ex_6_budding_mueller.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision Making I"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Céline Budding && Dorothea Müller "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as mlp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Extension-Drift Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler_maruyama(ffun, gfun, x0, t, **args):\n",
    "    \"\"\"Euler Maruyama method for stochastic differential equations. x0 must be a list.\"\"\"\n",
    "    dts = np.diff(t).astype(float)\n",
    "    res = np.zeros((len(t)+1, len(x0)))\n",
    "    res[0] = x0\n",
    "\n",
    "    for i in range(1, len(t)):\n",
    "        # Euler part.\n",
    "        res[i] = np.multiply(ffun(res[i-1], t, **args), dts[i-1]) + res[i-1]\n",
    "        \n",
    "        gfun_res = gfun(res[i-1], t, **args)\n",
    "        if isinstance(gfun_res, float) or isinstance(gfun_res, int):\n",
    "            gfun_res = np.repeat(gfun_res, res[i].shape[0])\n",
    "        \n",
    "        # For each component, sample from random normal distribution!\n",
    "        rand_vals = np.random.normal(0, 1, res[i].shape[0])\n",
    "        \n",
    "        for j, _ in enumerate(res[i]):\n",
    "            # For each component, sample noise independently from random normal distribution.\n",
    "            res[i, j] = res[i, j] + gfun_res[j] * rand_vals[j] * np.sqrt(dts[i-1])\n",
    "    return res[:len(t)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = [0]\n",
    "sigma = 0.5\n",
    "mu = 0.2\n",
    "t = np.linspace(0, 10, 1001)\n",
    "n_sm = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ffn = lambda x, t, **args: args['mu']\n",
    "gfn = lambda x, t, **args: args['sigma']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for run in range(n_sm):\n",
    "    res = euler_maruyama(ffn, gfn, x0, t, sigma = 0.5, mu = 0.2)\n",
    "    plt.plot(t, res)\n",
    "    \n",
    "plt.title(\"Random drift with sigma = 0.5 and mu = 0.2\")\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"X\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_up(a = 1, mu_val= [-0.1, 0, 0.1, 0.2, 0.5], n=200, sigma=0.5):\n",
    "\n",
    "    perc_up = np.zeros(len(mu_val))\n",
    "    res = np.zeros(len(t))\n",
    "    \n",
    "    for i, mu in enumerate(mu_val):\n",
    "    \n",
    "        n_successfull = 0\n",
    "        for _ in range(n):\n",
    "            \n",
    "            res[-1] = 0\n",
    "#             # Resample when no decision boundary is found\n",
    "            while(res[-1] < a and res[-1] > -a):\n",
    "                res = euler_maruyama(ffn, gfn, x0, t, mu=mu, sigma=sigma)\n",
    "#             res = euler_maruyama(ffn, gfn, x0, t, mu = mu, sigma=sigma)\n",
    "        \n",
    "            if res[-2] > a:\n",
    "                n_successfull +=1\n",
    "\n",
    "        perc_up[i] = n_successfull/n  * 100\n",
    "        \n",
    "    return perc_up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_val = [-0.1, 0, 0.1, 0.2, 0.5]\n",
    "a_val = [0.5, 1, 2]\n",
    "n = 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for a in a_val:\n",
    "    res_a = simulate_up(a = a)\n",
    "    plt.scatter(mu_val, res_a, label = f\"a = {a}\", alpha = 0.5)\n",
    "\n",
    "plt.title('Up trials for different values of mu and different a')\n",
    "plt.xlabel('Mu values')\n",
    "plt.ylabel('Percentage of up trials')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* For a lower mu, it is more likely that we end below the negative decision boundary and vice versa.\n",
    "\n",
    "* **What happens to this curve if you double, what if you halve the value of a?**\n",
    "If the value is halfed, the percentage of 'up' trials go down. This can be explained as random fluctuations are more likely to go over the decision boundary, even if it is in the different direction than the drift. Vice versa, if the decision boundary is really high, random flucuations are more likely to push the system over the decision boundary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will pick a value of mu = 0.05 to reach 70% up-trials."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_times(a = 1, mu_val= 0.05, n=2000, sigma=0.5):\n",
    "    res = np.zeros(len(t))\n",
    "    \n",
    "    yes_times = []\n",
    "    no_times = []\n",
    "    \n",
    "    for _ in range(n):   \n",
    "        res[-1] = 0\n",
    "        idx_greater = n+1\n",
    "        idx_smaller = n+1\n",
    "\n",
    "        # Resample when no decision boundary is found\n",
    "        while(res[-1] < a and res[-1] > -a):\n",
    "            res = euler_maruyama(ffn, gfn, x0, t, mu=mu, sigma=sigma).flatten()\n",
    "\n",
    "        # Compare occurences.\n",
    "        if res[res>a].size != 0:\n",
    "            idx_greater = np.argwhere(res>a)[0][0]\n",
    "\n",
    "        if res[res<-a].size != 0:\n",
    "            idx_smaller = np.argwhere(res<-a)[0][0]\n",
    "\n",
    "        if idx_greater < idx_smaller:\n",
    "            yes_times.append(t[idx_greater])\n",
    "\n",
    "        else:\n",
    "            no_times.append(t[idx_smaller])\n",
    "        \n",
    "    return yes_times, no_times "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "yes_time, no_time = simulate_times()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean for Up: 3.0774680732926156\n"
     ]
    }
   ],
   "source": [
    "plt.hist(yes_time, bins = 50)\n",
    "plt.title('Histogram for up trials with mu = 0.05')\n",
    "plt.xlabel('Reaction time')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()\n",
    "\n",
    "print(f\"Mean for Up: {np.mean(yes_time)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean for Down: 2.9240201005025126\n"
     ]
    }
   ],
   "source": [
    "plt.hist(no_time, bins = 50)\n",
    "plt.title('Histogram for down trials with mu = 0.05')\n",
    "plt.xlabel('Reaction time')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()\n",
    "\n",
    "print(f\"Mean for Down: {np.mean(no_time)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Is this what you would have expected?**\n",
    "\n",
    "* Size: We would have expected for the height of the up times to be even more higher in comparison to the down times, as also shown in the slides. This would be expected since the mean drift and the sigma affecting the drift are both positive, so many more trials should reach the up boundary than the down boundary. \n",
    "* Mean: The mean is similar between the distributions (what we would have expected). However, the mean should be a lot lower judging, judging from slide 38 the reaction times in the histogram should be 2.5 at max, not in the mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_up(comb, a = 1, n=100, sigma=0.5):\n",
    "\n",
    "    perc_up = np.zeros(len(comb))\n",
    "    res = np.zeros(len(t))\n",
    "    \n",
    "    for i, (mean, std) in enumerate(comb):\n",
    "        n_successfull = 0\n",
    "        for _ in range(n):\n",
    "            res[-1] = 0\n",
    "            # Resample when no decision boundary is found\n",
    "            while(res[-1] < a and res[-1] > -a):\n",
    "                res = euler_maruyama(ffn, gfn, x0, t, mu=mu, sigma=sigma, norm_mu=mean, norm_sigma=std)\n",
    "  \n",
    "            if res[-1] > a:\n",
    "                n_successfull +=1\n",
    "\n",
    "        perc_up[i] = n_successfull/n  * 100\n",
    "        \n",
    "    return perc_up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_times(norm_mu, norm_sigma, a = 1, n=2000, sigma=0.5):\n",
    "    res = np.zeros(len(t))\n",
    "    \n",
    "    yes_times = []\n",
    "    no_times = []\n",
    "    \n",
    "    for _ in range(n):   \n",
    "        res[-1] = 0\n",
    "        idx_greater = n+1\n",
    "        idx_smaller = n+1\n",
    "\n",
    "        # Resample when no decision boundary is found\n",
    "        while(res[-1] < a and res[-1] > -a):\n",
    "            res = euler_maruyama(ffn, gfn, x0, t, sigma=sigma, norm_mu=norm_mu, norm_sigma=norm_sigma).flatten()\n",
    "\n",
    "        # Compare occurences.\n",
    "        if res[res>a].size != 0:\n",
    "            idx_greater = np.argwhere(res>a)[0][0]\n",
    "\n",
    "        if res[res<-a].size != 0:\n",
    "            idx_smaller = np.argwhere(res<-a)[0][0]\n",
    "\n",
    "        if idx_greater < idx_smaller:\n",
    "            yes_times.append(t[idx_greater])\n",
    "\n",
    "        else:\n",
    "            no_times.append(t[idx_smaller])\n",
    "        \n",
    "    return yes_times, no_times "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "ffn = lambda x, t, **args: np.random.normal(args['norm_mu'], args['norm_sigma'])\n",
    "gfn = lambda x, t, **args: args['sigma']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, calculate where it stays around 70\\% up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_mu = [0.05, 0.1, 0.25, 0.5, 1.0, 1.5]\n",
    "all_sigma = [0.5, 1.0, 1.5, 2.0, 5.0, 10]\n",
    "\n",
    "comb = [(mu, sigma) for mu in all_mu for sigma in all_sigma]\n",
    "perc_up = simulate_up(comb, a = 1, n=100, sigma=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mu 0.05\t sigma 0.5: 70.0\n",
      "Mu 0.05\t sigma 1.0: 63.0\n",
      "Mu 0.05\t sigma 1.5: 66.0\n",
      "Mu 0.05\t sigma 2.0: 65.0\n",
      "Mu 0.05\t sigma 5.0: 63.0\n",
      "Mu 0.05\t sigma 10: 53.0\n",
      "Mu 0.1\t sigma 0.5: 76.0\n",
      "Mu 0.1\t sigma 1.0: 83.0\n",
      "Mu 0.1\t sigma 1.5: 82.0\n",
      "Mu 0.1\t sigma 2.0: 80.0\n",
      "Mu 0.1\t sigma 5.0: 77.0\n",
      "Mu 0.1\t sigma 10: 57.99999999999999\n",
      "Mu 0.25\t sigma 0.5: 100.0\n",
      "Mu 0.25\t sigma 1.0: 96.0\n",
      "Mu 0.25\t sigma 1.5: 98.0\n",
      "Mu 0.25\t sigma 2.0: 100.0\n",
      "Mu 0.25\t sigma 5.0: 89.0\n",
      "Mu 0.25\t sigma 10: 77.0\n",
      "Mu 0.5\t sigma 0.5: 100.0\n",
      "Mu 0.5\t sigma 1.0: 100.0\n",
      "Mu 0.5\t sigma 1.5: 100.0\n",
      "Mu 0.5\t sigma 2.0: 100.0\n",
      "Mu 0.5\t sigma 5.0: 100.0\n",
      "Mu 0.5\t sigma 10: 94.0\n",
      "Mu 1.0\t sigma 0.5: 100.0\n",
      "Mu 1.0\t sigma 1.0: 100.0\n",
      "Mu 1.0\t sigma 1.5: 100.0\n",
      "Mu 1.0\t sigma 2.0: 100.0\n",
      "Mu 1.0\t sigma 5.0: 100.0\n",
      "Mu 1.0\t sigma 10: 100.0\n",
      "Mu 1.5\t sigma 0.5: 100.0\n",
      "Mu 1.5\t sigma 1.0: 100.0\n",
      "Mu 1.5\t sigma 1.5: 100.0\n",
      "Mu 1.5\t sigma 2.0: 100.0\n",
      "Mu 1.5\t sigma 5.0: 100.0\n",
      "Mu 1.5\t sigma 10: 100.0\n"
     ]
    }
   ],
   "source": [
    "for i, (mu, sigma) in enumerate(comb):\n",
    "    print(f\"Mu {mu}\\t sigma {sigma}: {perc_up[i]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can select the values that result around 70%. However, we will only plot the best result as the simulation takes long (to rerun)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "good_comb = [(0.25, 10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For mu = 0.25, sigma = 10\n",
      "Distribution mean Up 0.9055908720456397\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distribution mean Down 0.8335705045278139\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for norm_mu, norm_sigma in good_comb:\n",
    "    print(f\"For mu = {norm_mu}, sigma = {norm_sigma}\")\n",
    "    yes_times, no_times = simulate_times(norm_mu, norm_sigma, n=2000, sigma=0.5)\n",
    "    plt.hist(yes_times, bins = 50)\n",
    "    plt.title('Histogram for up trials with mu = 0.05')\n",
    "    plt.xlabel('Reaction time')\n",
    "    plt.ylabel('Frequency')\n",
    "    print(\"Distribution mean Up\", np.mean(yes_times))\n",
    "    plt.show()\n",
    "    \n",
    "    plt.hist(no_times, bins=50)\n",
    "    plt.title('Histogram for down trials with mu = 0.05')\n",
    "    plt.xlabel('Reaction time')\n",
    "    plt.ylabel('Frequency')\n",
    "    print(\"Distribution mean Down\", np.mean(no_times))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean goes down, as we would have expected. However, the difference in frequency between up and down trials did not change, there are about 2x as many up as down trials, but we would expect there to be far less down trials. However, we tried different parameters to get this results and we did not manage to get both features, so we decided that the low reaction time was more relevant. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}