Can I generate a correlated data vector with a p-value of ~50% and it all lies outside the 1-sigma region?

can_i_do_it.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "31085290-c7ae-4170-a59e-1d6ba9749b30",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import ultraplot as uplt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e56e8e0d-4d5c-4c09-9907-175e3d10103c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "0590fd72-4ac7-4cc9-a3ff-8f5dce8edf62",
   "metadata": {},
   "outputs": [],
   "source": [
    "# first we generate a cov matrix with a ton of off diagonal covariance\n",
    "\n",
    "def make_cov_mat(*, dim, corr, var):\n",
    "    cvec = np.linspace(0.9999, 1, dim) * corr\n",
    "    corrmat = np.ones((dim, dim)) * np.outer(cvec, cvec)\n",
    "    corrmat[np.arange(dim), np.arange(dim)] = 1.0\n",
    "    varvec = np.linspace(0.1, 1, dim) * var\n",
    "    var = corrmat * np.outer(varvec, varvec)\n",
    "    return var\n",
    "\n",
    "dim = 50\n",
    "corr = 0.99\n",
    "var = 2.0\n",
    "\n",
    "cov = make_cov_mat(dim=dim, corr=corr, var=var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "046321af-75a2-4d17-bf74-913f82477e16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Figure(nrows=1, ncols=2, refwidth=2.5)"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 343,
       "width": 569
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make a plot to confirm\n",
    "\n",
    "fig, axs = uplt.subplots(nrows=1, ncols=2, share=0)\n",
    "m = axs[0, 0].pcolormesh(cov)\n",
    "axs[0, 0].colorbar(m, loc=\"t\", title=\"cov\")\n",
    "\n",
    "\n",
    "std = np.sqrt(np.diag(cov))\n",
    "corr = cov / np.outer(std, std)\n",
    "m = axs[0, 1].pcolormesh(corr, vmin=-1, vmax=1, cmap=\"div\")\n",
    "axs[0, 1].colorbar(m, loc=\"t\", title=\"corr\")\n",
    "\n",
    "axs.format(grid=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "6b1a9544-2ce4-4b31-a266-20afe0211c7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(nrows=1, ncols=1, refwidth=2.5)"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 302
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(nrows=1, ncols=1, refwidth=2.5)"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 304,
       "width": 302
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# now we make a bunch of draws and compute their chi2\n",
    "\n",
    "icov = np.linalg.inv(cov)\n",
    "seed = 42\n",
    "\n",
    "# use an odd number of draws so we can extract the draw at the median chi2\n",
    "ndraws = 1000\n",
    "if ndraws % 2 == 0:\n",
    "    ndraws += 1\n",
    "\n",
    "rng = np.random.RandomState()\n",
    "draws = rng.multivariate_normal(np.zeros(dim), cov, size=ndraws)\n",
    "\n",
    "# we could do fancy indexing but I will mess it up so doing to use a loop\n",
    "chi2s = []\n",
    "for i in range(ndraws):\n",
    "    draw = draws[i]\n",
    "    chi2s.append(\n",
    "        np.dot(draw.T, np.dot(icov, draw))\n",
    "    )\n",
    "chi2s = np.array(chi2s)\n",
    "\n",
    "assert chi2s.shape == (ndraws,)\n",
    "# plot the chi2\n",
    "\n",
    "fig, axs = uplt.subplots()\n",
    "\n",
    "axs.hist(chi2s, bins=40);\n",
    "axs.format(xlabel=\"chi2\", ylabel=\"number of points\")\n",
    "\n",
    "# now we plot the median chi2 data vector relative to the diagonal cov\n",
    "\n",
    "msk = chi2s == np.median(chi2s)\n",
    "assert np.sum(msk) == 1\n",
    "\n",
    "fig, axs = uplt.subplots()\n",
    "\n",
    "diagstd = np.std(draws, axis=0)\n",
    "\n",
    "\n",
    "x = np.arange(dim)\n",
    "axs.fill_between(x, -1, 1, color=\"orange\", alpha=0.5)\n",
    "\n",
    "for ind in np.where(msk)[0]:\n",
    "    axs.plot(x, draws[ind, :] / diagstd, color=\"r\", linestyle=\"dotted\")\n",
    "\n",
    "axs.format(xlabel=\"data vectpr index\", ylabel=\"(data - model)/std\", ylim=(-3, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "651dff28-ef5a-4d15-8bb7-1fc9bfc63a53",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:des-y6]",
   "language": "python",
   "name": "conda-env-des-y6-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}