02_Bootstrapping.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 02: Bootstrapping confidence intervals\n",
    "Previously, we saw how to obtain confidence intervals on our curve fit parameters using classical statistical distributions. As pointed out, that approach assumes the various fit parameters are *normally* distributed. That's often not the case with non-linear fits. The classical approach also assumes that uncertainty in your (y) data is evenly spread out among your (x) points. Again, particularly with non-linear fits, this is often not the case. We frequently have some areas with greater noise than others, so how do we retrieve confidence intervals that reflect this reality?\n",
    "\n",
    "Here, we'll explore the *bootstrapping* approach. In short, this technique repeatedly fits the desired function to random subsets of your data to answer the question of how the fit would change in response to slight variation. This gives us a distribution of reasonable parameter values, from which we can determine the most likely value as well as get a sense of how skewed these reasonable values are in one direction or the other.\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating more realistic data\n",
    "First, our usual imports and some synthetic data. I'll make this data a bit more complex than before, to illustrate a more likely scenario where experimental noise is not shared evenly among *x*-values. The details aren't important for this lesson, and largely arbitrary anyways, so skip ahead if you're uninterested. If you're curious, I took the same logistic Hill curve from before, normalized it so it fell between 0 and 1, then took the *logit* transform. This transform takes data bounded on (0,1) and puts them on an unbounded *log* scale. By applying Gaussian noise here then transforming the data back to \"normal\" space, I ensure the greatest noise lies at the midpoint of the curve (where it's steepest, as we'd expect) and that noise at the extremes tends towards the center slightly (again, as we'd expect from real data)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "import scipy.optimize as opt\n",
    "np.random.seed(42)           # For reproducibility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logit(x):\n",
    "    return np.log(x/(1-x))\n",
    "\n",
    "def logit_inv(y):\n",
    "    return 1/(np.exp(-y)+1)\n",
    "\n",
    "def Hill_eq(x,S0,Smax,x_crit,b):\n",
    "    return S0 + ( Smax - S0 )/( 1 + 10**((x_crit-x)*b) )\n",
    "\n",
    "def normalize(y,span):\n",
    "    return np.interp(y,(y.min(),y.max()),(0.5-span/2,0.5+span/2))\n",
    "\n",
    "def unnormalize(norm_y,span,y):\n",
    "    return np.interp(norm_y,(0.5-span/2,0.5+span/2),(y.min(),y.max()))\n",
    "    \n",
    "\n",
    "c = concentrations = 10**-np.arange(5.,12.)\n",
    "lg_c = np.log10(c)\n",
    "\n",
    "p_Hill = [0.3,1.5,-8,1.4]\n",
    "r = response = Hill_eq(lg_c,*p_Hill)\n",
    "\n",
    "xpts = np.linspace(lg_c.min(),lg_c.max(),100)\n",
    "ypts = Hill_eq(xpts,*p_Hill)\n",
    "\n",
    "span = 0.9\n",
    "\n",
    "logit_r = logit(normalize(r,span))\n",
    "\n",
    "n_r = n_reps = 10\n",
    "n_c = 7\n",
    "logit_data = np.array([np.random.normal(l_r,0.5,size = n_r) for l_r in logit_r])\n",
    "data = unnormalize(logit_inv(logit_data),span,r)\n",
    "# Make lg_c the same size as the data\n",
    "lg_c = np.tile(lg_c,[n_r,1]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, axs = plt.subplots(1,2,figsize=(12,4))\n",
    "\n",
    "axs[0].plot(lg_c,logit_data,'o',color='k',alpha = 0.5)\n",
    "axs[0].plot(xpts,logit(normalize(ypts,span)))\n",
    "axs[0].set_title('Logit-Transformed Data'+'\\n'+'Normally-distributed noise')\n",
    "\n",
    "axs[1].plot(lg_c,data,'o',color='k',alpha = 0.5)\n",
    "axs[1].plot(xpts,ypts)\n",
    "axs[1].set_title('Un-Transformed Data'+'\\n'+'Noise weighted towards center');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Classical confidence intervals\n",
    "Let's first fit this curve as before with classical confidence intervals. The functions we defined last time are now in the BenchtopUtils.py file; by placing the file next to this one in our directory, we can import it and use the functions it contains just like any other module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S0</th>\n",
       "      <th>Smax</th>\n",
       "      <th>x_crit</th>\n",
       "      <th>Hill Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95% CI Lower Limit</th>\n",
       "      <td>0.343509</td>\n",
       "      <td>1.510250</td>\n",
       "      <td>-7.900033</td>\n",
       "      <td>1.941098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Optimal Value</th>\n",
       "      <td>0.314152</td>\n",
       "      <td>1.479104</td>\n",
       "      <td>-7.952710</td>\n",
       "      <td>1.478391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95% CI Upper Limit</th>\n",
       "      <td>0.284795</td>\n",
       "      <td>1.447958</td>\n",
       "      <td>-8.005388</td>\n",
       "      <td>1.015683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Standard Error</th>\n",
       "      <td>0.014978</td>\n",
       "      <td>0.015891</td>\n",
       "      <td>0.026877</td>\n",
       "      <td>0.236079</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          S0      Smax    x_crit  Hill Coefficient\n",
       "95% CI Lower Limit  0.343509  1.510250 -7.900033          1.941098\n",
       "Optimal Value       0.314152  1.479104 -7.952710          1.478391\n",
       "95% CI Upper Limit  0.284795  1.447958 -8.005388          1.015683\n",
       "Standard Error      0.014978  0.015891  0.026877          0.236079"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "import BenchtopUtils as bu\n",
    "\n",
    "S0_g = data.min()\n",
    "Smax_g = data.max()\n",
    "x_crit_g = lg_c[np.argmax(data[:,0] < (Smax_g-S0_g)/2+S0_g)]\n",
    "b_g = 1\n",
    "guesses = (S0_g, Smax_g, x_crit_g, b_g)\n",
    "\n",
    "p_opt, p_cov = opt.curve_fit(Hill_eq, lg_c.flatten(), data.flatten())\n",
    "\n",
    "ypts = Hill_eq(xpts,*p_opt)\n",
    "\n",
    "ci, pi = bu.classical_fit_intervals(Hill_eq,p_opt,lg_c,data,xpts)\n",
    "\n",
    "plt.plot(lg_c,data,'o',color='k',alpha = 0.5)\n",
    "plt.plot(xpts,ypts)\n",
    "plt.fill_between(xpts, ypts-ci, ypts+ci, color = 'C0', alpha = 0.2)\n",
    "plt.fill_between(xpts, ypts-pi, ypts+pi, color = 'C0', alpha = 0.1)\n",
    "\n",
    "Hill_params = ('S0','Smax','x_crit','Hill Coefficient')\n",
    "\n",
    "bu.classical_fit_param_summary(p_opt,p_cov, names = Hill_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you look at the confidence intervals we get from this classical approach, you should notice that the shape is not quite what we'd expect. The data is tightest at the ends of the curve, yet that's where the CI is the widest. Conversely, the middle of the curve, where the data is noisiest, has the tightest CI. This is because the classical approach only takes into account the total spread in your data, and assumes that uncertainty is shared evenly along all points of the curve. Clearly this does not reflect the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Bootstrapped confidence intervals\n",
    "The bootstrapping approach is based on random resampling of your dataset. It's based on the principle that the noise in our data is based in part on random chance, so we were just as likely to have observed a slightly different dataset than the one we did. Bootstrapping generates random subsets of your data then fits the curve to this synthetic dataset. By repeating this hundreds or thousands of times, we can get a sense of how the fit parameters vary with subtle shifts in the data.\n",
    "\n",
    "### Slightly different data\n",
    "Let's first try this with a single synthetic dataset. First we take the fit of curve to our data from above, obtaining the *residuals*, or the distance between the predicted *y*-value and the actual *y*-value(s)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Predicted values\n",
    "y_fit = Hill_eq(lg_c,*p_opt)\n",
    "# Residuals\n",
    "resid = data - y_fit "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we'll go through each *x* value and randomly choose from the residuals at that point to generate our synthetic dataset. The key here is we are \"sampling with *replacement*\", meaning we can choose the same value multiple times. We'll keep the number of data points at each *x* the same. for brevity, we'll use a __[*list comprehension*](https://www.pythonforbeginners.com/basics/list-comprehensions-in-python)__ to step through each row of our data and randomly pick from the corresponding residuals. Then we'll add these sampled residuals to our predicted *y* values to generate our synthetic dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "resid_resamples = np.array([np.random.choice(resid[row], size = resid[row].size) for row in range(n_c)])\n",
    "new_y = y_fit+resid_resamples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now `new_y` is our new, synthetic dataset. Let's fit the same curve as above and look at the new fit parameters in `p_strapped` to see how they differ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit parameters for original data:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S0</th>\n",
       "      <th>Smax</th>\n",
       "      <th>x_crit</th>\n",
       "      <th>Hill Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95% CI Lower Limit</th>\n",
       "      <td>0.343509</td>\n",
       "      <td>1.510250</td>\n",
       "      <td>-7.900033</td>\n",
       "      <td>1.941098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Optimal Value</th>\n",
       "      <td>0.314152</td>\n",
       "      <td>1.479104</td>\n",
       "      <td>-7.952710</td>\n",
       "      <td>1.478391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95% CI Upper Limit</th>\n",
       "      <td>0.284795</td>\n",
       "      <td>1.447958</td>\n",
       "      <td>-8.005388</td>\n",
       "      <td>1.015683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Standard Error</th>\n",
       "      <td>0.014978</td>\n",
       "      <td>0.015891</td>\n",
       "      <td>0.026877</td>\n",
       "      <td>0.236079</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          S0      Smax    x_crit  Hill Coefficient\n",
       "95% CI Lower Limit  0.343509  1.510250 -7.900033          1.941098\n",
       "Optimal Value       0.314152  1.479104 -7.952710          1.478391\n",
       "95% CI Upper Limit  0.284795  1.447958 -8.005388          1.015683\n",
       "Standard Error      0.014978  0.015891  0.026877          0.236079"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit parameters for synthetic (resampled) data:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S0</th>\n",
       "      <th>Smax</th>\n",
       "      <th>x_crit</th>\n",
       "      <th>Hill Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95% CI Lower Limit</th>\n",
       "      <td>0.337504</td>\n",
       "      <td>1.497111</td>\n",
       "      <td>-7.803983</td>\n",
       "      <td>1.685426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Optimal Value</th>\n",
       "      <td>0.318557</td>\n",
       "      <td>1.475082</td>\n",
       "      <td>-7.847725</td>\n",
       "      <td>1.438260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95% CI Upper Limit</th>\n",
       "      <td>0.299611</td>\n",
       "      <td>1.453054</td>\n",
       "      <td>-7.891467</td>\n",
       "      <td>1.191094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Standard Error</th>\n",
       "      <td>0.009667</td>\n",
       "      <td>0.011239</td>\n",
       "      <td>0.022318</td>\n",
       "      <td>0.126107</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          S0      Smax    x_crit  Hill Coefficient\n",
       "95% CI Lower Limit  0.337504  1.497111 -7.803983          1.685426\n",
       "Optimal Value       0.318557  1.475082 -7.847725          1.438260\n",
       "95% CI Upper Limit  0.299611  1.453054 -7.891467          1.191094\n",
       "Standard Error      0.009667  0.011239  0.022318          0.126107"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,2,figsize = (12,4))\n",
    "axs[0].plot(lg_c,data,'o',color='k',alpha = 0.5)\n",
    "axs[0].plot(xpts,Hill_eq(xpts,*p_opt))\n",
    "axs[0].fill_between(xpts, Hill_eq(xpts,*p_opt)-ci, Hill_eq(xpts,*p_opt)+ci, color = 'C0', alpha = 0.2)\n",
    "axs[0].fill_between(xpts, Hill_eq(xpts,*p_opt)-pi, Hill_eq(xpts,*p_opt)+pi, color = 'C0', alpha = 0.1)\n",
    "axs[0].set_title('Observed Data')\n",
    "print('Fit parameters for original data:')\n",
    "classical_summary = bu.classical_fit_param_summary(p_opt,p_cov, names = ('S0','Smax','x_crit','Hill Coefficient'))\n",
    "display(classical_summary)\n",
    "\n",
    "\n",
    "p_strapped, cov_strapped = opt.curve_fit(Hill_eq, lg_c.flatten(), new_y.flatten())\n",
    "curve_strapped = Hill_eq(xpts,*p_strapped)\n",
    "\n",
    "ci, pi = bu.classical_fit_intervals(Hill_eq,p_opt,lg_c,data,xpts)\n",
    "\n",
    "axs[1].plot(lg_c,new_y,'o',color='k',alpha = 0.5)\n",
    "axs[1].plot(xpts,curve_strapped)\n",
    "axs[1].fill_between(xpts, curve_strapped-ci, curve_strapped+ci, color = 'C0', alpha = 0.2)\n",
    "axs[1].fill_between(xpts, curve_strapped-pi, curve_strapped+pi, color = 'C0', alpha = 0.1)\n",
    "axs[1].set_title('Resampled Data')\n",
    "\n",
    "print('Fit parameters for synthetic (resampled) data:')\n",
    "display(bu.classical_fit_param_summary(p_strapped,cov_strapped, names = ('S0','Smax','x_crit','Hill Coefficient')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the fit parameters shifted slightly with the new dataset. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making sure synthetic data is realistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's a catch here. Some of our random choices will result in a row of \"replicates\" that are all identical. In this case, the standard deviation at this *x*-point will be zero, which will confuse the `curve_fit` algorithm as it will try to force the curve through this point exactly. Each iteration, we need to make sure we don't have any rows in `resid_resamples` that contain only a single value. We'll take a slightly roundabout way to do this as consisely as possible.\n",
    "\n",
    "First, we'll convert the row (a Numpy array) to a __[*set*](https://snakify.org/en/lessons/sets/)__. A set is simply a list that can only contain unique values. If we try to convert a list of values with duplicates into a *set*, the duplicates are discarded. Thus, by taking the *length* of a set derived from a row in our array, we can tell how many unique values that row contains. If the length of the resulting set is exactly 1, we know that row contained only a single value. We'll use python's `all` functionality to make sure that every row in `resid_resamples` has at least two unique values. In the full bootstrapping `for` loop, we'll use a `while` loop within each iteration to keep sampling the residuals until we get a sample that passes this test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The original row:\n",
      "[0.02087072 0.0130539  0.02087072 0.02087072 0.02087072 0.00433507\n",
      " 0.02087072 0.02087072 0.02087072 0.02087072]\n",
      "\n",
      "The set of unique values derived from that row:\n",
      "{0.020870715639874637, 0.013053895778806224, 0.004335072652595251}\n",
      "\n",
      "Length of that set:\n",
      "3\n",
      "\n",
      "Is that set longer than 1?\n",
      "True\n",
      "\n",
      "Is the set of unique values derived from each row longer than 1?\n",
      "[True, True, True, True, True, True, True]\n",
      "\n",
      "Do all rows contain at least two unique values?\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "print( 'The original row:' )\n",
    "print( resid_resamples[0] )\n",
    "print()\n",
    "print( 'The set of unique values derived from that row:' )\n",
    "print( set(resid_resamples[0]) )\n",
    "print()\n",
    "print( 'Length of that set:' )\n",
    "print( len(set(resid_resamples[0])) )\n",
    "print()\n",
    "print( 'Is that set longer than 1?' )\n",
    "print( len(set(resid_resamples[0])) > 1 )\n",
    "print()\n",
    "print( 'Is the set of unique values derived from each row longer than 1?' )\n",
    "print( [len(set(resid_resamples[row])) > 1 for row in range(n_c)] )\n",
    "print()\n",
    "print( 'Do all rows contain at least two unique values?' )\n",
    "print( all(len(set(resid_resamples[row])) > 1 for row in range(n_c)) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (Nearly) Every possible permutation\n",
    "\n",
    "Now for the true bootstrapping method, let's repeat this process a few hundred or thousand times and leverage the power of large numbers to get a real sense of our distributions. I'll use the `tqdm` module here (named for the Arabic word for progress), which simply provides a nice progress bar for a `for` loop when you wrap it around the iterator (here, `range`). Because we're drawing *so* many samples, bootstrapping can take a little time, so it's nice to have an idea of how long you'll have to wait for it to finish. On my machine, 10000 iterations takes about 16 seconds.\n",
    "\n",
    "Note that here it is crucial to provide initial parameter guesses to `curve_fit` each iteration for it to converge quickly. On my machine, it's nearly a *five-fold* improvement in speed: the `for` loop processes about 600 iterations per second if I provide initial guesses, compared to 120 iterations per second if I don't. Additionally, if you don't provide updated guesses based on each synthetic dataset, the fitting algorithm may fail to converge at all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████████████████████████████████████| 10000/10000 [00:42<00:00, 235.15it/s]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm                    # Use for JupyterLab or Spyder\n",
    "#from tqdm import tqdm_notebook as tqdm  # Use for classic Jupyter\n",
    "\n",
    "n_straps= 10000\n",
    "p_strapped = np.zeros([n_straps,p_opt.size])    # Create a matrix of zeros to store the parameters from each bootstrap iteration\n",
    "curve_strapped = np.zeros([n_straps,xpts.size]) # Another matrix to store the predicted curve for each iteration\n",
    "\n",
    "for i in tqdm(range(n_straps)):\n",
    "    \n",
    "    valid_sample = False\n",
    "    while not valid_sample:\n",
    "        resid_resamples = np.array([np.random.choice(resid[row],size = resid[row].size) for row in range(n_c)])\n",
    "        if all(len(set(resid_resamples[row])) > 1 for row in range(n_c)): valid_sample = True\n",
    "    \n",
    "    new_y = y_fit+resid_resamples\n",
    "    \n",
    "    S0_g = new_y.min()\n",
    "    Smax_g = new_y.max()\n",
    "    x_crit_g = lg_c[np.argmax(new_y[:,0] < (Smax_g-S0_g)/2+S0_g),0]\n",
    "    b_g = 1\n",
    "    guesses = (S0_g, Smax_g, x_crit_g, b_g)\n",
    "    \n",
    "    p_strapped[i], _ = opt.curve_fit(Hill_eq, lg_c.flatten(), new_y.flatten(), p0 = guesses)\n",
    "    curve_strapped[i] = Hill_eq(xpts,*p_strapped[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have 10000 variations on our curve fit, determining the CI for our curve is as simple as finding the appropriate percentile at each point. Here, we'll plot the true underlying curve, the original \"optimal\" fit, and the median curve from our distribution. Let's compare it to the classical CIs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "CI = 95\n",
    "\n",
    "c_lower = np.percentile(curve_strapped,(100+CI)/2,axis = 0)\n",
    "c_median = np.percentile(curve_strapped,50,axis = 0)\n",
    "c_upper = np.percentile(curve_strapped,(100-CI)/2,axis = 0)\n",
    "\n",
    "fig, axs = plt.subplots(1,2,figsize = (12,4))\n",
    "\n",
    "axs[0].plot(lg_c,data,'o',color='k',alpha = 0.5)\n",
    "axs[0].plot(xpts,Hill_eq(xpts,*p_Hill), 'k:', label = 'True Curve')\n",
    "\n",
    "median = axs[0].plot(xpts, c_median, color = 'C0', label = 'Bootstrapped Median')\n",
    "axs[0].fill_between(xpts, c_upper, c_lower, color = plt.getp(median[0],'color'), alpha = 0.25, label = '{:}% CI'.format(CI))\n",
    "axs[0].plot(xpts,Hill_eq(xpts,*p_opt), ls = '--', color = 'C1', label = '\"Optimal\" Fit')\n",
    "axs[0].legend()\n",
    "axs[0].set_title('Bootstrapped Fit and 95% CI')\n",
    "\n",
    "axs[1].plot(lg_c,data,'o',color='k',alpha = 0.5)\n",
    "axs[1].plot(xpts,Hill_eq(xpts,*p_Hill), 'k:')\n",
    "axs[1].plot(xpts,Hill_eq(xpts,*p_opt))\n",
    "axs[1].fill_between(xpts, Hill_eq(xpts,*p_opt)-ci, Hill_eq(xpts,*p_opt)+ci, color = 'C0', alpha = 0.25)\n",
    "axs[1].set_title('Classical Fit and 95% CI');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first difference you should notice is that the bootstrapped CIs follow our intuition better than the classical CIs do: the confidence interval is wide in regions with more noise in the underlying data (the middle of the curve) and narrow in regions with tightly clustered observed data. Because the classical approach assumes the same \"shape\" of the CI profile regardless of the underlying data or model, it presents us with the same narrow waist and wide extremes that it did for the simple linear fit we performed in the previous tutorial. Furthermore, the bootstrapped fit contains the true curve within the 95% CI at all points, whereas the classical CI does not, implying the bootstrapped CI is more representative. It's worth pointing out the technical definition of the 95% CI: *if you repeat the fitting procedure over and over, the CI should contain the true value 95% of the time*. Note that this is __not__ the same as saying *there's a 95% chance that the true value is within my CI*. \n",
    "\n",
    "Also, we can see that the \"optimal\" and median curves overlap more or less exactly in our bootstrapped model. Our 95% CI is also notably asymmetrical in *x* around the median value. This is the power of the bootstrap method: it makes no assumptions about your data and so can detect when slight variations have asymmetrical impacts on the fit.\n",
    "\n",
    "Let's look at the 95% CIs on our parameter values as well and see how they compare to the classical method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classical fit parameter intervals:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S0</th>\n",
       "      <th>Smax</th>\n",
       "      <th>x_crit</th>\n",
       "      <th>Hill Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95% CI Lower Limit</th>\n",
       "      <td>0.343509</td>\n",
       "      <td>1.510250</td>\n",
       "      <td>-7.900033</td>\n",
       "      <td>1.941098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Optimal Value</th>\n",
       "      <td>0.314152</td>\n",
       "      <td>1.479104</td>\n",
       "      <td>-7.952710</td>\n",
       "      <td>1.478391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95% CI Upper Limit</th>\n",
       "      <td>0.284795</td>\n",
       "      <td>1.447958</td>\n",
       "      <td>-8.005388</td>\n",
       "      <td>1.015683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Standard Error</th>\n",
       "      <td>0.014978</td>\n",
       "      <td>0.015891</td>\n",
       "      <td>0.026877</td>\n",
       "      <td>0.236079</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          S0      Smax    x_crit  Hill Coefficient\n",
       "95% CI Lower Limit  0.343509  1.510250 -7.900033          1.941098\n",
       "Optimal Value       0.314152  1.479104 -7.952710          1.478391\n",
       "95% CI Upper Limit  0.284795  1.447958 -8.005388          1.015683\n",
       "Standard Error      0.014978  0.015891  0.026877          0.236079"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Bootstrapped fit parameter intervals:\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
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       "        vertical-align: top;\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S0</th>\n",
       "      <th>Smax</th>\n",
       "      <th>x_crit</th>\n",
       "      <th>Hill Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95% CI Lower Limit</th>\n",
       "      <td>0.304745</td>\n",
       "      <td>1.466923</td>\n",
       "      <td>-8.064169</td>\n",
       "      <td>1.300664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Median Value</th>\n",
       "      <td>0.314249</td>\n",
       "      <td>1.478735</td>\n",
       "      <td>-7.953472</td>\n",
       "      <td>1.501864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95% CI Upper Limit</th>\n",
       "      <td>0.325011</td>\n",
       "      <td>1.489143</td>\n",
       "      <td>-7.852754</td>\n",
       "      <td>1.827931</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          S0      Smax    x_crit  Hill Coefficient\n",
       "95% CI Lower Limit  0.304745  1.466923 -8.064169          1.300664\n",
       "Median Value        0.314249  1.478735 -7.953472          1.501864\n",
       "95% CI Upper Limit  0.325011  1.489143 -7.852754          1.827931"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_upper = np.percentile(p_strapped,(100+CI)/2,axis = 0)\n",
    "p_median = np.percentile(p_strapped,50,axis = 0)\n",
    "p_lower = np.percentile(p_strapped,(100-CI)/2,axis = 0)\n",
    "\n",
    "boot_summary = pd.DataFrame(data = [p_lower,p_median,p_upper],\n",
    "                            index = ('{:}% CI Lower Limit'.format(CI),'Median Value','{:}% CI Upper Limit'.format(CI)),\n",
    "                            columns = Hill_params)\n",
    "print('Classical fit parameter intervals:')\n",
    "display(classical_summary)\n",
    "print()\n",
    "print('Bootstrapped fit parameter intervals:')\n",
    "display(boot_summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, pay attention to the symmetry (or lack thereof) in the fit intervals about the median. The median of the Hill Coefficienct is much closer to the 2.5%ile than the 97.5%ile.\n",
    "\n",
    "We can even take this a step further. We have 10000 data points representing reasonable values for each parameter, allowing us to visualize the entire distribution. We'll use the `seaborn` library to help us here, because it contains functions that make it easy to view distributions. In particular, the `distplot` function shows us a histogram with a *Kernel Density Estimate* (KDE) overlain on top. KDEs circumvent many of the problems posed by histograms, as explained __[here](https://seaborn.pydata.org/tutorial/distributions.html)__. Among other advantages, it allows us to get a robust modal value for our paramter (maximum of the KDE). The choice between whether the modal or median value of a paramater is more representative is largely philosophical and will likely depend on the use case, but they differ signifiantly only for highly skewed distributions, and both are less sensitive to outliers than the mean. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x216 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "_,n_p = p_strapped.shape\n",
    "mode = np.zeros([n_p,])\n",
    "\n",
    "fig, axs = plt.subplots(1, n_p, figsize = (4*n_p,3))\n",
    "for p in range(n_p):\n",
    "    param = p_strapped[:,p]\n",
    "    valid_param = param[~np.isnan(param)]\n",
    "    sns.distplot(valid_param, ax = axs[p])\n",
    "    axs[p].axvline(np.percentile(valid_param, (100-CI)/2, axis = 0), ls = '--', color = 'k')\n",
    "    axs[p].axvline(np.percentile(valid_param, 50, axis = 0), ls = ':', color = 'k')\n",
    "    axs[p].axvline(np.percentile(valid_param, (100+CI)/2, axis = 0), ls = '--', color = 'k')\n",
    "\n",
    "    KDE = axs[p].get_children()[-14]\n",
    "    mode[p] = KDE.get_xdata()[np.argmax(KDE.get_ydata())]\n",
    "\n",
    "    axs[p].set_title(Hill_params[p] + '\\n' + 'mode = {:.3f}'.format(mode[p]))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A bit of Bayes\n",
    "\n",
    "A downside of the classical nonparametric resampling performed above is that some of the bootstrapped data can be quite artificial. Since we are sampling with replacement, roughly a third of our data points (specifically, $(1-1/n)^n \\rightarrow e^{-1}$) will be absent from each bootstrapped collection. Doing this 10,000 times, it's not unreasonable that some of the collections contain data from only one *x* value, leading to weird outliers in our parameter values. We can address this and give our bootstrap __[a more Bayesian flavor](http://www.sumsar.net/blog/2015/04/the-non-parametric-bootstrap-as-a-bayesian-model/)__ by giving random *weights* to the data points (drawn from a Dirichlet prior via a Gamma distribution). In essense that's what we were doing anyways, but with the classical bootstrap the weights are discrete (0,1,2,3, etc) with a reasonable likelihood of assigning 0. In the Bayesian bootstrap, the weights are continuous and there's no possibility of assigning 0 weight. To implement this, we skip the resampling and just generate weights for `curve_fit` to use. Note that the `sigma` input to `curve_fit` is uncertainty, the inverse of weight, so we have to invert the weights. Each iteration would now look like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "wts = np.random.gamma(1,1,size = new_y.flatten().size)\n",
    "wts /= sum(wts)\n",
    "p_strapped[i], _ = opt.curve_fit(\n",
    "    Hill_eq, lg_c.flatten(), new_y.flatten(),\n",
    "    p0 = guesses,\n",
    "    sigma = 1/wts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Portable functions\n",
    "Finally, let's wrap all of these operations into flexible functions that we can use for any curve. We'll let the bootstrapping function itself be flexible to different input sizes and shapes (replicating and reshaping the *x* or *y* data appropriately), different methods of determining initial guesses from each synthetic dataset, as well as different approaches to the resampling itself. The approach outlined above is one that I would consider *conservative* or *non-parametric*, becuase it only samples directly from the observed data, and *piecewise* or *local*, becuase it only chooses new residuals at each *x* from the residuals actually observed at that *x*. Other approaches, which I would term *non-conservative* or *parametric*, fit a normal distribution to the residuals, then sample that normal distribution. Additionally, others choose new residuals from the total pool of residuals observed anywhere along the curve. This *non-piecewise* or *global* approach is ideal if you have only one *y* for every *x*, e.g. time-series or spectral data, in which case the piecewise approach would be non-sensical."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "import scipy.optimize as opt\n",
    "import seaborn as sns\n",
    "from tqdm import tqdm#_notebook as tqdm\n",
    "\n",
    "# Performing the bootstrap algorithm\n",
    "def bootstrap_fits(func, x, y, n_straps = 1000, res = 100, xpts = None, guess_gen = None,\n",
    "                 fit_kws = {}, parametric = False, piecewise = True, bayes = True):\n",
    "    # If y is a vector of length 'm', x must also be a vector of length 'm'\n",
    "    # If y is a matrix of shape 'm x n', with replicates in different columns, x must either be a vector of length 'm' or a matrix of shape 'm x n'\n",
    "\n",
    "    # Resampling approaches:\n",
    "    def pw_not_pm(data):\n",
    "        m,n = data.shape\n",
    "        valid_sample = False\n",
    "        while not valid_sample:\n",
    "            resamples = np.array([np.random.choice(data[row],size = n) for row in range(m)])\n",
    "            if all(len(set(resamples[row])) > 1 for row in range(m)): valid_sample = True\n",
    "        return resamples\n",
    "    def pw_and_pm(data):\n",
    "        m,n = data.shape\n",
    "        sigma = [data[row].std() for row in range(m)]\n",
    "        return np.array([np.random.normal(0, sigma[row], size = n) for row in range(m)])\n",
    "    def pm_not_pw(data):\n",
    "        sigma = data.std()\n",
    "        return np.random.normal(0, sigma, size = data.shape)\n",
    "    def not_pm_nor_pw(data):\n",
    "        return np.random.choice(data.flat, size = data.shape)    \n",
    "    \n",
    "    def resample(data, piecewise, parametric):\n",
    "        return {(True,False)  : pw_not_pm,\n",
    "                (True,True)   : pw_and_pm,\n",
    "                (False,True)  : pm_not_pw,\n",
    "                (False,False) : not_pm_nor_pw}[piecewise, parametric](data)\n",
    "        \n",
    "    # Number of unique x values\n",
    "    n = len(set(x.flatten()))\n",
    "\n",
    "    # Number of replicates\n",
    "    m = y.size//n\n",
    "    \n",
    "    if y.ndim == 1:\n",
    "        # Piecewise bootstrapping is nonsensical if there's only one y per x\n",
    "        piecewise = False\n",
    "    elif x.ndim == 1:\n",
    "        # If x is 1D while y is not, tile it so it is\n",
    "        x = np.tile(x,[m,1]).T\n",
    "\n",
    "    # Generate points at which to evaluate the curves\n",
    "    if xpts is None: xpts = np.linspace(x.min(),x.max(),res)\n",
    "    elif xpts.size == 2: xpts = np.linspace(xpts[0],xpts[1],res)\n",
    "\n",
    "    if guess_gen is not None:\n",
    "        # Generate guesses for this dataset\n",
    "        guesses = guess_gen(x,y)\n",
    "    else:\n",
    "        # Default guesses\n",
    "        guesses = None\n",
    "        \n",
    "    # Predict y values\n",
    "    p_opt, _ = opt.curve_fit(\n",
    "        func, x.flatten(), y.flatten(),\n",
    "        p0 = guesses,\n",
    "        **fit_kws) \n",
    "    y_fit = func(x,*p_opt)\n",
    "\n",
    "    # Get the residuals\n",
    "    resid = y - y_fit\n",
    "\n",
    "    p_strapped = np.zeros([n_straps,p_opt.size])    # Create a matrix of zeros to store the parameters from each bootstrap iteration\n",
    "    curve_strapped = np.zeros([n_straps,xpts.size]) # Another matrix to store the predicted curve for each iteration\n",
    "\n",
    "    for i in tqdm(range(n_straps)):\n",
    "        valid_fit = False\n",
    "        while valid_fit is False:\n",
    "            if not bayes:\n",
    "                # Choose new residuals based on the specified method\n",
    "                resid_resamples = resample(resid, piecewise, parametric)\n",
    "        \n",
    "                # Generate a synthetic dataset from the sampled residuals\n",
    "                new_y = y_fit+resid_resamples\n",
    "        \n",
    "                if guess_gen is not None:\n",
    "                    # Generate guesses for this dataset\n",
    "                    guesses = guess_gen(x,new_y)\n",
    "                else:\n",
    "                    # Default guesses\n",
    "                    guesses = np.ones(len(p_opt))\n",
    "        \n",
    "                # Additional keyword arguments to curve_fit can be passed as a dictionary via fit_kws\n",
    "                try:\n",
    "                    p_strapped[i], _ = opt.curve_fit(\n",
    "                        func, x.flatten(), new_y.flatten(),\n",
    "                        p0 = guesses,\n",
    "                        **fit_kws)\n",
    "                except RuntimeError: continue\n",
    "                else: valid_fit = True\n",
    "                \n",
    "            else:\n",
    "                # For a Bayesian flavor, give weights to each data point drawn from a gamma-distributed prior\n",
    "                wts = np.random.gamma(1,1,size = y.size)\n",
    "                wts /= sum(wts)\n",
    "                try:\n",
    "                    p_strapped[i], _ = opt.curve_fit(\n",
    "                        func, x.flatten(), y.flatten(),\n",
    "                        p0 = guesses,\n",
    "                        sigma = 1/wts,\n",
    "                        **fit_kws)    \n",
    "                except RuntimeError: continue\n",
    "                else: valid_fit = True        \n",
    "            \n",
    "        curve_strapped[i] = func(xpts,*p_strapped[i])\n",
    "\n",
    "    return p_strapped, curve_strapped\n",
    "\n",
    "# Plot the bootstrapped curve and its confidence intervals\n",
    "def bootstrap_plot(xpts,bootstrap_curves, CI = 95, line_kws ={},fill_kws={}):\n",
    "    c_lower = np.percentile(bootstrap_curves,(100-CI)/2,axis = 0)\n",
    "    c_median = np.percentile(bootstrap_curves,50,axis = 0)\n",
    "    c_upper = np.percentile(bootstrap_curves,(100+CI)/2,axis = 0)\n",
    "\n",
    "    # Additional keyword arguments to plot or fill_between can be passed as a dictionary via line_kws and fill_kws, respectively\n",
    "    med = plt.plot(xpts, c_median, **line_kws)\n",
    "    if 'alpha' not in fill_kws.keys(): fill_kws['alpha'] = 0.25\n",
    "    ci = plt.fill_between(xpts, c_upper, c_lower, color = plt.getp(med[0],'color'), **fill_kws)\n",
    "    return med, ci\n",
    "\n",
    "# Summarize parameters and confidence intervals resulting from the bootstrap algorithm\n",
    "def bootstrap_summary(bootstrap_params, CI = 95, names = None):\n",
    "    p_lower = np.percentile(bootstrap_params,(100-CI)/2,axis = 0)\n",
    "    p_median = np.percentile(bootstrap_params,50,axis = 0)\n",
    "    p_upper = np.percentile(bootstrap_params,(100+CI)/2,axis = 0)\n",
    "\n",
    "    summary = pd.DataFrame(data = [p_lower,p_median,p_upper],\n",
    "                       index = ('{:}% CI Lower Limit'.format(CI),'Median Value','{:}% CI Upper Limit'.format(CI)),\n",
    "                       columns = names)\n",
    "    return summary\n",
    "\n",
    "# Plot the bootstrapped distributions for each parameter and label with the modal value derived from its KDE\n",
    "def bootstrap_dists(bootstrap_params, CI = 95, names = None, rug_kws = {}, kde_kws = {}):\n",
    "    _,n_p = bootstrap_params.shape\n",
    "    mode = np.zeros([n_p,])\n",
    "    \n",
    "    fig, axs = plt.subplots(1, n_p, figsize = (4*n_p,3))\n",
    "    for p in range(n_p):\n",
    "        sns.distplot(bootstrap_params[:,p], ax = axs[p], **rug_kws, **kde_kws)\n",
    "        axs[p].axvline(np.percentile(bootstrap_params[:,p], (100-CI)/2, axis = 0), ls = '--', color = 'k')\n",
    "        axs[p].axvline(np.percentile(bootstrap_params[:,p], 50, axis = 0), ls = ':', color = 'k')\n",
    "        axs[p].axvline(np.percentile(bootstrap_params[:,p], (100+CI)/2, axis = 0), ls = '--', color = 'k')\n",
    "\n",
    "        KDE = axs_[p].lines[0]\n",
    "        mode[p] = KDE.get_xdata()[np.argmax(KDE.get_ydata())]\n",
    "        \n",
    "        axs[p].set_title(names[p] + '\\n' + 'mode = {:.3f}'.format(mode[p]))\n",
    "        \n",
    "    return fig, axs, mode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define our \"guess generator\" and then run the bootstrap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Hill_guesses(x,y):\n",
    "    x = x.flatten()\n",
    "    y = y.flatten()\n",
    "    S0_g = y.min()\n",
    "    Smax_g = y.max()\n",
    "    x_crit_g = x[np.argmax(y < (Smax_g-S0_g)/2+S0_g)]\n",
    "    b_g = 1\n",
    "    return (S0_g, Smax_g, x_crit_g, b_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████████████████████████████████████| 10000/10000 [01:02<00:00, 159.89it/s]\n"
     ]
    }
   ],
   "source": [
    "p_strapped, curve_strapped = bootstrap_fits(Hill_eq, lg_c, data, n_straps = 10000, guess_gen = Hill_guesses, bayes = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x216 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lg_c,data,'o',color='k',alpha = 0.5)\n",
    "\n",
    "bootstrap_plot(xpts,curve_strapped);\n",
    "bootstrap_dists(p_strapped, names = ('S0','Smax','x_crit','Hill Coefficient'));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S0</th>\n",
       "      <th>Smax</th>\n",
       "      <th>x_crit</th>\n",
       "      <th>Hill Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95% CI Lower Limit</th>\n",
       "      <td>0.304701</td>\n",
       "      <td>1.467337</td>\n",
       "      <td>-8.061434</td>\n",
       "      <td>1.302110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Median Value</th>\n",
       "      <td>0.314220</td>\n",
       "      <td>1.478847</td>\n",
       "      <td>-7.952036</td>\n",
       "      <td>1.500095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95% CI Upper Limit</th>\n",
       "      <td>0.324622</td>\n",
       "      <td>1.489376</td>\n",
       "      <td>-7.852841</td>\n",
       "      <td>1.811520</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          S0      Smax    x_crit  Hill Coefficient\n",
       "95% CI Lower Limit  0.304701  1.467337 -8.061434          1.302110\n",
       "Median Value        0.314220  1.478847 -7.952036          1.500095\n",
       "95% CI Upper Limit  0.324622  1.489376 -7.852841          1.811520"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(bootstrap_summary(p_strapped, names = ('S0','Smax','x_crit','Hill Coefficient')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Better CI placement\n",
    "The 95% CIs we used above spanned the natural range between the 2.5th %ile and the 97.5th %ile, but that may not always be an ideal placement. If your data is highly skewed, say with a long tail extending out to the right, the confidence interval should probably be shifted to reflect the asymmetric confidence. The rigorous way to do this is with what's known as Bias-Corrected and Accelerated (BCa) confidence intervals.\n",
    "\n",
    "I won't pretend to understand the math behind this, look __[here](https://www.webpages.uidaho.edu/~chrisw/stat514/bootstrapcimethods1.pdf)__ for the equations involved and __[here](https://github.com/cgevans/scikits-bootstrap/blob/master/scikits/bootstrap/bootstrap.py)__ for an implementation in Python. As far as I understand, the technique first estimates the skewness in the data with a *jackknife*, an approach similar to the bootstrap but, rather than take an arbitrary number of random subsamples, it systematically recomputes the parameter of interest by successively leaving out one data point at a time. The *acceleration* factor compares the mean of these values to the overall mean and corrects for this bias in conjunction with quantiles from the normal distribution. So, without further explanation, here's a function to calculate BCa intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bootstrap_bca(func, x, y, bootstrap_params, CI=95, names = None, guess_gen = None, fit_kwargs = {}):\n",
    "    from scipy.special import erfinv\n",
    "    from scipy.special import erf\n",
    "    import warnings\n",
    "\n",
    "    def norm_cdf(x):\n",
    "        return 0.5*(1+erf(x/2**0.5))\n",
    "    \n",
    "    def norm_ppf(x):\n",
    "        return 2**0.5 * erfinv(2*x-1)\n",
    "    \n",
    "    def jackknife(data):\n",
    "        \"\"\"\n",
    "    Given data points data, where axis 0 is considered to delineate points, return\n",
    "    a list of arrays where each array is a set of jackknife indexes.\n",
    "    For a given set of data Y, the jackknife sample J[i] is defined as the data set\n",
    "    Y with the ith data point deleted.\n",
    "        \"\"\"\n",
    "        base = np.arange(0,len(data))\n",
    "        return (np.delete(base,i) for i in base)\n",
    "    \n",
    "    x = x.flatten()\n",
    "    y = y.flatten()\n",
    "    \n",
    "    straps,n_p = bootstrap_params.shape\n",
    "    \n",
    "    if guess_gen is not None:\n",
    "        guesses = guess_gen(x,y)\n",
    "    else:\n",
    "        guesses = None\n",
    "    \n",
    "    p_opt,_ = opt.curve_fit(func,x,y, p0=guesses, **fit_kwargs)\n",
    "    \n",
    "    z0 = norm_ppf( 1.0*np.sum(bootstrap_params < p_opt, axis=0)  / straps )\n",
    "    \n",
    "    idx_jack = jackknife(y)\n",
    "    p_jack = np.array([opt.curve_fit(func,x[idx],y[idx], p0=guesses, **fit_kwargs)[0] for idx in idx_jack])\n",
    "    p_jmean = np.mean(p_jack,axis=0)\n",
    "    \n",
    "    \n",
    "    # Acceleration value\n",
    "    a = np.sum((p_jmean - p_jack)**3, axis=0) / (\n",
    "        6.0 * np.sum((p_jmean - p_jack)**2, axis=0)**1.5)\n",
    "    \n",
    "    alphas = np.array([100-CI,100+CI])/200.\n",
    "    \n",
    "    zs = z0 + norm_ppf(alphas)[:,np.newaxis]\n",
    "    \n",
    "    avals = norm_cdf(z0 + zs/(1-a*zs))\n",
    "    \n",
    "    nvals = np.round((straps-1)*avals)\n",
    "    \n",
    "    if np.any(np.isnan(avals)):\n",
    "        warnings.warn(\"Some values were NaN; results are probably unstable \" +\n",
    "                      \"(all values were probably equal)\",\n",
    "                      stacklevel=2)\n",
    "        return\n",
    "    if np.any(nvals == 0) or np.any(nvals == straps-1):\n",
    "        warnings.warn(\"Some values used extremal samples; \" +\n",
    "                      \"results are probably unstable.\",\n",
    "                      stacklevel=2)\n",
    "        return\n",
    "    elif np.any(nvals < 10) or np.any(nvals >= straps-10):\n",
    "        warnings.warn(\"Some values used top 10 low/high samples; \" +\n",
    "                      \"results may be unstable.\",\n",
    "                      stacklevel=2)\n",
    "    \n",
    "    p_lower, p_median, p_upper = [np.zeros(n_p) for _ in range(3)]\n",
    "    \n",
    "    avals *= 100\n",
    "    \n",
    "    for p in range(n_p):\n",
    "        p_lower[p] = np.percentile(bootstrap_params[:,p],avals[0,p])\n",
    "        p_median[p] = np.percentile(bootstrap_params[:,p],50)\n",
    "        p_upper[p] = np.percentile(bootstrap_params[:,p],avals[1,p])\n",
    "        \n",
    "    summary = pd.DataFrame(data = [p_lower,p_median,p_upper],\n",
    "                        index = ('{:}% CI Lower Limit'.format(CI),\n",
    "                                 'Median Value',\n",
    "                                 '{:}% CI Upper Limit'.format(CI)),\n",
    "                        columns = names)\n",
    "    \n",
    "    return summary, avals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BCa percentile intervals:\n",
      "[[ 2.49070631  2.22573319  1.9796777   0.843539  ]\n",
      " [97.49041678 97.23933603 96.91997574 94.06280921]]\n",
      "\n",
      "BCa CIs:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S0</th>\n",
       "      <th>Smax</th>\n",
       "      <th>x_crit</th>\n",
       "      <th>Hill Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95% CI Lower Limit</th>\n",
       "      <td>0.304697</td>\n",
       "      <td>1.467093</td>\n",
       "      <td>-8.065814</td>\n",
       "      <td>1.267062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Median Value</th>\n",
       "      <td>0.314220</td>\n",
       "      <td>1.478847</td>\n",
       "      <td>-7.952036</td>\n",
       "      <td>1.500095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95% CI Upper Limit</th>\n",
       "      <td>0.324617</td>\n",
       "      <td>1.489122</td>\n",
       "      <td>-7.856449</td>\n",
       "      <td>1.736512</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          S0      Smax    x_crit  Hill Coefficient\n",
       "95% CI Lower Limit  0.304697  1.467093 -8.065814          1.267062\n",
       "Median Value        0.314220  1.478847 -7.952036          1.500095\n",
       "95% CI Upper Limit  0.324617  1.489122 -7.856449          1.736512"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Standard CIs:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S0</th>\n",
       "      <th>Smax</th>\n",
       "      <th>x_crit</th>\n",
       "      <th>Hill Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>95% CI Lower Limit</th>\n",
       "      <td>0.304701</td>\n",
       "      <td>1.467337</td>\n",
       "      <td>-8.061434</td>\n",
       "      <td>1.302110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Median Value</th>\n",
       "      <td>0.314220</td>\n",
       "      <td>1.478847</td>\n",
       "      <td>-7.952036</td>\n",
       "      <td>1.500095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95% CI Upper Limit</th>\n",
       "      <td>0.324622</td>\n",
       "      <td>1.489376</td>\n",
       "      <td>-7.852841</td>\n",
       "      <td>1.811520</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          S0      Smax    x_crit  Hill Coefficient\n",
       "95% CI Lower Limit  0.304701  1.467337 -8.061434          1.302110\n",
       "Median Value        0.314220  1.478847 -7.952036          1.500095\n",
       "95% CI Upper Limit  0.324622  1.489376 -7.852841          1.811520"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary, avals = bootstrap_bca(Hill_eq, lg_c, data, p_strapped, guess_gen = Hill_guesses, names = ('S0','Smax','x_crit','Hill Coefficient'))\n",
    "print('BCa percentile intervals:')\n",
    "print(avals)\n",
    "print()\n",
    "print('BCa CIs:')\n",
    "display(summary)\n",
    "print()\n",
    "print('Standard CIs:')\n",
    "display(bootstrap_summary(p_strapped, names = ('S0','Smax','x_crit','Hill Coefficient')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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