beta_sd, trnfrac)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit model using OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fit_and_test_model(Xr, Yr, Xp, Yp):\n",
    "    # Do OLS to find beta_est\n",
    "    beta_est, res, rank, sing = np.linalg.lstsq(Xr, Yr)\n",
    "\n",
    "    # Predict\n",
    "    Yp_est = np.dot(Xp, beta_est)\n",
    "\n",
    "    # Get performance\n",
    "    corr = mcorr(Yp, Yp_est)\n",
    "    \n",
    "    return beta_est, Yp_est, corr\n",
    "\n",
    "beta_est, Yp_est, corr = fit_and_test_model(Xr, Yr, Xp, Yp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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MvKp9+7yhJp7bLl87GzjaOlcCbwO2AJ61xEORJEmSJtZUhw7g0TQh4oNAJdk/ycva+RkP\nH1F+v3Z55oht5wI3AnskWTlUp+ao87F2ue+iei9JkiRNgWm/vOqh7fJm4IvAAwc3JjkXOKiqrm5X\n7dYuLxluqKrWJ7kcuD+wM/DNJHcAtgeuq6ofjtj/pe1y1yUdhSRJkjTBpn2k427t8qXAeprJ4VsD\nDwI+DuwFnDxQfhuaUYt1jLYOSFuOgeWGygNsu9COS5IkSdNi2kPH7PHdAhxQVRdU1Q1V9VXgT4Hv\nAnsnedjYeihJkiRNuWkPHde2yy9U1bcHN1TVjcB/tm//oF0Oj2QMm10/2+66ofUbK79RSWoDr9Xz\nbUeSJEnLV5LVc32nHEd/pj10fLNdzvWlf3b9Vu3y4na523DB9ta6O9GMmlwGUFU/A74PbJ1kuxHt\n79IubzNHZC5VlQ28Vs+3HUmSJC1fVbV6ru+U4+jPtIeOs2jmaDwgyagP+Lfb5eUD5QEeN6LsXjTh\n5IKqumVoH5mjzuzTzs9eSKclSZKkadJr6EhylyR/muSxSW7X575GaS+p+giwA3DEUN8eAzwWuIZf\n3u72FOBq4KlJdh8ouyXwmvbtO4Z28852eWSSbQfq7AgcDtxE87RySZIkaVnq5Ja5SZ4HPBN4fFWt\nbdftTjNn4k5tsc8n2be9JGlTOhx4MPDmJPvT3Dp3J+CJNJdKPbuqrgOoquvaJ5ifAqxJcgJNKDmA\n5ra3J1fVSYONV9VnkryZ5qnkX05yKrASOJjmrlXPH55PIkmSJC0nXY10HAwwGzhaR9F86T4WOB14\nCLd9mnfvqup7wO7AP9PMsfhbmkulTgMeUVUfGip/GrA3zcMAnwz8Dc1zPl4IPHWOfbyE5qnjVwGH\nAU8DvgI8oare3v1RSZIkSZOjq4cD7kITLABIcleaL+7vqarntOs+C/w5cHRH+5y39uF/f9u+5lP+\nAmD/Be7jeOD4hfdOkiRJmm5dhY47Az8aeP8ImsnVg6MI59FcgiVpE5qZmVk97j5IkqTlravLq64B\n7jLwfi/gVuCCgXUFbNnR/iRJkiRNiK5Cx9eBJ7R3q9qWZu7D56pq3UCZHWjmPEiSJElaRroKHf8I\n3AP4DvBdYDtgeAL1w4EvdbQ/SZIkSROik9BRVf8BPJdmxONi4MVV9b7Z7Un2BX6D5ha6kiRJkpaR\nriaSU1XvAt41x7ZzaG6fK0mSJGmZ6fWJ5JIkSZK0qJGOJPde7A59OrckSZK0vCz28qoraG6BmwXW\nK+B2i9ynJEmSpAm02NDxr4usV4usJ0mSJGlCLSp0VNUzO+6HJEmSpCnlRHJJkiRJverslrmzktwf\nuD9wh8FndUiSJElanjob6Ujy4CQXAl8DTgHeO7BtnyQ3JDmgq/1JkiRJmgydhI4kuwLnALsC/wh8\njF+9s9W5wDXAk7vYnyRJkqTJ0dVIxypgC+DhVfVC4HODG6vqVuAzwEM72p8kSZKkCdFV6HgU8MGq\n+toGynwH2L6j/UmSJEmaEF2Fjt+kCRUbEprREEmSJEnLSFeh40fAfTdS5gFsPJhIkiRJmjJdhY6z\ngCckud+ojUkeSnMJ1n92tD9JkiRJE6Kr0PF6YD1wbpLnAfcASPLbSf4P8FHgeuDojvYnSZIkaUJ0\n8nDAqvpmkicB/w68bWDTl9vltcCfVtWVXexPkiRJ0uTo7InkVXVmkp2BZwB7AHcG1tHcKve4qlrb\n1b4kSZIkTY5U1bj7ICBJAVRVNlZWWoiZmZnV4+6Dpt+qVatWj7sPkqT5Gcf3zq6eSH7kPMpsm+SD\nXexPkiRJ0uToaiL53yf5eJK7jdqYZA/gi8ATO9qfJEmSpAnRVeh4P/BHwJeS/NHghiQvAz4FbAcc\n0dH+JEmSJE2ITkJHVT0D+CvgjsCZSV6TZPskZwKvA64A9qiqY7rYnyRJkqTJ0dVIB1V1HPAQ4BvA\nK4HLgccAHwB+v6q+0NW+JEmSJE2OzkJH62LgzPbfvw78GHh9VV3f8X4kSZIkTYjOQkeSewJrgBcD\nXwHeQPOsjs8meU5X+5EkSZI0Wbq6Ze4TaO5O9Ujg/wP+oKpeAewDrAXemeSkJHfsYn+SJEmSJkdX\nIx2n0Tzd/OCqel5V3QxQVecDvwd8FDiIJphIkiRJWka6Ch0XAg+uqpOHN1TVT6rqAOBFwPYd7U+S\nJEnShFjRUTt7VtUtGypQVW9Ncl5H+5MkSZI0IToJHYOBI8m9aC6p2hZYB1xUVd9ty13Yxf4kSZIk\nTY6uRjpIsiPNJPJHD22qJJ8E/rqqruhqf5IkSZImQyehI8l2wPk0czauBM4FfgDcA/hDmiDy6SS7\nV9VVXexTkiRJ0mToaqTj72gCx8uBN1XV+tkNSVYALwDe2JY7vKN9SpIkSZoAXd29an/gE1X1xsHA\nAVBVv6iqo4FPtOUkSZIkLSNdhY7tgM9vpMyFNJdbSZIkSVpGugodPwV22EiZe9HczUqSJEnSMtJV\n6DgPOCjJI0ZtTPIw4M9oJptLkiRJWka6mkj+D8CfAGuSnAicTXP3qu2AfYE/B25ty0mSJElaRrp6\nOOCFSZ4MHA/8RfsatBY4tKo2Nu9DkiRJ0pRZdOhIcgRwfFVdC1BVH02yA3Ag8PvANrRPJAc+XFU/\n66C/kiRJkibMUkY63gK8LsmpwLuq6ryquh74QPuSJEmSpCVNJP8X4BfAXwKfSvKNJC9KcqduuiZJ\nkiRpGiw6dFTVc2ieu3EY8FlgN+Bo4HtJ/j3Jvt10UZIkSdIkW9Itc6vqZ1X1nqp6OPAg4BjgBuBg\n4KwkFyd5aZK7dtBXSZIkSROoq+d0UFVfraojgO2BpwFrgF2ANwDfSXJSkj/qan+SJEmSJkNnoWNW\nVd1cVf9WVfsBu9KEjrXAQcB/dr0/SZIkSZu3zkPHkJ/SBI7r2/fpeX+SJEmSNjNdPZH8fyUJ8Fjg\n2cATgF9vN50LvKvr/UmSJEnavHUWOpLcCzgUeBZw73b1T4D3Au+uqku62pckSZKkybGk0JFkBc1o\nxmHAY2gu1yrgbODdwAer6paldlKSJEnS5Fp06EjyBuDpwHbtqh8Dx9GMavxPB32TJEmSNAWWMtLx\nUppRjU/QzNU4rap+0UmvJEmSJE2NpYSO19GMalzRUV8kSZIkTaFFh46qOrLLjkiSJEmaTn0/p0OS\nJEnSMmfokCRJktQrQ4ckSZKkXhk6JEmSJPXK0CFJkiSpV4YOSZIkSb3qJHQk2TLJXknu0kV7kiRJ\nkqZHVyMd9wTWAHt11J4kSZKkKbHohwMm+bWqunUD21cBr66q2y12H9JyNzMzs3rcfZAkSVqqRYcO\n4JoknwLOBq4YsT3tS5IkSdIytpTQcSLwKOBPBtb9nyR3BT4F1FI6JkmSJGk6LDp0VNVzAJLsCDwF\neD3wcGC/tsj6dvtzgDVVdclSOipJkiRpMi15InlVXQF8sH17CHA/4K+BL7Tr3gl8M8n3kvzbUvcn\nSZIkabIsZSL5m4CzgHP55aVU1Y5oXJLkt4CHAPcH9gX2aV+SJEmSlpGljHQcDnwUWAt8qF13/yRb\nDRaqqour6p1V9dSq2n4J++tMkqclubV9/dUcZfZMckaStUluSPKlJEckmfMzS3JIks8muS7JtUnO\nSbJ/f0ciSZIkbf6WEjp+E3gMcDTw83bd39Pc1eo84PEASVYuqYcdS3Iv4J+B69tVt5nwnuRAmhGc\nRwKnAscAK4G3ACfM0e7RwHHA3YF3Ae8Hfgf4SJLDuz0KSZIkaXIsZSL5jcAngU8mORa4hOZLOTST\nyR/U/vvaJP9F8/DANVV17uK7uzRJQhMMfkwzOvOSEWXuCLwbuAXYp6ouate/mub2wAclObiqThyo\nsyfwIuBS4KFVta5dfxRwIXB0ko9W1ZV9Hp8kSZK0OerqieSzPl1VL66qBwOvbde9HdgGWAWc0/H+\nFupvaeaXPAu4YY4yBwF3AU6YDRwAVXUz8Kr27fOG6jy3Xb52NnC0da4E3gZs0e5TkiRJWna6Dh2D\nbgWoqpdU1e7AnYEn9bi/DUpyf5rb+r61qs7fQNHZW/6eOWLbucCNwB5Dl43tR3OZ1qg6H2uX+y6s\nx5IkSdJ06Cp0XAUcCnx+rgJVdW1VndbR/hYkyQrgfTRPTn/lRorv1i5v81yRqloPXE5zWdrObdt3\nALYHrq+qH45o79J2ueuCOy5JkiRNgaU8kfx/VdX1wHuHVq9h83kq+auB3wMe0V4mtSHb0PR73Rzb\n1wFpyzGw3FB5gG3n11VJkiRpunQSOkapqjU0wWOskjwMeAVwVFX997j7I0mSJC03fc7pGLv2sqp/\nBS6mmcg+stjQ++GRjGGz668dKD+4fmPlNyhJbeC1ej5tSJIkaXlLsnqu75Tj6M9Uhw5ga2AX4AHA\nTQMPBLyV5pIrgHe362Zv93txu9xtqK3ZELMTze10LwOoqp8B3we2TrLdiD7s0i5vM0dklKrKBl6r\n59OGJEmSlreqWj3Xd8px9Ke3y6s2EzcB72H03JLdgQcD59EEjQva9WcBfwE8jts+CHAvYCvgU1V1\ny8D6s4Cnt3XeO1Tn8e3y7EUdgSRJkjThpjp0VNVNwGGjtrWXKj0YOL6qjh3YdArwBuCpSY6pqgvb\n8lsCr2nLvGOouXfShI4jk3y4qq5t6+wIHE4Tfo7r4JAkSZKkiTPVoWMxquq6JIfRhI81SU4ArgEO\noLnt7clVddJQnc8keTPNU8m/nORUYCVwMM1dq55fVd/elMchSZIkbS6Wc+go5rilb1WdlmRv4Ejg\nycCWwLeAFwL/NEedlyT5Cs3IxmHAeuAimrtmndF99yVJkqTJsGxDR1XNADMb2H4BsP8C2zweOH6J\nXZMkSZKmyrTfvUqSJEnSmBk6JEmSJPXK0CFJkiSpV4YOSZIkSb0ydEiSJEnqlaFDkiRJUq+W7S1z\nJUndmZmZWb3UNlatWrXkNiRJmydHOiRJkiT1ytAhSZIkqVeGDkmSJEm9MnRIkiRJ6pWhQ5IkSVKv\nDB2SJEmSemXokCRJktQrQ4ckSZKkXhk6JEmSJPXK0CFJkiSpV4YOSZIkSb0ydEiSJEnqlaFDkiRJ\nUq8MHZIkSZJ6ZeiQJEmS1CtDhyRJkqReGTokSZIk9crQIUmSJKlXhg5JkiRJvTJ0SJIkSeqVoUOS\nJElSrwwdkiRJknpl6JAkSZLUK0OHJEmSpF4ZOiRJkiT1ytAhSZIkqVeGDkmSJEm9MnRIkiRJ6pWh\nQ5IkSVKvDB2SJEmSemXokCRJktQrQ4ckSZKkXhk6JEmSJPXK0CFJkiSpVyvG3QFpWs3MzKwedx8k\nSZI2B450SJIkSeqVoUOSJElSrwwdkiRJknpl6JAkSZLUK0OHJEmSpF4ZOiRJkiT1ytAhSZIkqVeG\nDkmSJEm9MnRIkiRJ6pWhQ5IkSVKvDB2SJEmSemXokCRJktQrQ4ckSZKkXhk6JEmSJPXK0CFJkiSp\nV4YOSZIkSb0ydEiSJEnqlaFDkiRJUq8MHZIkSZJ6ZeiQJEmS1CtDhyRJkqReGTokSZIk9WrFuDsg\nSRLAzMzM6i7aWbVqVSftSJK640iHJEmSpF4ZOiRJkiT1ytAhSZIkqVeGDkmSJEm9MnRIkiRJ6pWh\nQ5IkSVKvDB2SJEmSemXokCRJktQrQ4ckSZKkXhk6JEmSJPVqqkNHkjsleXaSDyW5NMkNSa5Ncl6S\nQ5Nkjnp7Jjkjydq2zpeSHJFkzs8rySFJPpvkunYf5yTZv7+jkyRJkibDVIcO4CnAu4CHAp8B3gKc\nCvw28C/AScMVkhwInAs8si17DLCyrXvCqJ0kORo4Drh7u7/3A78DfCTJ4Z0ekSRJkjRhVoy7Az27\nGHhCVZ0+uDLJK4HPAk9O8qSq+mC7/o7Au4FbgH2q6qJ2/auBs4GDkhxcVScOtLUn8CLgUuChVbWu\nXX8UcCFwdJKPVtWVPR+rJEmStFma6pGOqjpnOHC0638IvLN9u/fApoOAuwAnzAaOtvzNwKvat88b\nau657fK1s4GjrXMl8DZgC+BZSzkOSZIkaZJNdejYiF8MLQH2a5dnjih/LnAjsEeSlUN1ao46H2uX\n+y6hn5IkSdJEW5ahI8kK4Bnt28GwsFu7vGS4TlWtBy6nuSRt57adOwDbA9e3oyfDLm2Xu3bQbUmS\nJGkiLcvk8NuYAAAWkElEQVTQAbweeCBwelV9YmD9NjSjFutG1mrWpy3HwHJD5QG2XXxXJUmSpMm2\n7EJHkr+lmfj9DeDpY+7ObSSpDbxWj7t/kiRJ2vwlWT3Xd8px9Gfa7171K5L8DfBW4GvAo6rq2qEi\nwyMZw2bXz9ZbN7R+Y+U3qqpGPjtEkiRJmq+qWg2sHrVtHMFj2Yx0JHkB8E/AV4B9q+pHI4pd3C53\nG97QzgPZieZ2upcBVNXPgO8DWyfZbkR7u7TL28wRkSRJkpaLZRE6krwMeDPwBZrAcfUcRc9ql48b\nsW0vYCvggqq6ZahO5qjz+HZ59oI7LUmSJE2JqQ8dSf4OeB3weZpLqtZuoPgpwNXAU5PsPtDGlsBr\n2rfvGKoz+7yPI5NsO1BnR+Bw4Caap5VLkiRJy9JUz+lIcggwA6wHzgdekNxmysTlVXU8QFVdl+Qw\nmvCxJskJwDXAATS3vT25qk4arFxVn0nyZprJ6V9OciqwEjiY5q5Vz6+qb/d1jJIkSdLmbqpDB7Bj\nu/w14AVzlFkDHD/7pqpOS7I3cCTwZGBL4FvAC2nmhNxGVb0kyVdoRjYOowk5FwFHVdUZSz4KSZIk\naYJNdeioqhmakY6F1rsA2H+BdY5nILxIkiRJakz9nA5JkiRJ42XokCRJktSrqb68SlqsmZmZ1ePu\ngyRJ0rRwpEOSJElSrwwdkiRJknpl6JAkSZLUK0OHJEmSpF4ZOiRJkiT1ytAhSZIkqVeGDkmSJEm9\nMnRIkiRJ6pUPB5QkTZUuHu65atWqJbchSfolRzokSZIk9crQIUmSJKlXhg5JkiRJvTJ0SJIkSeqV\noUOSJElSrwwdkiRJknpl6JAkSZLUK0OHJEmSpF4ZOiRJkiT1ytAhSZIkqVeGDkmSJEm9MnRIkiRJ\n6pWhQ5IkSVKvDB2SJEmSemXokCRJktQrQ4ckSZKkXq0YdwekLs3MzKwedx8kSZL0qxzpkCRJktQr\nQ4ckSZKkXhk6JEmSJPXK0CFJkiSpV04klyRpSBc3pVi1atWS25CkaeFIhyRJkqReOdIhSVIHTjrp\noH0G369ezeqFtlG18DqSNAkMHZIk6TaSpQcgQ5SkWV5eJUmSJKlXjnRIkrSZ6GJ0ARxhkLT5caRD\nkiRJUq8MHZIkSZJ65eVVkiRNma4u05Kkrhg6JEnL3vDtbiVJ3fLyKkmSJEm9MnRIkiRJ6pWXV0mS\nJpaXRUnSZHCkQ5IkSVKvDB2SJEmSemXokCRJktQrQ4ckSZKkXjmRXJuNmZmZ1ePugySpO109pLDK\nhx1Kk86RDkmSJEm9MnRIkiRJ6pWXV0mSxsJnbEjS8uFIhyRJkqReGTokSZIk9crQIUmSJKlXhg5J\nkiRJvXIiuSRpwZwErk2pi+d9+KwPabwMHZIk9eABD/jaPktt4+tff+CapfdEksbPy6skSZIk9cqR\nDnViZmZm9bj7IEmSpM2TIx2SJEmSemXokCRJktQrL6+SJElTzztgSePlSIckSZKkXhk6JEmSJPXK\ny6skSZLmwUu0pMUzdEjSMuPTxCVJm5qhQ5KkzZRPNZc0LZzTIUmSJKlXhg5JkiRJvfLyKkmSpE2k\ni8no4IR0TR5DhyRNCCeAS5ImlZdXdSjJPZMcm+T7SW5KcnmStyTZdtx9U/9OOumkfcbdBy2O526y\nXXXVP+w47j5osZ6yz7h7oMVLsnrcfdDkcKSjI0nuA1wA3BX4MPBN4GHAEcDjkjyiqtaOsYvq2de/\n/vW9gTXj7ocWznM32dau/bcdttvulVeMux+bq837Dlgn+7M32VaBl3lpfgwd3Xk7TeB4flW9bXZl\nkjcBLwReCzxvTH2TJElTxAcVatIYOjrQjnI8Grh8MHC0VgF/DTwtyYur6oau9jszM7M18IAlNvML\n4IAOuiNJkiSNZOjoxr7t8uPDG6rq+iSfpgklDwfO7nC/2wJ/vMQ2buyiI9I0cwK3JElLY+joxm7t\n8pI5tn+LJnTsQrehQ5IkaeJ5udj0M3R0Y5t2uW6O7bPrvYuVNms/+cmdbr9u3R23WkobW2xx8y2/\n9Vs/+OlS+7JpRxdWO5ohbcDmPRldi9XFF/2unjui6ZeqGncfJl6SdwHPBp5dVceO2P5a4BXAK6rq\nDXO04YmQJEnSJlNV2VT78jkd3Zgdydhmju2z66/dBH2RJEmSNiteXtWNb7bL3ebYvku7nGvOxyZN\nmpIkSdKm5OVVHUiyM3ApcDlw3xr4UJP8BvADoIC7VZV3i5IkSdKy4uVVHaiqy2hul7sTcPjQ5hng\n9sD7DBySJElajhzp6Eg72nEBcDfgNJpLrh4G7ANcDOxZVdeMrYOSJEnSmBg6OpTknsD/Ax4H3Bn4\nPvAhYKaq5rqdriRJkjTVDB2SJEmSeuWcDkmSJEm9MnRIkiRJ6pWhY0yS7JnkjCRrk9yQ5EtJjkgy\n73OSZJckL0tydpLvJLk5yVVJPpxknx67v6x1dO5WtHWOS/LFJD9PcmuSv+qz78tFknsmOTbJ95Pc\nlOTyJG9Jsu042tHCdPG5JzkoyTFJzkvy0/bn63199ltLP3dJ7pTk2Uk+lOTS9nfste15PDSJz7Tq\nUUc/e29Iclb7veSG9v+VX0rymiR377P/y1kf/79K8rT2d2cn30+c0zEGSQ4ETgVuAE4E1gIH0Dxc\n8JSqeso82zkBeArwNeD8tp37tW3dDjiiqo7p/ACWsQ7P3bZt3QJ+CNwC3At4dlUd20PXl40k96G5\nk9xdgQ/zyzvJ7UtzJ7lHVNXaTdWOFqbD8/dF4EHAdcD3aH43vr+qntFT15e9Ls5dkucCb6e5Ecs5\nwLeB7YAnAdsAp1bVn/V1DMtZhz97NwMXAl8HfgTcAdgDeAhwddvOt/o4huWqj/9fJbkX8BWaAYqt\n6eL7SVX52oQv4I40P4Q3Ar8/sH4L4NPArcDB82zrEOB3R6zfC7gZuAnYbtzHPC2vjs/drwOPBe7e\nvl/d1j903Mc56S/gP9vP8vCh9W9q179jU7bja2znbx/gPu2/927r/uu4j2+aX12cO5ovSfuPWH93\n4Mq2nSeN+1in8dXhz97KOda/pm3nPeM+1ml7df3/KyDAJ4FvAW/s6vvJ2D+o5fYCDm1P3nEjtu3b\nblvTwX4+7i/nyTl3ho7OztF92s/xf0Zs2xq4nuYv37ffFO34Gs/5G1F3H0PHZJ67oXZe0e7jH8d9\nvNP22kTn73fbfXxs3Mc7Ta8+zh1wBLAeeGSX30+c07Hp7dcuzxyx7Vyav6LvkeTXl7ifW4aWWrpN\nde60ePu2y48Pb6iq62lGpO4APHwTtaOF8XOfXJvi3P1iaKnubIrz94R2uWYJbei2Oj13Se4PvB54\na1Wd31UnwYnk47Bbu7xkeENVrQcuB1YAOy92B0l2AB4F/Izmy7C60fu505LNeY5as9cR77KJ2tHC\n+LlPrl7PXZIVwOx8nFF/+NHSdH7+krwkyep2MvN5wKuBfwHevPhuaoTOzl37c/Y+4ArglUvu2ZAV\nXTeojdqGZvLwXE8oX0dzLd2i7jaQZAvgA8BK4MjySehd6vXcqRPbtMsNnSPY+Dnqqh0tjJ/75Or7\n3L0eeCBwelV9YpFtaG59nL8X08zFmfVp4ISq8gqMbnV57l4N/B7NxPObl9qxYY50LEKSKwZuITaf\n1ya5TWOS29Ek1D1pfrDftCn2O0k213MnSRotyd8CLwK+ATx9zN3RPFXVParq12iCx5No7qz08SRP\nG2/PNEqSh9HMmzqqqv67j3040rE4l9LcMnW+vjfw79m/hm8zR9nZ9dcupENt4Hg/cBDNrVz9oR5t\nszt36tTsX3SWeo66akcL4+c+uXo5d0n+Bngrza3hH1VVnvt+9PazV1U/Bj6c5CKaS4DeRPN9Rd1Y\n8rlrL6v6V5rb666aq9iiejfA0LEIVfVHS6h+MbA7zTV4Xxjc0J70nWgmf1823wbbicsfoAkcHwCe\nUe3tB/SrNrdzp859s13uNsf22Wta57r2tet2tDB+7pOr83OX5AU01/9/hSZwXL347mkjev/Zq6pv\nJ/kG8KAkd6+qHy62Lf2KLs7d1gPlbprjGZzvTvJumrvHvXDBvcTQMQ5nAX8BPA44YWjbXsBWwKfm\ne81jkpXASTQPqDu+qp7VYV/1qzo9d+rFOe3y0UkyGL6T/AbwCJobLPzXJmpHC+PnPrk6PXdJXga8\njuYPPI8uH8TZt031s7c9zdzI65fYjn6pi3N3E/AemnMzbHfgwcB5NH98vWCxHXVOx6Z3Cs0TOZ+a\nZPfZlUm2pHlwDsA7BiskuWOS+yXZbmj9FsCHaALHv9A8R0L96ezcqR9VdRnNbQN3Ag4f2jwD3B54\nX1XdCM0IVXt+dl5KO+pGV+dPm16X5y7J39EEjs/TjHAYOHrW1flLskuS21zmk+TXkryWZl7HJ6vq\nZ30cx3LUxbmrqpuq6rCqes7wC/hIW+z4dt3Ji+1rvApn00tyIM0X2Jto/mJ+DU1w2BU4uaoOHir/\nTOBYhkYykhxH81Tyq4G3z7G7c6rqU10fw3LV1blrt70cuF/79veAB9H8BeHSdt15VfWefo5kerW/\nSC8A7gacRjP0/DCaB8RdDOxZVde0ZXekuRzuyqraabHtqDsdnr8nAk9s324HPKYtO3vf+R9X1Ut7\nPJRlp4tzl+QQ4DiaB5MdA/x0xK4ur6rj+zqO5aqj8/cCmsB4Hs1tV39CM5F8b5ovxVcC+1bVFf0f\n0fLR1e/NOdpeTXNXq2dX1bFL6uhSny7oa9FPkNwTOB1YSzOx+Us0T4DMiLKH0PwCPnZo/Tnt+vU0\nT4scfq0HXj3uY522VxfnbuD83TpwDgfP5cg6vuZ9ju5JE/a+D9xM8wyVNwPbDJXbsf28L1tKO742\nv/NHMxlyrp+vOc+5r/Geu6HzNur/a7cCZ4/7OKf11cH5eyBNWPwC8GOaeY5rab4QvwLYetzHOK2v\nrv6/N6LdVe3P45KfSO5IhyRJkqReOadDkiRJUq8MHZIkSZJ6ZeiQJEmS1CtDhyRJkqReGTokSZIk\n9crQIUmSJKlXhg5JkiRJvTJ0SJIkSeqVoUOSJElSrwwdkiRJknpl6JAkSZLUK0OHJEmSpF4ZOiRJ\nkiT1ytAhSZIkqVeGDkmSJEm9MnRIksYuyY5Jbk1y3DTsZ7GSHJfkR0luv8B6D2mP61l99U2SlsLQ\nIUkTKsn9khyT5KtJ1iW5Ocn3knw0yaFJVo67j4tQS6m8gFCxpP30IcnvAk8Hjq6qGxZSt6o+D5wO\n/H2SrfronyQthaFDkiZQklcDXwMOB64FjgPeCJwB7AL8C/DpsXVwfGpoOey7wP2AV2ya7izI3wM3\nAP+8yPpvALYHntdZjySpIyvG3QFJ0sIkeSWwGvg28GdV9bkRZR4LvHQTd21zkKHlr6iqXwCXbLru\nzE+SewP7Ax9Y6CjHrKo6P8kVwF8Db+6we5K0ZI50SNIESbIjTeD4OfDHowIHQFX9J/DHQ3WfkuTc\n9lKsG5J8OcnLR12GNXiZUpJdk5zYzjVYn2SvjWzfe6CdhyU5JclV7eVf307yziT3WMAxPzPJqUku\na/u9Lsn5Sf5yqNxq4LL27SFt/2Zfhwwf1xz7mtdnNHT8OyY5IcnVSW5M8rkk+8/3+FrPpAlKJyyw\n3rCTgF2SPHKJ7UhSpxzpkKTJ8iya393/XlVf31DBqvr57L+T/APwcuDHwPuB62lCyT8Aj03ymKq6\nZUQz9wH+C7gYeB+wFfDTjWxf1+7zUOBdwI3AfwDfAXYFng08IcnDq+o78zjmtwNfBdYAPwDu0vb9\nfUl2q6pXt+XOAbYBjgC+CHx4oI0vDLV5m8uvFvkZ7QD8N/A/wPHAnYGDgdOS/FFVrZnH8QE8GriV\npV8Sdz7wf4HHtP+WpM1DVfny5cuXrwl5AWfRfDk9dAF19mjrXAHcbWD97WjCwK3AK4bq7NiuvxV4\nzYg2N7Z9V5rRmEuAewxt2w/4BfDBEe0dO6KtnUas+3Xgk+0+th9Yv8Nc7WxoPwv9jIaO/++G2npM\nu/70eZ6fLYCbgG/Osf3JwDE0IWor4BDg9TTB6KFDZe/W7vuccf+36suXL1+DLy+vkqTJMntZ0ncX\nUOfQdvmaqvrR7MqqWg+8mOZL6rPnqHsVMLOBtufa/jyaEZkjquoHgxuq6mzgIzSjHXfYWOer6vIR\n626hGQFZATxqYNPIuRzzsNjP6ArgNUN9+zjNqM5D57nv7YGVjDinSbYA/qCqng88EDgZuJTmpgF/\nSHO3q8F9/4gm0O08z31L0ibh5VWSNP1+n+ZyorOHN1TVt5J8D9gxyW9U1XVDRb5Uoy+72tj2Pdrl\nPkkeNmL73WhGEXYDLtpQ59tJ1i+jCRf3ovlr/6DtN1R/nhb7GX2xqkbdKes7wKjjHuWu7XLtiG17\nAxe0c0ruSXNZ3aeT3Kstf8qIOmsH2pSkzYKhQ5Imyw9obvl6zwXU2Wag7lxt3hPYFhgOHVdtpO25\ntt+5XW7oDloFbHCkI8nOwGfbvp0LnEkzZ2Q9sBPNpUZbbKSP87HYz+jaOcr/gvnfrGU2tIwapVlH\nM2fm4TTHeRJANXNhHjxHe17FIGmzY+iQpMlyHrAvzV/9j51nnXXt8h788u5Og+4xVG7Qxh6iN9f2\nde22barq+o32cG4vAu4EPLOq/nVwQ5I/pwkdXVjKZ7RUV7fLOw1vqKr/BkiyH3B1VX11Hu39JvD9\n7ronSUvnX0MkabIcB9wCPDnJ/TdUcOA2rxfR/BV9nxFl7kvzF/zLq+qnw9uX4DPtPvdaYjv3pQkv\np47YtveIdevb5e0WuJ9xfEazvkczIX5Do1f7Ap/aWENJ7k5z7KOCkySNjaFDkiZIVV1J85yOlcDp\nSXYfVS7J42kuRYJfjoi8KsldBsrcDjia5sv2ezru6j/ThKO3JNllRP9WJvnDebRzedu/fYfqP5bR\nE7uvaZc7LKy7Y/mMgP+9tfFngfsm2XZ4e5KtaOaHrJlHc3/QLjcaUCRpU/LyKkmaMFX1uiQrgFXA\n55JcAFxI81yJu9OMLtwX+Fxb/jNJ3kjz/IavJjkFuAF4PM0dkc4Djuq4jxe3z+k4FvhakjOBb9Hc\n6vbeNHde+iHwgI009XaaZ5Oc3Pb7B8BvA4+lmd9w8NB+r0/yX8AfJnl/u8/18P+3d/eqUQVhGIDf\n6b0ALb0Bm6Qy2ikIqWwiCopoIwarCAkIabwAG0ErSZPGRixstLGysA02eh1aCZ/FrBAkidnNGYnw\nPM0WszPn41TzMj8nb6tq74h6R7yjeW7Sep/kUpKVJO/+aLuYHjI/HmOcldnvhzmeDTCclQ6A/1BV\nPU2ffD9PPwR9N8nj9EnytyT30yexv/+/leTmrO1OkkezpidJrlbVzwE17iZZSrKb5EKS9SS30q9z\nfZ3k4THG2Etf5fiUZDXJgyRnklxP8vKQbrfTJ+7XkmynX+l72KHr/c+a8h1V/n4eZr+d9HB044C2\nc0k+V9WXowZorbUka0m+VtVJPzIIMKl28E1/AMC/1Fp7k+RKkrNV9X2B/pfTt1VtVNWzqesDOAkr\nHQBwOmynf4NkfcH+m+mH0l9MVhHARKx0AMAp0Vp7lb6N7HxV/Zij33L6YfR7VbUzqDyAhQkdAADA\nULZXAQAAQwkdAADAUEIHAAAwlNABAAAMJXQAAABDCR0AAMBQQgcAADCU0AEAAAwldAAAAEMJHQAA\nwFBCBwAAMJTQAQAADCV0AAAAQwkdAADAUEIHAAAw1C8PXJG1qx2DegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113f32110>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 271,
       "width": 398
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(corr[Mreal:], 25, ec='none', fc='0.5', alpha=0.5); # voxels that don't care for stimulus in gray\n",
    "hist(corr[:Mreal], 25, ec='none', fc='b', alpha=0.5); # voxels that do care in blue\n",
    "xlabel(\"Correlation ($r$)\")\n",
    "ylabel(\"# Voxels\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluate significance of prediction performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from model_significance import exact_correlation_pvalue, correlation_pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method 1: Exact test (assumes Gaussianity)\n",
    "When two Gaussian random variables have zero covariance, the distribution of their sample correlation coefficient, $r$, is given by [\\[ref\\]](https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient#Use_the_exact_distribution):\n",
    "$$f(r) = \\frac{(1-r^2)^{\\frac{n-4}{2}}}{B(\\frac{1}{2},\\frac{n-2}{2})}$$\n",
    "where $B$ is the beta function and $n$ is the number of samples.\n",
    "\n",
    "To compute a p-value we find the probability of finding a correlation at least as high as our observed correlation, $\\hat{r}$, given the null distribution: \n",
    "$$P(r \\ge \\hat{r}) = \\int_\\hat{r}^1 f(r) dr$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "exact_pvals = np.array([exact_correlation_pvalue(c, T*(1-trnfrac)) for c in corr])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Methods 2 & 3: Bootstrap and parametric bootstrap\n",
    "For this bootstrap test we compute an empirical bootstrap distribution for $r$ by resampling across time. In the ordinary bootstrap we compute the p-value by finding the fraction of bootstrap samples for which $r<0$. Thus the smallest p-value that can be obtained with the ordinary bootstrap test is $\\frac{1}{n_B}$, where $n_B$ is the number of bootstrap samples. \n",
    "\n",
    "In the parametric bootstrap we approximate the Fisher transform of the bootstrap distribution using a Gaussian distribution. Then we compute the p-value as the integral of the Gaussian mass below zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "bs_pvals, bs_conf, pbs_pvals, pbs_conf, bscorrs = zip(*[correlation_pvalue(a, b, nboot=1000) \n",
    "                                                        for a,b in zip(Yp.T, Yp_est.T)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method 4: Jackknife\n",
    "For the jackknife test we split the data by time into chunks of length 10, then compute the correlation with each chunk withheld. These correlations are bias-corrected using the standard jackknife formula. Then we compute the standard error of the mean (SEM) of the unbiased correlations across the jackknife samples, figure out how many SEMs we need to get the desired level of significance, and check whether each voxel passes that threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n"
     ]
    }
   ],
   "source": [
    "def jackknife_test(Yp_est, Yp, corr, desired_pval=0.01, split_length=10):\n",
    "    j = int(Yp.shape[0] / split_length) # number of jackknife samples\n",
    "    print \"Doing %d jackknife samples of length 10\" % j\n",
    "\n",
    "    est_splits = np.vsplit(Yp_est, j)\n",
    "    real_splits = np.vsplit(Yp, j)\n",
    "\n",
    "    def jk_iter(lst):\n",
    "        for ho in range(len(lst)):\n",
    "            yield [lst[ii] for ii in range(len(lst)) if not ho==ii]\n",
    "\n",
    "    # Compute correlations leaving out each jackknife set\n",
    "    jk_corrs = [mcorr(np.vstack(a), np.vstack(b)) for a,b in zip(jk_iter(est_splits), jk_iter(real_splits))]\n",
    "\n",
    "    # Compute unbiased estimate of jackknife correlation \n",
    "    unbiased_jk_corrs = [j*corr - (j - 1) * jc for jc in jk_corrs]\n",
    "\n",
    "    # Compute standard error of the mean for each set of unbiased jackknife correlations\n",
    "    jk_sems = np.vstack(unbiased_jk_corrs).std(0) / np.sqrt(j)\n",
    "\n",
    "    # Figure out how many SEMs away from zero we need to get desired p-value\n",
    "    # divide by two because two-sided?\n",
    "    num_sems = scipy.stats.norm.ppf(1 - desired_pval / 2)\n",
    "    print \"SEMs:\", num_sems\n",
    "\n",
    "    # Compute jackknife significance\n",
    "    jk_signif = (corr - num_sems * jk_sems) > 0\n",
    "    \n",
    "    return jk_signif\n",
    "\n",
    "jk_signif = jackknife_test(Yp_est, Yp, corr, desired_pval=0.01, split_length=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot some things"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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F259cVa9I8v1J/m6S26vqgavtPjN+DwAAMITZgnp3n+zu968e1umeu2pNvzrJrd39ih2n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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ed20d0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 257,
       "width": 373
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(np.log10(exact_pvals[jk_signif]), 25, ec='none', fc='blue', alpha=0.5, log=True);\n",
    "hist(np.log10(exact_pvals[~jk_signif]), 50, ec='none', fc='red', alpha=0.5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fyTY0GY5zUdOwITXs21VzxqLUJOPJROQW+3K/pP2wtLX7PPWIWLXLoc5JTwGW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\niVNqBeBJRT51/f3k8B73u+R+Qu5WPs8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iOfb7usvezx32ujg1r6i8ufj+xRCnGOIUR6xG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\nokCSJElacBYFkiRJ0oL7f/0po8ffl9coAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112e6c390>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 260,
       "width": 386
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "loglog(exact_pvals[:Mreal], pbs_pvals[:Mreal], 'r.')\n",
    "loglog(exact_pvals[Mreal:], pbs_pvals[Mreal:], 'k.')\n",
    "grid();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute power, FDR, and true p-value for each method\n",
    "To compare the 4 methods for computing p-values (or significance) I'm computing three metrics: \n",
    "* power (i.e. the fraction of responsive voxels that are labeled significant), \n",
    "* false discovery rate (FDR; i.e. the fraction of significant voxels that are non-responsive), \n",
    "* and, as a sanity check, the actual p-value (i.e. the fraction of non-responsive voxels that are labeled significant)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "p = 0.01 # desired p-value\n",
    "\n",
    "# assign significance for methods 1-3 (jackknife done above)\n",
    "exact_signif = np.array(exact_pvals) < p\n",
    "pbs_signif = np.array(pbs_pvals) < p\n",
    "bs_signif = np.array(bs_pvals) < p\n",
    "\n",
    "# define functions for computing power, FDR, and true p-value\n",
    "power = lambda sg: sg[:Mreal].mean()\n",
    "fdr = lambda sg: sg[Mreal:].sum() / sg.sum().astype(float)\n",
    "truep = lambda sg: sg[Mreal:].mean()\n",
    "\n",
    "# compute metrics for each method\n",
    "exact_power = power(exact_signif)\n",
    "exact_fdr = fdr(exact_signif)\n",
    "exact_truep = truep(exact_signif)\n",
    "\n",
    "bs_power = power(bs_signif)\n",
    "bs_fdr = fdr(bs_signif)\n",
    "bs_truep = truep(bs_signif)\n",
    "\n",
    "pbs_power = power(pbs_signif)\n",
    "pbs_fdr = fdr(pbs_signif)\n",
    "pbs_truep = truep(pbs_signif)\n",
    "\n",
    "jk_power = power(jk_signif)\n",
    "jk_fdr = fdr(jk_signif)\n",
    "jk_truep = truep(jk_signif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Power:\n",
      "  Exact: 0.562\n",
      "  Bootstrap: 0.559\n",
      "  Par. bootstrap: 0.568\n",
      "  Jackknife: 0.512\n"
     ]
    }
   ],
   "source": [
    "print \"Power:\"\n",
    "print \"  Exact:\", exact_power\n",
    "print \"  Bootstrap:\", bs_power\n",
    "print \"  Par. bootstrap:\", pbs_power\n",
    "print \"  Jackknife:\", jk_power"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FDR:\n",
      "  Exact: 0.135384615385\n",
      "  Bootstrap: 0.146564885496\n",
      "  Par. bootstrap: 0.154761904762\n",
      "  Jackknife: 0.135135135135\n"
     ]
    }
   ],
   "source": [
    "print \"FDR:\"\n",
    "print \"  Exact:\", exact_fdr\n",
    "print \"  Bootstrap:\", bs_fdr\n",
    "print \"  Par. bootstrap:\", pbs_fdr\n",
    "print \"  Jackknife:\", jk_fdr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True p-value:\n",
      "  Exact: 0.00977777777778\n",
      "  Bootstrap: 0.0106666666667\n",
      "  Par. bootstrap: 0.0115555555556\n",
      "  Jackknife: 0.00888888888889\n",
      "\n",
      "p-value for difference between true and desired p-value:\n",
      "  Exact: 0.873793926183\n",
      "  PBS: 0.137843841196\n",
      "  BS: 0.524627603113\n",
      "  Jackknife: 0.633631303124\n"
     ]
    }
   ],
   "source": [
    "print \"True p-value:\"\n",
    "print \"  Exact:\", exact_truep\n",
    "print \"  Bootstrap:\", bs_truep\n",
    "print \"  Par. bootstrap:\", pbs_truep\n",
    "print \"  Jackknife:\", jk_truep\n",
    "\n",
    "# How unexpected are the differences between the desired p-value and true p-value?\n",
    "print \"\"\n",
    "print \"p-value for difference between true and desired p-value:\"\n",
    "print \"  Exact:\", scipy.stats.binom_test(exact_signif[Mreal:].sum(), M - Mreal, p)\n",
    "print \"  PBS:\", scipy.stats.binom_test(pbs_signif[Mreal:].sum(), M - Mreal, p)\n",
    "print \"  BS:\", scipy.stats.binom_test(bs_signif[Mreal:].sum(), M - Mreal, p)\n",
    "print \"  Jackknife:\", scipy.stats.binom_test(jk_signif[Mreal:].sum(), M - Mreal, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here it seems like the exact test and two bootstrap-based tests have better power than the jackknife test, and the exact and jackknife tests have better FDR than the bootstrap-based tests. But it's unclear how real those differences are.\n",
    "\n",
    "Testing the bootstrap is expensive, but the exact and jackknife tests are easy. Let's run them a few times and see how repeatable these results are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n",
      "Doing 29 jackknife samples of length 10\n",
      "SEMs: 2.57582930355\n"
     ]
    }
   ],
   "source": [
    "reps = 10\n",
    "p = 0.01\n",
    "\n",
    "exact_powers = []\n",
    "exact_fdrs = []\n",
    "jk_powers = []\n",
    "jk_fdrs = []\n",
    "\n",
    "for rep in range(reps):\n",
    "    beta_real, X, Y, Xr, Xp, Yr, Yp = generate_data(T, N, M, Mfrac, noise_sd, beta_sd, trnfrac)\n",
    "    beta_est, Yp_est, corr = fit_and_test_model(Xr, Yr, Xp, Yp)\n",
    "    \n",
    "    exact_signif = np.array([exact_correlation_pvalue(c, T*(1-trnfrac)) for c in corr]) < p\n",
    "    jk_signif = jackknife_test(Yp_est, Yp, corr, desired_pval=p, split_length=10)\n",
    "    \n",
    "    exact_powers.append(power(exact_signif))\n",
    "    exact_fdrs.append(fdr(exact_signif))\n",
    "    \n",
    "    jk_powers.append(power(jk_signif))\n",
    "    jk_fdrs.append(fdr(jk_signif))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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k2oVg8NqqOjjJDye5W5IvJzm3u/9ln94JAABsUvMWEo6aHD+5RPklGULCkdl7SOgkd0ny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\nQgJsbZck+YcM/2j8U5K/Wuy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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115de7b10>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 255,
       "width": 388
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
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RZiKzncDvA5uqarrhUadLQ88CTp2yrWhaKAatDjuAs6bs/07gbuDf0ASSvYHv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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b23350>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 255,
       "width": 388
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot([exact_powers, jk_powers], labels=[\"Exact\", \"Jackknife\"]);\n",
    "ylabel(\"Power\");\n",
    "\n",
    "figure()\n",
    "boxplot([exact_fdrs, jk_fdrs], labels=[\"Exact\", \"Jackknife\"]);\n",
    "ylabel(\"FDR\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here it seems like the difference in power is real: the exact test is more powerful than the jackknife test under current assumptions. There seems to be no real difference in FDR."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Just for fun: confirm beta-based null distribution on bivariate correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.special\n",
    "import scipy\n",
    "\n",
    "fnull = lambda r,n: (1-r**2)**((n-4.0)/2.0)/scipy.special.beta(0.5, (n-2)/2.0)\n",
    "\n",
    "n = 100\n",
    "m = 100000\n",
    "null_corrs = np.array([np.corrcoef(np.random.randn(n), np.random.randn(n))[0,1] for _ in range(m)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1121f2190>]"
      ]
     },
     "execution_count": 265,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uSa3jivvxRDCcaZcBzsqjFElqRwZ3SWqdbAg1uGdk22Wo/MeOJPUsg7sktY4r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\nTNwlSZKkFjBxlyRJklrgf5U+tdj3W+C4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1121a9cd0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 255,
       "width": 375
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.linspace(-1, 1, 1000)\n",
    "null_pdf = fnull(r, n)\n",
    "\n",
    "hist(null_corrs, 20, normed=True, ec='none', fc='0.5')\n",
    "plot(r, null_pdf, 'r', lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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