{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
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"iopub.status.busy": "2021-11-16T10:24:48.031306Z",
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"shell.execute_reply": "2021-11-16T10:24:49.019251Z"
},
"slideshow": {
"slide_type": "slide"
},
"tags": [
"hide_input",
"hide_output"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" \n",
" \n",
" >\n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"### BEGIN hide_toggle\n",
"### Update 30/10-'20\n",
"def hide_toggle_code(off=0):\n",
" \"\"\"This function generates HTML code to toggle the display of an input\n",
" cell.\n",
" \n",
" The output of the cell will still be displayed. This can be used\n",
" to hide (from immediate view) some code to generate data or the\n",
" like. It can also be used to hide other notebook explicit\n",
" implementations - e.g., C++ processing, or the like.\n",
" \n",
" Note, calling this function alone will not enable toggling.\n",
" Instead, we must wrap the generated code in an\n",
" `IPython.display.HTML` object and return that as the cell value.\n",
" This will let IPython evaluate the HTML code and pass it on to the\n",
" browser.\n",
" \n",
" If all one wants is to toggle a cell one can use the function\n",
" `hide_toggle` below. However, we can also combine the code\n",
" generated here with other HTML code - for example _style_\n",
" declarations and pass that along embedded in an HTML object.\n",
" \n",
" Parameters\n",
" ----------\n",
" off : int \n",
" Offset of cell to hide relative to the cell calling this function \n",
" \n",
" Returns\n",
" -------\n",
" code : str \n",
" HTML code to enable toggling of the cell\n",
"\n",
" \"\"\"\n",
" from random import randint \n",
" from IPython.display import HTML \n",
" \n",
" jp_cell = 'document.getElementsByClassName(\"jp-Cell jp-mod-selected\")[0]'\n",
" jq_cell = '$(\"div.cell.code_cell.rendered.selected\")'\n",
" toggle_text = 'Please close'\n",
" cell_id = str(randint(1,2**64))\n",
" func_name = f'code_toggle_{cell_id}'\n",
" \n",
" scr1 = f'''\n",
" \n",
" '''\n",
" but = f'''\n",
" \n",
" >\n",
" \n",
" '''\n",
" scr2 = f'''\n",
" \n",
" '''\n",
" return scr1+but+scr2 \n",
"\n",
"def hide_toggle(off=0,cnt=None):\n",
" \"\"\"This will wrap the HTML code returned from the above function\n",
" in an `IPython.display.HTML` object so that the notebook will \n",
" evaluate the HTML code. \n",
" \n",
" This function is what we will use most of the time. However, \n",
" the function `hide_toggle_code` can be combined with other code \n",
" and then be put into an HTML object to let the notebook evaluate\n",
" all the code. \n",
"\n",
" Parameters \n",
" ----------\n",
" off : int \n",
" Cell offset relative to calling cell which we should toggle \n",
" cnt : int or None \n",
" If not None, set the execution count to this number \n",
" (currently broken)\n",
" \n",
" Returns\n",
" -------\n",
" object : IPython.display.HTML \n",
" HTML object wrapping code to toggle cell \n",
" \"\"\"\n",
" from IPython.display import HTML\n",
" if cnt is not None:\n",
" get_ipython().execution_count = cnt\n",
" return HTML(hide_toggle_code(off))\n",
"### END hide_toggle\n",
"\n",
"\n",
"### BEGIN setup_matplotlib\n",
"### Update 30/10-'20\n",
"def _setup_matplotlib():\n",
" \"\"\"Set-up Matplotlib parameters. \n",
" \n",
" We specify that we want both PDF and PNG images, and \n",
" that the default image size should be 8 by 8 inches \n",
" \n",
" We also disable warnings about too many open figures \n",
" \"\"\"\n",
" %matplotlib inline \n",
" from matplotlib import rcParams \n",
" \n",
" rcParams['figure.max_open_warning'] = 0\n",
" rcParams['font.serif'] = ['Palatino'] + rcParams['font.serif']\n",
" rcParams['font.family'] = ['serif']\n",
" rcParams['mathtext.fontset'] = 'dejavuserif'\n",
" rcParams['axes.formatter.use_mathtext'] = True\n",
"\n",
" f = None\n",
" try:\n",
" # IPython >= 7.23 depcrates set_matplotlib_formats\n",
" from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
" f = set_matplotlib_formats\n",
" \n",
" except Exception as e:\n",
" try:\n",
" from IPython.display import set_matplotlib_formats\n",
" f = set_matplotlib_formats\n",
" except Exception as e:\n",
" pass \n",
"\n",
" if f is not None:\n",
" set_matplotlib_formats('png','pdf')\n",
" \n",
"_setup_matplotlib()\n",
"### END setup_matplotlib\n",
"_setup_matplotlib()\n",
"\n",
"### BEGIN css_styling\n",
"### Update 30/10-'20\n",
"def css_styling_code():\n",
" \"\"\"This function returns HTML code to customize the CSS \n",
" of the notebook \n",
" \n",
" - The text font to be Palatino (serif)\n",
" - Headers are oblique (italic)\n",
" - Extra spacing below H1 headers \n",
" - Extra spacing spacing above H1 headers \n",
" - Headers have larger fonts, and is set in normal weight\n",
" - Remove padding around code cells \n",
" - Code uses the fint \"Source Code Pro\" (or monospace)\n",
" - Code background is changed to light yellow \n",
" - Output background is set to lavender\n",
" \n",
" The function combines these CSS declarations with the HTML \n",
" code from `hide_toggle_code` above so what we automatically \n",
" hide this code from the user. \n",
" \"\"\"\n",
" styles = '''\n",
" \n",
" \n",
" '''\n",
" return styles\n",
"\n",
"def css_styling():\n",
" from IPython.display import HTML \n",
" \n",
" return HTML(hide_toggle_code()+css_styling_code())\n",
"### END css_styling\n",
"css_styling()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
},
"tags": [
"title"
]
},
"source": [
"### Christian Holm Christensen \n",
"\n",
"# Bootstrap \n",
"## Estimate statistical uncertainties \n",
"## Version 0.1 - May 2019 (English)\n",
"\n",
"> Bootstrapping is a method to estimate the statistical uncertainty of some quantity when \n",
"> straight-forward error propagation is not feasible. In this note, we will investigate the \n",
"> technique of bootstrapping through example using Python\n",
">\n",
"> This document is available in many formats at https://cholmcc.gitlab.io/nbi-python\n",
"\n",
"\n",
"### Niels Bohr Institutet "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"toc": false
},
"source": []
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Introduction\n",
"\n",
"The technique of bootstrapping is a way to estimate the _statistical uncertainty_ of some quantity. It is most often used when the variance of the quantity (or more formally _estimator_) is not feasible to calculate directly from the data. Some examples are \n",
"\n",
"- The median of a variable \n",
"- Correlation coefficient between two variables \n",
"\n",
"or more complicated quantities such as the azimuthal anisotropic flow calculated from so-called $Q$-cumulants (see f.eks. [here](http://gitlab.com/cholmcc/mcorrelations)). That is, if we are estimating a simple quantity like the mean of a sample, we would _not_ use the bootstrap method, since the variance of the mean \n",
"\n",
"$$\\operatorname{Var}[\\bar{x}] = \\frac{\\operatorname{Var}[x]}{N}\\quad,$$\n",
"\n",
"with sample size $N$, is easily computed from the sample directly. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# The method\n",
"\n",
"The method of bootstrapping was invented by Bradly Efron (see for example L.Wasserman [All of Statistics](http://www.stat.cmu.edu/~larry/all-of-statistics/), Chapter 8), goes roughly like this \n",
"\n",
"- Suppose we are interested in the quantity $T$ calculated over the data $X$ (more formally, \n",
" $T$ is a _statistics_). We estimate $T$ via the estimator $\\hat{T}$ over the sample \n",
" $X_1,X_2,\\ldots X_N$, of size $N$. We are interested in estimating the variance $\\operatorname{Var}(T(X))$ \n",
"- First, estimate the $T$ over our sample $X$\n",
"- Secondly, for some number of iterations $B$, do \n",
" - Select, at random _with_ replacement, $N$ samples from the original sample \n",
" - Calculate the estimate $T$ over this sample \n",
"- Finally, calculate the variance of $T$ estimated over the $B$ generated samples. \n",
"\n",
"The underlying reasoning hinges on the law of large numbers, which says that for sufficiently large number of independent identitical distributed variable the distribution will tend to a normal distribution. Thus, by making $B$ (a large number) of simulations, we can approximate the original estimator variance by the variance of the simulations. \n",
"\n",
"Each simulation is performed by sampling the original sample $X_1,X_2,\\ldots,X_N$ exactly $N$ times with replacement. By _with replacement_ we mean that the probability to draw $X_i$ is exactly $1/N$ for all $N$ samples in the simulation. Thus, in our simulation sample the multiplicty of any $X_i$ is anywhere from 0 to N. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Implementation "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"We can implement a general solution to the bootstrap method in Python. The first thing we need is the ability to make our simulation samples. Here, we can use the standard function `random.choices`. To see this, let us pick as the sample the numbers between 0 and 9 (inclusive), and make some simulation samples "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.039122Z",
"iopub.status.busy": "2021-11-16T10:24:49.025219Z",
"iopub.status.idle": "2021-11-16T10:24:49.043321Z",
"shell.execute_reply": "2021-11-16T10:24:49.044017Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[8, 7, 0, 1, 0, 6, 0, 2, 1, 2]\n",
"[4, 1, 0, 9, 3, 6, 3, 8, 7, 4]\n",
"[4, 8, 5, 5, 8, 0, 7, 0, 5, 0]\n",
"[8, 7, 5, 4, 7, 3, 3, 2, 1, 8]\n",
"[2, 2, 1, 9, 4, 3, 9, 0, 4, 1]\n"
]
}
],
"source": [
"import random \n",
"random.seed(123456)\n",
"data = list(range(10))\n",
"for _ in range(5):\n",
" print(random.choices(data,k=len(data)))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Secondly, our solution will need to accept some estimator function $\\hat T$ to operator on our simulation samples. We will simple take that as an argument in form of a callable. The final input to our solution in the choice of number of simulations $B$. Since we may want to calculate other statistics than the variance on our bootstrap sample, we will return the entire list of $B$ estimates of $T$ over all simulations. Thus, our solution becomes "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.053832Z",
"iopub.status.busy": "2021-11-16T10:24:49.052905Z",
"iopub.status.idle": "2021-11-16T10:24:49.055976Z",
"shell.execute_reply": "2021-11-16T10:24:49.056714Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"def bootstrap(data,estimator,size=1000,*args):\n",
" \"\"\"Perform the bootstrap simulation run. \n",
" \n",
" Parameters\n",
" ----------\n",
" data : \n",
" The data to analyse. This can be any indexable object. That is, we must be \n",
" able to do\n",
" \n",
" >>> v = data[i]\n",
" \n",
" estimator : callable \n",
" This function is evaluated over data (with the same type as the data argument) \n",
" repeatedly to calculate the estimator on the bootstrap simulation. It must\n",
" accept a single argument of the same type as data. Additional arguments can \n",
" be passed in the args argument. \n",
" size : int, positive \n",
" The number of bootstrap simulations. This number should be large (>1000). \n",
" *args : dict \n",
" Additional arguments to pass to estimator function \n",
" \n",
" Returns\n",
" -------\n",
" value : generator\n",
" The estimator function evaluated over size bootstrap simulations. One can \n",
" calculate the variance of this list to get the estimate of the estimator \n",
" variance \n",
" \"\"\"\n",
" from random import choices \n",
" \n",
" def _inner(data,estimator):\n",
" \"\"\"Inner function to generate simulation sample and evaluate the estimator\"\"\"\n",
" return estimator(choices(data,k=len(data)),*args)\n",
"\n",
" return (_inner(data,estimator) for _ in range(size)) "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Thus, to calculate the bootstrap estimate of the variance of an estimator, we simply pass in our indexable data and our estimator function, get back a generator (which we can evaluate immediately using `list`, if needed) on which we can calculate the variance. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Intermezzo - some helpers"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"Below we want to calculate the variance and quantiles of samples, so we will define a few helper functions. The first one will return the mean and the variance of a sample "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.066022Z",
"iopub.status.busy": "2021-11-16T10:24:49.064042Z",
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"shell.execute_reply": "2021-11-16T10:24:49.068270Z"
},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"def meanVar(x,ddof=0):\n",
" n = len(x)\n",
" m = sum(x)/n\n",
" v = sum([(xx-m)**2 for xx in x])/(n-ddof)\n",
" return m,v"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Again, we could have used _NumPy_ for this, but for the sake of illustration we code it up ourselves. Let us make a sample $\\sim U(0,1)$ and calculate the mean (0.5) and variance (1/12):"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.079577Z",
"iopub.status.busy": "2021-11-16T10:24:49.078315Z",
"iopub.status.idle": "2021-11-16T10:24:49.083784Z",
"shell.execute_reply": "2021-11-16T10:24:49.084834Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.500 +/- 0.082 (expect 0.500 and 0.083)\n"
]
}
],
"source": [
"m, v = meanVar([random.random() for _ in range(1000)])\n",
"print('{:.3f} +/- {:.3f} (expect {:.3f} and {:.3f})'.format(m,v,.5,1/12))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The next function will calculate the $\\alpha$ quantile of a sample. Essentially what we need to do is order the data and return the element at index $\\alpha N$ where $N$ is the number of samples. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.096083Z",
"iopub.status.busy": "2021-11-16T10:24:49.094677Z",
"iopub.status.idle": "2021-11-16T10:24:49.098849Z",
"shell.execute_reply": "2021-11-16T10:24:49.099869Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"def quantile(x,alpha,key=None):\n",
" return sorted(x,key=key)[int(alpha*len(x))]"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Let us try this on a sample $\\sim N(0,1)$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.105883Z",
"iopub.status.busy": "2021-11-16T10:24:49.104696Z",
"iopub.status.idle": "2021-11-16T10:24:49.117320Z",
"shell.execute_reply": "2021-11-16T10:24:49.118955Z"
},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 5% quantile: -1.807\n",
"50% quantile: -0.103\n",
"95% quantile: +2.103\n"
]
}
],
"source": [
"x = [random.normalvariate(0,1) for _ in range(100)]\n",
"print(' 5% quantile: {:+.3f}'.format(quantile(x,.05)))\n",
"print('50% quantile: {:+.3f}'.format(quantile(x,.50)))\n",
"print('95% quantile: {:+.3f}'.format(quantile(x,.95)))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Example\n",
"\n",
"The following example is due to Bradly Efron (reproduced in L.Wasserman [All of Statistics](http://www.stat.cmu.edu/~larry/all-of-statistics/), Chapter 8). A law school is interested in the correlation between LSAT ([Law School Achievement Test](https://www.lsac.org/lsat)) and GPA ([Grade Point Average](https://en.wikipedia.org/wiki/Grading_in_education#United_States)) scores. That is \n",
"\n",
"$$\n",
"\\hat\\theta = \\frac{\\sum_i(Y_i-\\bar Y)(Z_i-\\bar Z)}{\n",
" \\sqrt{\\sum_i(Y_i-\\bar Y)^2}\\sqrt{\\sum_i(Z_i-\\bar Z)^2}}\\quad,\n",
"$$\n",
"\n",
"where $Y$ is the LSAT score, and $Z$ the GPA score. First, let us get some data to work on."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.128601Z",
"iopub.status.busy": "2021-11-16T10:24:49.122800Z",
"iopub.status.idle": "2021-11-16T10:24:49.133558Z",
"shell.execute_reply": "2021-11-16T10:24:49.135291Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"lsat=[576, 635, 558, 578, 666, 580, 555, 661, 651, 605, 653, 575, 545, 572, 594]\n",
"gpa =[3.39,3.30,2.81,3.03,3.44,3.07,3.00,3.43,3.36,3.13,3.12,2.74,2.76,2.88,2.96]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, we have 15 samples of correlated LSAT and GPA scores. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We need a function calculate the correlation $\\hat\\theta$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.145981Z",
"iopub.status.busy": "2021-11-16T10:24:49.140826Z",
"iopub.status.idle": "2021-11-16T10:24:49.153488Z",
"shell.execute_reply": "2021-11-16T10:24:49.155008Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"import math\n",
"def corr(y,z):\n",
" ym,yv = meanVar(y)\n",
" zm,zv = meanVar(z)\n",
" num = sum([(yi-ym)*(zi-zm) for yi,zi in zip(y,z)])/len(y)\n",
" den = math.sqrt(yv)*math.sqrt(zv)\n",
" theta = num / den\n",
" return theta"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We could have used _NumPy_ here to perform this calculation more easily, but for the sake of illustration we write it out. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Now, our general `bootstrap` function expects the callable to take a single data argument, so we will wrap `corr` in another function below. Let us write a function that calculates $\\hat\\theta$ and estimates the standard deviation of $\\hat\\theta$ using the bootstrap method. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.162363Z",
"iopub.status.busy": "2021-11-16T10:24:49.159806Z",
"iopub.status.idle": "2021-11-16T10:24:49.172571Z",
"shell.execute_reply": "2021-11-16T10:24:49.173900Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"def corrLsatGpa(lsat,gpa,b=1000):\n",
" def est(data):\n",
" \"\"\"Wrapper\"\"\"\n",
" y = [lsat for lsat,_ in data]\n",
" z = [gpa for _,gpa in data]\n",
" return corr(y,z)\n",
"\n",
" theta = corr(lsat,gpa) # The estimate \n",
" data = [[lsat,gpa] for lsat,gpa in zip(lsat,gpa)] # Retructure\n",
" boot = list(bootstrap(data,est,b)) # Get the bootstrap estimates \n",
" bm, bv = meanVar(boot)\n",
" return theta,math.sqrt(bv),boot"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"The function above returns \n",
"\n",
"- $\\hat\\theta$ the estimate of the correlation, \n",
"- $\\widehat{\\mathrm{se}}(\\hat\\theta)=\\sqrt{\\operatorname{Var}^{\\mathrm{boot}}[\\hat\\theta]}$ the bootstrap estimate of the standard deviation, and \n",
"- the estimates of $\\hat\\theta$ over the bootstrap simulations. \n",
"\n",
"The last return value is mainly done in the interest of visualising the simulation. Let us run the example and plot \n",
"\n",
"- The correlation of the LSAT and GPA score \n",
"- The bootstrap estimates of $\\hat\\theta$ together with the estimates "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's make a function to plot results"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.180914Z",
"iopub.status.busy": "2021-11-16T10:24:49.178738Z",
"iopub.status.idle": "2021-11-16T10:24:49.193934Z",
"shell.execute_reply": "2021-11-16T10:24:49.195165Z"
},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt \n",
"def plot1(ax,data,theta,se,label):\n",
" b,_,_ = ax.hist(data, density=True, alpha=.5,label=label,histtype='step')\n",
" t = max(b)\n",
" ax.plot([theta,theta],[0,t],'--r',label='Estimate')\n",
" ax.fill_between([theta-se,theta+se],[t,t],alpha=.5,\n",
" label=r'$\\widehat{\\mathrm{se}}$',color='y')\n",
" ax.set_xlabel(r'$\\hat\\theta$')\n",
" ax.legend()\n",
" print('{:10s} {:.5f} +/- {:.5f}'.format(label, theta, se))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"caption": "Left: GPA versus LSAT data. Right: Bootstrap estimate of uncertainty",
"execution": {
"iopub.execute_input": "2021-11-16T10:24:49.203334Z",
"iopub.status.busy": "2021-11-16T10:24:49.201299Z",
"iopub.status.idle": "2021-11-16T10:24:52.703483Z",
"shell.execute_reply": "2021-11-16T10:24:52.704082Z"
},
"label": "fig:lsatgpa:first",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Correlation between LSAT and GPA: 0.776 +/- 0.132\n",
"Bootstrap 0.77637 +/- 0.13242\n"
]
},
{
"data": {
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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"theta, std, boot = corrLsatGpa(lsat,gpa)\n",
"print('Correlation between LSAT and GPA: {:.3f} +/- {:.3f}'.format(theta,std))\n",
"\n",
"fig, ax = plt.subplots(ncols=2,figsize=(10,6))\n",
"\n",
"ax[0].plot(lsat,gpa,'o')\n",
"ax[0].set_xlabel('LSAT')\n",
"ax[0].set_ylabel('GPA')\n",
"ax[0].set_title('The data')\n",
"plot1(ax[1],boot,theta,std,'Bootstrap')\n",
"fig.tight_layout();"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Simulating\n",
"\n",
"It is worth noting, that the method of bootstrapping is based on the law or large numbers. That is what necessitates that we perform a relative large number of simulations to get an estimate of the variance of our estimator. \n",
"\n",
"To see this, let us run the above example with a varying number of steps ranging from 3 to 10000 and then plot the estimated standard deviation as a function of the number of steps. "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"caption": "Uncertainty estimate $\\widehat{se}(\\hat\\theta)$ versus number of simulations $B$",
"execution": {
"iopub.execute_input": "2021-11-16T10:24:52.743164Z",
"iopub.status.busy": "2021-11-16T10:24:52.723217Z",
"iopub.status.idle": "2021-11-16T10:25:03.104331Z",
"shell.execute_reply": "2021-11-16T10:25:03.103691Z"
},
"label": "fig:lsatgpa:sqrtN",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"bs = [3, 6, 10, 30, 60, 100, 300, 600, 1000, 3000, 6000, 10000]\n",
"ob = []\n",
"os = []\n",
"for b in bs:\n",
" ob.append([b]*10)\n",
" os.append([corrLsatGpa(lsat,gpa,b)[1] for _ in range(10)])\n",
"\n",
"plt.figure(figsize=(10,6))\n",
"plt.scatter(ob,os)\n",
"plt.xscale('log')\n",
"plt.xlabel('$B$')\n",
"plt.ylabel(r'$\\widehat{se}(\\hat\\theta)$')\n",
"plt.title('Uncertainty estimate as a function of number of simulations');"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"The exact shape of the curve depends on the state of the random number generator used by `random.choices`, but in general we see that the estimate of $\\widehat{se}(\\hat\\theta)$ does not stabilize until $B$ is sufficiently large. Thus, we _must_ ensure sufficiently large number of simulations when applying the bootstrap method, or our estimate of the variance of the estimator is wholly uncertain. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Confidence intervals\n",
"\n",
"We can estimate confidence intervals from our bootstrap estimate of the variance in three ways "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Normal confidence interval\n",
"\n",
"In this method, we assume that the estimator is roughly normal, and we can give the standard $2\\sigma$ confidence limits \n",
"\n",
"$$ \\hat\\theta - 2\\widehat{se}(\\hat\\theta), \\hat\\theta + 2\\widehat{se}(\\hat\\theta)\\quad.$$\n",
"\n",
"Let us code this up in a function."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.112210Z",
"iopub.status.busy": "2021-11-16T10:25:03.110568Z",
"iopub.status.idle": "2021-11-16T10:25:03.115038Z",
"shell.execute_reply": "2021-11-16T10:25:03.115591Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"def bootstrapNormalCL(theta,boot,z=2):\n",
" \"\"\"Calculate the normal confidence limits on the estimate \n",
" theta and bootstrap sample boot. z specifies the number of \n",
" standard errors\n",
" \n",
" Parameters\n",
" ----------\n",
" theta : value \n",
" Estimate \n",
" boot : data \n",
" Bootstrap sample \n",
" z : factor \n",
" Number of standard errors \n",
" \n",
" Return\n",
" ------\n",
" low, high : tuple \n",
" Confince interval \n",
" \"\"\"\n",
" _, var = meanVar(boot)\n",
" se = math.sqrt(var)\n",
" return theta - z * se, theta + z * se"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us calculate the confidence interval for the LSAT versus GPA example above "
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.122071Z",
"iopub.status.busy": "2021-11-16T10:25:03.121248Z",
"iopub.status.idle": "2021-11-16T10:25:03.124461Z",
"shell.execute_reply": "2021-11-16T10:25:03.125038Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Confidence limits (normal): 0.512,1.041\n"
]
}
],
"source": [
"nlim = bootstrapNormalCL(theta,boot)\n",
"print('Confidence limits (normal): {:.3f},{:.3f}'.format(*nlim))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Quantile confidence interval \n",
"\n",
"An alternative, which does not assume $\\hat\\theta$ is roughly normal, but will tend to underestimate the confidence range is to calculate the $\\alpha$ and $1-\\alpha$ quantiles. That is, we quote the confidence limits as \n",
"\n",
"$$ Q_{\\alpha}(\\hat\\theta), Q_{1-\\alpha}(\\hat\\theta)\\quad, $$\n",
"\n",
"where $Q_{\\alpha}$ is the $\\alpha$ quantile of the bootstrap samples. Again, we will code this up in a function. "
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.131211Z",
"iopub.status.busy": "2021-11-16T10:25:03.130207Z",
"iopub.status.idle": "2021-11-16T10:25:03.133640Z",
"shell.execute_reply": "2021-11-16T10:25:03.132836Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"def bootstrapQuantileCL(theta,boot,alpha=0.05):\n",
" \"\"\"Calculate the quantile confidence limits on the estimate \n",
" theta and the bootstrap sample boot, where alpha is the percentile \n",
" below and above\n",
" \n",
" Parameters\n",
" ----------\n",
" theta : value \n",
" Estimate \n",
" boot : data \n",
" Bootstrap sample \n",
" alpha : percentage \n",
" Percentage below and above the confidence limits \n",
" \n",
" Return\n",
" ------\n",
" low, high : tuple \n",
" Confidence interval \n",
" \"\"\"\n",
" return quantile(boot,alpha), quantile(boot,1-alpha)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us, again, calculate the 5% and 95% confidence limits on the LSAT versus GPA example above "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.139474Z",
"iopub.status.busy": "2021-11-16T10:25:03.138661Z",
"iopub.status.idle": "2021-11-16T10:25:03.141961Z",
"shell.execute_reply": "2021-11-16T10:25:03.142520Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Confidence limits (quantile): 0.531,0.950\n"
]
}
],
"source": [
"qlim = bootstrapQuantileCL(theta,boot,0.05)\n",
"print('Confidence limits (quantile): {:.3f},{:.3f}'.format(*qlim))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Pivotal confidence interval \n",
"\n",
"This method uses the estimate $\\hat\\theta$ and the $\\alpha$ quantiles of the bootstrap simulations, and give the confidence limits as \n",
"\n",
"$$ 2\\hat\\theta - Q_{1-\\alpha}(\\hat\\theta), 2\\hat\\theta - Q_{\\alpha}(\\hat\\theta)\\quad,$$\n",
"\n",
"where $Q_{\\alpha}$ is the $\\alpha$ quantile of the bootstrap samples. We code this up in a function."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.149189Z",
"iopub.status.busy": "2021-11-16T10:25:03.145223Z",
"iopub.status.idle": "2021-11-16T10:25:03.151309Z",
"shell.execute_reply": "2021-11-16T10:25:03.151838Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"def bootstrapPivotCL(theta,boot,alpha=0.05):\n",
" \"\"\"Calculate the quantile confidence limits on the estimate \n",
" theta and the bootstrap sample boot, where alpha is the percentile \n",
" below and above\n",
" \n",
" Parameters\n",
" ----------\n",
" theta : value \n",
" Estimate \n",
" boot : data \n",
" Bootstrap sample \n",
" alpha : percentage \n",
" Percentage below and above the confidence limits \n",
" \n",
" Return\n",
" ------\n",
" low, high : tuple \n",
" Confidence interval \n",
" \"\"\"\n",
" return 2*theta - quantile(boot,1-alpha),2*theta-quantile(boot,alpha) "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"And, we use this on the example above "
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.157961Z",
"iopub.status.busy": "2021-11-16T10:25:03.157144Z",
"iopub.status.idle": "2021-11-16T10:25:03.160656Z",
"shell.execute_reply": "2021-11-16T10:25:03.161286Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Confidence limits (pivot): 0.603,1.022\n"
]
}
],
"source": [
"plim = bootstrapPivotCL(theta, boot, 0.05)\n",
"print('Confidence limits (pivot): {:.3f},{:.3f}'.format(*plim))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"For comparison we will plot these limits together "
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"caption": "Comparison of confidence interval estimates from Bootstrap",
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.166077Z",
"iopub.status.busy": "2021-11-16T10:25:03.164834Z",
"iopub.status.idle": "2021-11-16T10:25:03.753179Z",
"shell.execute_reply": "2021-11-16T10:25:03.754035Z"
},
"label": "fig:lsatgpa:cl",
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
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\n",
"image/png": 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rqXpktqHqXTkB+AIwvQ5Hn2+59vL3viAzOzKzY4stHCGSJAl6f+rnAaCjzfYtgd6GYp4BTo6IJ4C/Be5p2fdgT09HRCzrY62tdgX2rntd1q/vtbz1gOd6VjLzoZZ9NwPX1EM9nwH2BP4nMz8G7Ad8OCIeBf4IPFyf/3jLte6ph5a2BubXm5cB62fmn4GeXqJJwGzgbfV1LgeuqO9RPrs6NZRMmFC9dnU1WYWk5fTWo/JDYNvWYY56jkoH1T+6AE/zUq/Da1vOvRC4OjPPBG5c7rq5gvs9X90idunlaZpfUs35OAs4A7i2zTGPUA3l9NR9Zs+EV2B74KHMfD4zT83MfeuQArBxZp6YmV+qP9ul9fnTeoaL6td1gd/X6wFsCPyu5X6jgEOBrwKbAE9k5pL6PEmlede7qkVSUVbao5KZSyPiAODTEfEHYAsggHe1TKS9gKrnpAt4FXBARNwIXEQ15HEL8GZgs4h4PdWE2ddFxDuoAs4mEfF/M/Niqom704CRwNepek4Or+89HtilvvYRdU0PUfVqfKtN+VcBX2xZfww4rz5nF14ailrekRHxHFVPyQiqoRuohqW+GBG/BnYGDs/MpfW+3YCulnWAs4CTMvOFiPgecGpE7A58bQX3ldSkY49tugJJbUT1UE0fD454O9Xjvjdn5hd7O75pEfE5YE5mXr0G79ETqqav7Imi/ujo6Mju7u7VcSlJkooXEXdkZrupJv37ZtrMvJVqUuqgkJmnRMSua/g2o4FjMvPJNXwfSWuSc1SkIq31X6GfmXPX8PV/2/tRkiRpVaz1X6EvSZIGL4OKJEkqlkFFkiQVa62foyJJfXLIIU1XIKkNg4okARx1VNMVSGrDoR9JAliypFokFcUeFUkC2K/+E1x+j4pUFHtUJElSsQwqkiSpWAYVSZJULIOKJEkqlpNpJQlg8uSmK5DUhkFFksCgIhXKoR9JAnjiiWqRVBR7VCQJ4OCDq1e/R0Uqij0qkiSpWAYVSZJULIOKJEkqlkFFkiQVy8m0kgTw0Y82XYGkNgwqkgQwaVLTFUhqw6EfSQJ45JFqkVQUe1QkCeDww6tXv0dFKoo9KpIkqVgGFUmSVCyDiiRJKpZBRZIkFcvJtJIE8OlPN12BpDYMKpIEcMABTVcgqQ2HfiQJ4L77qkVSUexRkSSAI4+sXv0eFako9qhIkqRiGVQkSVKxDCqSJKlYBhVJklQsJ9NKEsBnP9t0BZLaMKhIEsDEiU1XIKkNh34kCWDOnGqRVBR7VCQJYOrU6tXvUZGKYo+KJEkqlkFFkiQVy6AiSZKKZVCRJEnFcjKtJAGccUbTFUhqw6AiSQB77tl0BZLacOhHkgB+9rNqkVQUe1QkCeCkk6pXv0dFKoo9KpIkqVgGFUmSVCyDiiRJKpZBRZIkFcvJtJIEMGNG0xVIasOgIkkA48Y1XYGkNhz6kSSAm26qFklFsUdFkgBOP716nTix2TokvYw9KpIkqVgGlX6IiOEDeZ4kSUNdo0M/ETEeOBVYF3h7Zi6LiDHA6cCmwMmZOXcA6vgX4MuZudkK9m8AnAF8PiI2ruu7ExgDLMrMU3u5xZiI+BhwUmY+txpL79XYadcO5O2kwWuP46pXf2ekPpt31v5r/B6N9qhk5iygC3gemFFvWwDMBK4aiJBS3/PbwOKVHPIl4L8ycyEwCvheZp6dmccAh0bEm3u5/nzgNqBzRcdExJSI6I6I7oULF/b7M0iStDYqZTLtkcB3IuIDmfnN1h0RMR0YQRWqns3MUyPig8CZwHlUvRq71e/PBM4FdgU2By4B9gG2B96VmX+MiA2By4BZwA7AdzJzhVP96+P3Bz4MkJm/WO6QYcD/1sfuB+wLPAh8HLge+CXwdeA64CsRcXJmvrD8fTLzAuACgI6OjuytwSRJGgpKCSpLgPcAsyLixV6UiNgH+LvMfFe9fl1E7J2Zl0TEvwK/yMxTIqIjM7vrbXdm5tkRcRWwUWYeERFfBN4JXAm8APxHZt4UEaOowsTKnkncDngyM18RHiLiPcD1mXlvRGxHFZLGZeafI2J9YFQdQAD+VM9VeTXw6Ko3Vf8MRLecJElrSjGTaTPzIWAycDnQM1dkV6reiR4PUPWe9PhNfW53y7b/qV+fann/B2Cj+n0AE+qeminAFr2Uth7winklEbEXsBfwyXrTe4EbM/PP9foWwPJjOMuA9Xu5n6Qm/OAH1SKpKMUEFYDM/AlwPtWcEKiGTbZrOWR7YE7rKatwmw8BW2XmaVQ9IL15hGpeyosiYn+qIaVjgC0j4q1UbflUvX99YCLwnZZzAtgQ+N0q1CxpTTv33GqRVJRGg0pEvA0YD3w8Il4FkJn/DtxSv78B+HlEnBkRZwGzM/PGiHgn8Lr6vC3qa/VsmxwRf0vVG3N4RLyhvscBEfFqqqGe7SPibOBYYJP6qZ9NIuIjy9eYmY8Cv62fRqKeOHsZsEdd59VUc10uAXaIiJOALwBT6onBPXYDujJz6eppPUmS1n7RZuqFlhMRuwKfAD6Smc+vwvkjqSbUTs/Meb0d39HRkd3d3b0dJml1mjCheu3qarIKaUiKiDsys6PdvqKGfkpVPyZ9MssNAfXDaOCYvoQUSZL0klKe+ilePQS0quf+dnXWIknSUGFQkSSASy9tugJJbRhUJAlg662brkBSG85RkSSAyy6rFklFsUdFkgDOO696nTSp2TokvYw9KpIkqVgGFUmSVCyDiiRJKpZBRZIkFcvJtJIEcMUVTVcgqQ2DiiQBbL550xVIasOhH0kCmDmzWiQVxaAiSWBQkQplUJEkScUyqEiSpGIZVCRJUrEMKpIkqVg+nixJAD/6UdMVSGrDoCJJABts0HQFktpw6EeSAL761WqRVBSDiiQBXH55tUgqikFFkiQVy6AiSZKKZVCRJEnFMqhIkqRi+XiyJAF0dTVdgaQ27FGRJEnFMqhIkqRiGVQkSVKxDCqSJKlYBhVJklQsg4okSSqWQUWSJBXLoCJJkoplUJEkScWKzGy6Bi0nIhYC8/t4+ObAE2uwnLWRbdY/tlf/2Wb9Y3v139rWZq/LzC3a7TCoDHIR0Z2ZHU3XMZjYZv1je/WfbdY/tlf/DaU2c+hHkiQVy6AiSZKKZVAZ/C5ouoBByDbrH9ur/2yz/rG9+m/ItJlzVCRJUrHsUZEkScUyqEiSpGIZVCRJUrEMKpIkqVjrNF2AehcRE4H3Ao8DmZmntDnmNmBpvfp8Zr5jAEssTh/bbAfgMOBPwNuBzsy8fUALLUhvbRYRY4GfAI/UmzYG5mbm5AEssxh9/Bk7DhhL9Q2i2wNHZOafBrLOkvSxzT4JvAb4X2A94MQcwk99RMSWwOnAbpn5lhUc02u7DmqZ6VLwAmwAPACsV69fCbyjzXGdTddaytKXNgOGA9cCw+r1vwa2aLr2wttsNDCxZf0U4G1N115we20JPNnyM3Y18C9N1154m40D5rSsXwm8p+naG263g4EDgO5VbdfBvjj0U763AvMz88/1+v8D9m9z3C4RcUJEdEZEu/1DSV/a7C1AAJ+IiBOp/kOwNv3djP7qtc0yc1Fm3gQQEesBHZn504Etsxh9+RlbAjxL1fMEsCFwz8CUV6S+tNn2vNRjB/AgMKR7hzPzCuDplRzS138jBi2Hfsr3V7z8h/SP9bbl/Vtm3h4Rw4FZEfF0Zs4akArL05c2ex3VL/hhmbk4Ir5F9Y/KzAGpsDx9/Tnr8T7gu2u0orL12l6Z+cd66OeyiHgUWED1f75DVV9+xn4BnBkRI4E/Ax28PLjolfr7uzvo2KNSvseBjVrWN663vUzWcysy83ngv4G9BqS6MvWlzf4I3JuZi+v1nwIT1nxpxerTz1mLfwYuW6MVla3X9oqIccBxwP5ZzeN5Ajh5gOorUa9tlpnzgCnAdOAYqh6ohweovsGqv7+7g45BpXyzgdfVXe0Af081t6JnciMRsWNEHNFyzvYM7f9z67XNgJ8Do+seKKh6WO4fyCIL05c2o17fC/hZZi4b0ArL0pf2eg3wZGY+V68/CowcyCIL09efsScz8zOZOQPYFPj2ANY4aLS02QrbdW3hV+gPAhHxTqoJVQuBZZl5SkQMoxq/nUA1ZPEV4E6qND0C+FRmvtBMxc3rrc0yc15EvAf4h/qY1wKfyKH9REavbVYf912qthrKc3r68nv5CPAlqqfxngL+BpiamY82UnAB+vh7OYuqV/jPwK/rORpDVkS8HfgAsC9wHnAuVdu0ttkr2rWpetcEg4okSSqWQz+SJKlYBhVJklQsg4okSSqWQUWSJBXLoCJJkoplUJEkICI2jojPRsRGvR8taaAYVCSpMh24Bfhc04VIeonfoyJJkorlHyWUNORFxAbA8VTfJrsHMD0zH2u2Kkng0I8kAXwNuDUzL6L6A5VHNVyPpJpBRdKQFhE7A2/OzFvqTesAWzVYkqQWDv1IGur+CXgyIqbV6/sD1zdYj6QWBhVJQ902wDcz8wKAiDgcuLrZkiT1cOhH0lD3GPAcQERMAO7MzLubLEjSS+xRkTTUnQecFhEBvA44suF6JLXwe1QkSVKxHPqRJEnFMqhIkqRiGVQkSVKxDCqSJKlYBhVJklQsg4okSSqWQUWSJBXLoCJJkoplUJEkScX6/1Zw4MKAYe7FAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,4))\n",
"\n",
"plt.plot([theta,theta],[-.5,2.5],'--r',label='Estimate')\n",
"for i, l in enumerate([nlim,qlim,plim]):\n",
" plt.plot(l,[i,i],'-',lw=3)\n",
"plt.yticks([0,1,2],[r'Normal ($2\\sigma$)',\n",
" 'Quantile (5-95)%',\n",
" 'Pivot (5-95)%'])\n",
"plt.xlabel(r'$\\hat\\theta$')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We note that the normal and pivot confidence limits exceed 1 on the high end, which indicate that these two estimates tend to overestimate the size of the confidence interval. The quantile confidence limits, on the other hand is probably on the low side, but does reflect the distribution of the bootstrap sample in this example. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Another example \n",
"\n",
"This example comes from the exercises of L.Wasserman [All of Statistics](http://www.stat.cmu.edu/~larry/all-of-statistics/), Chapter 8. \n",
"\n",
"We have a sample of 100 observations $X \\sim N(5,1)$, and we are interested in the statistics $\\theta = e^\\mu$, for which we will use the estimator $\\hat\\theta = e^{\\bar{X}}$. We will use the bootstrap method to calculate the standard uncertainty and 95% confidence limits on $\\hat\\theta$. \n",
"\n",
"First, let us make our sample, and calculate our estimator "
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.762026Z",
"iopub.status.busy": "2021-11-16T10:25:03.761025Z",
"iopub.status.idle": "2021-11-16T10:25:03.764511Z",
"shell.execute_reply": "2021-11-16T10:25:03.765133Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"hat(theta) = 169.10\n"
]
}
],
"source": [
"data = [random.normalvariate(5,1) for _ in range(100)]\n",
"theta = math.exp(sum(data)/len(data))\n",
"print('hat(theta) = {:.2f}'.format(theta)) "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Next, we generate our bootstrap sample and calculate the standard uncertainty and confidence limits using all three methods above and plot them with the distribution of $e^{X}$ as well as the bootstrap distribution."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"caption": "Bootstrap estimate of uncertainty on $e^{X}$, as well as confindence limits",
"execution": {
"iopub.execute_input": "2021-11-16T10:25:03.800339Z",
"iopub.status.busy": "2021-11-16T10:25:03.780951Z",
"iopub.status.idle": "2021-11-16T10:25:05.885575Z",
"shell.execute_reply": "2021-11-16T10:25:05.886825Z"
},
"label": "fig:expx:bootstrap",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Bootstrap 169.10419 +/- 16.40896\n",
"Normal confidence limits: 136.29 - 201.92\n",
"Quantile confidence limits: 143.82 - 197.33\n",
"Pivot confidence limits: 140.88 - 194.39\n"
]
},
{
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"boot = list(bootstrap(data,lambda d:math.exp(sum(d)/len(d))))\n",
"_, var = meanVar(boot)\n",
"\n",
"plt.figure(figsize=(8,4))\n",
"plt.hist([math.exp(x) for x in data],25,alpha=.5,density=True,label='Data')\n",
"plot1(plt.gca(),boot,theta,math.sqrt(var),'Bootstrap')\n",
"\n",
"cln = ['Normal','Quantile','Pivot']\n",
"clm = [bootstrapNormalCL,bootstrapQuantileCL,bootstrapPivotCL]\n",
"for n, m, y in zip(cln,clm,[.03, .032, .034]):\n",
" l = m(theta,boot)\n",
" plt.plot(l,[y,y],'-',lw=4,label=n)\n",
" print('{:10s} confidence limits: {:.2f} - {:.2f}'.format(n,*l))\n",
" \n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We immediately see that the bootstrap sample is much more narrowly centred around the estimate, and the width of the distribution reflect well the expected variance \n",
"\n",
"$$\\operatorname{Var}[\\theta] \\approx \\left(\\frac{\\partial\\theta}{\\partial \\bar x}\\right)^2\\delta^2 \\bar x \n",
"= e^{2\\bar{x}}\\operatorname{Var}[\\bar x]\n",
"= e^{2\\bar{x}}\\frac{\\operatorname{Var}[x]}{N}\n",
"\\quad,$$\n",
"\n",
"which, taking the square root, evaluates to "
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:05.898138Z",
"iopub.status.busy": "2021-11-16T10:25:05.896721Z",
"iopub.status.idle": "2021-11-16T10:25:05.905897Z",
"shell.execute_reply": "2021-11-16T10:25:05.914688Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"15.820\n"
]
}
],
"source": [
"mx, vx = meanVar(data)\n",
"print('{:.3f}'.format(math.sqrt(math.exp(mx)**2*vx/len(data))))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Another (simpler) approach - Jackknife\n",
"\n",
"This approach was developed by Maurice Quenouille (see appendix to L.Wasserman [All of Statistics](http://www.stat.cmu.edu/~larry/all-of-statistics/), Chapter 8) and predates the bootstrap method. The idea is again to use the observed data to simulate variations in the sample and then estimate the sample variance from these simulations. \n",
"\n",
"- Suppose we are interested in the quantity $T$ calculated over the data $X$ (more formally, \n",
" $T$ is a _statistics_). We estimate $T$ via the estimator $\\hat{T}$ over the sample \n",
" $X_1,X_2,\\ldots X_N$, of size $N$. We are interested in estimating the variance $\\operatorname{Var}(T(X))$ \n",
"- First, estimate the $T$ over our sample $x$\n",
"- Secondly, for $N$ iterations, we do\n",
" - For the $i^{\\mathrm{th}}$ iteration, calculate the estimate $T$ leaving out the $i^{\\mathrm{th}}$ \n",
" data point. That is we take the sample $X_1,\\ldots,X_{i-1},X_{i+1},\\ldots,X_N$ and calculate the \n",
" estimate on that sample\n",
"- Finally, calculate the variance of $T$ estimated over the $N$ generated samples given by \n",
"\n",
" $$\\operatorname{Var}[T] = \\frac{N-1}{N}\\sum_i^{N} \\left(T_i - \\bar{T}\\right)^2\\quad,$$\n",
" \n",
" where $T_i$ is the estimate calculated over the $i^{\\mathrm{th}}$ jackknife sample and $\\hat{T}$ is \n",
" the mean of the estimate calculated over all jackknife samples. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can code this up in a general function. As before, we expect an indexable data set and a function to calculate the estimator. "
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:05.931151Z",
"iopub.status.busy": "2021-11-16T10:25:05.929148Z",
"iopub.status.idle": "2021-11-16T10:25:05.936288Z",
"shell.execute_reply": "2021-11-16T10:25:05.937554Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"def jackknife(data,estimator,*args):\n",
" \"\"\"Generate the jackknife samples and evaluate the estimator over\n",
" these. \n",
" \n",
" Parameters\n",
" ----------\n",
" data : \n",
" The data to calculate the jackknife samples over \n",
" estimator : callable \n",
" The function to calculate the estimator \n",
" \n",
" Returns\n",
" -------\n",
" jack : \n",
" The estimator calculated over all jackkknife samples \n",
" \"\"\"\n",
" def _inner(data,estimator,i):\n",
" return estimator((data[j] for j in range(len(data)) if j != i),*args)\n",
" \n",
" return (_inner(data,estimator,i) for i in range(len(data)))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Example - LSAT versus GPA\n",
"\n",
"Let us apply this method to our example above of the correlation between LSAT and GPA"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:05.955134Z",
"iopub.status.busy": "2021-11-16T10:25:05.944138Z",
"iopub.status.idle": "2021-11-16T10:25:05.963498Z",
"shell.execute_reply": "2021-11-16T10:25:05.965340Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"def jkLsatGpa(lsat,gpa):\n",
" def est(data):\n",
" \"\"\"Wrapper\"\"\"\n",
" d = list(data)\n",
" y = [lsat for lsat,_ in d]\n",
" z = [gpa for _,gpa in d]\n",
" return corr(y,z)\n",
"\n",
" theta = corr(lsat,gpa) # The estimate \n",
" data = [[lsat,gpa] for lsat,gpa in zip(lsat,gpa)] # Retructure\n",
" jk = list(jackknife(data,est)) # Get the bootstrap estimates \n",
" jm, jv = meanVar(jk)\n",
" return theta,math.sqrt(jv*(len(data)-1)),jk"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We run this example and compare to the previous result of $0.776\\pm 0.127$"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"caption": "Jackknife estimate of uncertainty on LSAT versus GPA correlation",
"execution": {
"iopub.execute_input": "2021-11-16T10:25:05.980575Z",
"iopub.status.busy": "2021-11-16T10:25:05.979396Z",
"iopub.status.idle": "2021-11-16T10:25:08.065768Z",
"shell.execute_reply": "2021-11-16T10:25:08.067379Z"
},
"label": "fig:lsatgpa:jk",
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"LSAT versus GPA correlation: 0.776 +/- 0.143\n",
"Jackknife 0.77637 +/- 0.14252\n"
]
},
{
"data": {
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\n",
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"theta, std, jk = jkLsatGpa(lsat,gpa)\n",
"print(\"LSAT versus GPA correlation: {:.3f} +/- {:.3f}\".format(theta,std))\n",
"\n",
"plt.figure()\n",
"plot1(plt.gca(),jk,theta,std,'Jackknife')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Example - generated data\n",
"\n",
"We use the jackknife method on our generated data from above. First, we calculate our estimate $\\hat\\theta=e^{\\bar{X}}$ of the sample $X\\sim N(5,1)$"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:08.075492Z",
"iopub.status.busy": "2021-11-16T10:25:08.074156Z",
"iopub.status.idle": "2021-11-16T10:25:08.082171Z",
"shell.execute_reply": "2021-11-16T10:25:08.083552Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"theta = math.exp(sum(data)/len(data))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"which is clearly the same as before, and then we perform our jackknife analysis to finde the variance. We plot the result as before "
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"caption": "Jackknife estimate of uncertainty on $e^{X}$",
"execution": {
"iopub.execute_input": "2021-11-16T10:25:08.096944Z",
"iopub.status.busy": "2021-11-16T10:25:08.089149Z",
"iopub.status.idle": "2021-11-16T10:25:09.951026Z",
"shell.execute_reply": "2021-11-16T10:25:09.954023Z"
},
"label": "fig:expx:jk",
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Jackknife 169.10419 +/- 15.88762\n"
]
},
{
"data": {
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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def est(data):\n",
" d = list(data)\n",
" return math.exp(sum(d)/len(d))\n",
"jk = list(jackknife(data,est))\n",
"_, var = meanVar(jk)\n",
"std = math.sqrt(var*(len(data)-1))\n",
"plot1(plt.gca(),jk,theta,std,'Jackknife')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Clearly, the jackknife method does not produce as wide simulated distributions as the bootstrap method does, and consequently, the estimates of the variance are more uncertain. If possible, one should opt for the bootstrap method over the jackknife method. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# When **not** to do bootstrap or jackknife"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## A simple estimator \n",
"Suppose we have analysed millions of events $\\{E_1,\\ldots\\}$ for a particular observable $X$. We have split our events $E_i$ into $N$ sub-samples \n",
"\n",
"$$\n",
"\\bigcup_i^N S_i = \\{E_1,\\ldots\\}\\quad,\n",
"$$\n",
"\n",
"and calculated $X$ in each of these sub-samples. We thus have the sample \n",
"\n",
"$$\\{X_1,\\ldots,X_N\\}\\quad.$$ \n",
"\n",
"All the observations $X_i$ are independent identically distributed (iid) random variable, in that \n",
"\n",
"$$\\forall i,j\\in\\{1,\\ldots,N\\}\\wedge i\\neq j: S_j \\cap S_i = \\emptyset\\quad,$$ \n",
"\n",
"and the events $E_i$ are assumed to be equal ins some meaning of that word. Thus, we want to estimate \n",
"$\\theta$ over and its variance. Our estimator is then the mean of the $N$ samples \n",
"\n",
"$$\\hat\\theta = \\frac{1}{N}\\sum_{i=1}^N X_i\\quad,$$ \n",
"\n",
"and we will use the bootstrap and jackknife methods for estimating the variance and standard uncertainty."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Here, we will choose $N=10$ and $X\\sim N(0,1)$ without loss of generality. Thus, we expect to find that \n",
"\n",
"$$\\hat\\theta = 0 \\pm 0.1\\quad.$$\n",
"\n",
"Let us generate the data"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:09.962488Z",
"iopub.status.busy": "2021-11-16T10:25:09.960368Z",
"iopub.status.idle": "2021-11-16T10:25:09.969453Z",
"shell.execute_reply": "2021-11-16T10:25:09.970827Z"
}
},
"outputs": [],
"source": [
"data = [random.normalvariate(0,1) for _ in range(10)]"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We can of course calculate the mean and the variance directly from this sample to obtained the sample mean and standard uncertainty "
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:09.978075Z",
"iopub.status.busy": "2021-11-16T10:25:09.975990Z",
"iopub.status.idle": "2021-11-16T10:25:09.988680Z",
"shell.execute_reply": "2021-11-16T10:25:09.989972Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sample mean = 0.070 and variance = 0.530 -> 0.070 +/- 0.230\n"
]
}
],
"source": [
"m, v = meanVar(data,1)\n",
"e = math.sqrt(v/len(data))\n",
"mes = '{:10s} mean = {:.3f} and variance = {:.3f} -> {:.3f} +/- {:.3f}'\n",
"print(mes.format('Sample', m, v, m, e))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us now use the bootstrap method to perform the calculation"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:09.996370Z",
"iopub.status.busy": "2021-11-16T10:25:09.994576Z",
"iopub.status.idle": "2021-11-16T10:25:10.018484Z",
"shell.execute_reply": "2021-11-16T10:25:10.022870Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Bootstrap mean = 0.070 and variance = 0.048 -> 0.070 +/- 0.220\n"
]
}
],
"source": [
"def est(data):\n",
" d = list(data)\n",
" return sum(d)/len(d)\n",
"boot = list(bootstrap(data, est))\n",
"meanb, varb = meanVar(boot)\n",
"eb = math.sqrt(varb)\n",
"print(mes.format('Bootstrap', m, varb, m, eb))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"And finally we use the jackknife method "
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:10.033009Z",
"iopub.status.busy": "2021-11-16T10:25:10.030200Z",
"iopub.status.idle": "2021-11-16T10:25:10.048574Z",
"shell.execute_reply": "2021-11-16T10:25:10.050545Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Jackknife mean = 0.070 and variance = 0.006 -> 0.070 +/- 0.230\n"
]
}
],
"source": [
"jk = list(jackknife(data,est))\n",
"meanj, varj = meanVar(jk)\n",
"ej = math.sqrt(varj*(len(data)-1))\n",
"print(mes.format('Jackknife', m, varj, m, ej))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us plot the various samples "
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"caption": "Estimates of uncertainty $\\widehat{se}(\\hat\\theta)$ with $\\hat\\theta$ simple Left: direct evaluation, middle: Bootstrap, right: Jackknife",
"execution": {
"iopub.execute_input": "2021-11-16T10:25:10.058949Z",
"iopub.status.busy": "2021-11-16T10:25:10.056616Z",
"iopub.status.idle": "2021-11-16T10:25:14.028153Z",
"shell.execute_reply": "2021-11-16T10:25:14.029249Z"
},
"label": "fig:simple:compare_all",
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Direct 0.07026 +/- 0.23028\n",
"Bootstrap 0.07026 +/- 0.21978\n",
"Jackknife 0.07026 +/- 0.23028\n"
]
},
{
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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(ncols=3,figsize=(10,6),sharex=True)\n",
"plot1(ax[0], data, m, e, 'Direct')\n",
"plot1(ax[1], boot, m, eb, 'Bootstrap')\n",
"plot1(ax[2], jk, m, ej, 'Jackknife')\n",
"fig.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As is clear from the results above, it makes little sense to use the bootstrap or jackknife methods for estimating the variance if the estimator in question is a simple estimator such as the mean. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## A more complicated example\n",
"\n",
"Suppose, again, we are analysing millions of events which we may split into some number $N$ of sub-samples. For each sub-sample $i$ we calculate some quantity from which we will derive a complicated estimator $\\hat\\theta_i$. This could for example be \n",
"\n",
"$$\\hat\\theta_i = \\frac{-a + 2b}{c^3}\\quad,$$\n",
"\n",
"where $a$, $b$, and $c$ are calculated over the sub-samples. The final estimator over the sub-samples is then the average \n",
"\n",
"$$\\hat\\theta = \\frac{1}{N}\\sum_i \\hat\\theta_i\\quad.$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us try to simulate this case. We will generate 10000 events with \n",
"\n",
"- $a \\sim N(1,1)$\n",
"- $b \\sim N(5,1)$\n",
"- $c \\sim N(3,1)$ \n",
"\n",
"from which we will select $N=10$ sub-samples and calculate the means of $a,b$, and $c$."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:14.036469Z",
"iopub.status.busy": "2021-11-16T10:25:14.034401Z",
"iopub.status.idle": "2021-11-16T10:25:14.057625Z",
"shell.execute_reply": "2021-11-16T10:25:14.059346Z"
}
},
"outputs": [],
"source": [
"events = [(random.normalvariate(1,1),\n",
" random.normalvariate(5,1),\n",
" random.normalvariate(3,1))\n",
" for _ in range(1000)]\n",
"data = list(zip(*[events[i::len(events)//10] \n",
" for i in range(len(events)//10)]))\n",
"data = [(sum(a for a,_,_ in sub)/len(sub),\n",
" sum(b for _,b,_ in sub)/len(sub),\n",
" sum(c for _,_,c in sub)/len(sub)) \n",
" for sub in data]"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us define the estimator function which calculates the average over $\\hat\\theta_i$, and evaluate it on the 10 subsamples "
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:14.066890Z",
"iopub.status.busy": "2021-11-16T10:25:14.064749Z",
"iopub.status.idle": "2021-11-16T10:25:14.080437Z",
"shell.execute_reply": "2021-11-16T10:25:14.081862Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimator 0.3319428026358412\n"
]
}
],
"source": [
"def est(data):\n",
" def _inner(a,b,c):\n",
" return (-a + 2*b) / c**3\n",
" d = list(data)\n",
" return sum(_inner(a,b,c) for a,b,c in d)/len(d)\n",
"\n",
"theta = est(data)\n",
"print('Estimator {}'.format(theta))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let us do the bootstrap and jackknife methods to estimate the variance of $\\hat\\theta$, as well as direct estimate from the $N$ sub-sample results "
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:14.088479Z",
"iopub.status.busy": "2021-11-16T10:25:14.086624Z",
"iopub.status.idle": "2021-11-16T10:25:14.116720Z",
"shell.execute_reply": "2021-11-16T10:25:14.118479Z"
},
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"dirc = [(-a + 2*b)/c**3 for a,b,c in data]\n",
"dmean,dvar = meanVar(dirc)\n",
"dstd = math.sqrt(dvar / len(dirc))\n",
"\n",
"boot = list(bootstrap(data,est))\n",
"bmean, bvar = meanVar(boot)\n",
"bstd = math.sqrt(bvar)\n",
"\n",
"jack = list(jackknife(data,est))\n",
"jmean, jvar = meanVar(jack)\n",
"jstd = math.sqrt(jvar * (len(data)-1))"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"caption": "Estimates of uncertainty $\\widehat{se}(\\hat\\theta)$ with $\\hat\\theta$ complicated. Left: direct evaluation, middle: Bootstrap, right: Jackknife",
"execution": {
"iopub.execute_input": "2021-11-16T10:25:14.126345Z",
"iopub.status.busy": "2021-11-16T10:25:14.124031Z",
"iopub.status.idle": "2021-11-16T10:25:18.322112Z",
"shell.execute_reply": "2021-11-16T10:25:18.323453Z"
},
"label": "fig:complicated:compare_all",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sub-samples 0.33194 +/- 0.00882\n",
"Bootstrap 0.33194 +/- 0.00842\n",
"Jackknife 0.33194 +/- 0.00929\n"
]
},
{
"data": {
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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(ncols=3,figsize=(10,6),sharex=True)\n",
"plot1(ax[0],dirc,theta,dstd,'Sub-samples')\n",
"plot1(ax[1],boot,theta,bstd,'Bootstrap')\n",
"plot1(ax[2],jack,theta,jstd,'Jackknife')\n",
"fig.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, we see that the bootstrap and jackknife methods does not provide significant advantages over direct calculation of the variance from the $N$ sub-samples. This is, of course, because the final estimator is a simple average of the sub-samples. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Estimates from full event data\n",
"\n",
"We will continue the example above, where we however will store $a,b,c$ as calculated in _each_ event and our final estimator becomes \n",
"\n",
"$$\\hat\\theta = \\frac{-\\bar{a} + 2\\bar{b}}{\\bar{c}^3}\\quad.$$ \n",
"\n",
"We will thus perform the bootstrap analysis by sampling new events from our empirical distributions of $a,b,$ and $c$ and calculate the estimator value for each of those samples. Note, in this case, it is not easy to calculate the variance directly from the data, so we will refrain from doing so. "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We use the events generated above to do our estimate and variance estimates, but first, we need a function to calculate the mean of $a,b,$ and $c$ over all events."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:18.337018Z",
"iopub.status.busy": "2021-11-16T10:25:18.332190Z",
"iopub.status.idle": "2021-11-16T10:25:18.339459Z",
"shell.execute_reply": "2021-11-16T10:25:18.340230Z"
}
},
"outputs": [],
"source": [
"def est(data):\n",
" d = list(data)\n",
" a = sum(aa for aa,_,_ in d) / len(d)\n",
" b = sum(bb for _,bb,_ in d) / len(d)\n",
" c = sum(cc for _,_,cc in d) / len(d)\n",
" return (-a + 2*b) / c**3"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Let us calculate the estimate "
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:18.347230Z",
"iopub.status.busy": "2021-11-16T10:25:18.346316Z",
"iopub.status.idle": "2021-11-16T10:25:18.349835Z",
"shell.execute_reply": "2021-11-16T10:25:18.350495Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimator: 0.3304604423307452\n"
]
}
],
"source": [
"theta = est(events)\n",
"print('Estimator: {}'.format(theta))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Regular propagation of uncertainties, including covariance, gives \n",
"\n",
"\\begin{align*}\n",
"\\operatorname{Var}[\\theta] &= \n",
" \\left(-\\frac{1}{\\bar c^3}\\right)^2\\frac{\\operatorname{Var}[a]}{N} + \n",
" \\left(\\frac{2}{\\bar c^3}\\right)^2\\frac{\\operatorname{Var}[b]}{N} +\n",
" \\left(-\\frac{3(-\\bar a+2\\bar b)}{\\bar c^4}\\right)^2\\frac{\\operatorname{Var}[c]}{N}\\\\\n",
" &\\quad +\n",
" 2\\left[\\frac{-1}{\\bar c^3}\\frac{2}{\\bar c^3}\\frac{\\operatorname{Cov}[a,b]}{N}+\n",
" \\frac{-1}{\\bar c^3}\\frac{-3(-\\bar a+2\\bar b)}{c^4}\\frac{\\operatorname{Cov}[a,c]}{N}+\n",
" \\frac{2}{\\bar c^3}\\frac{-3(-\\bar a+2\\bar b)}{c^4}\\frac{\\operatorname{Cov}[b,c]}{N}\n",
" \\right]\n",
" \\\\\n",
" &= \n",
" \\frac{1}{\\bar c^6 N}\\left(\\operatorname{Var}[a] + \n",
" 4(\\operatorname{Var}[b]-\\operatorname{Cov}[a,b])+\n",
" \\frac{3}{\\bar c}(-\\bar a + 2\\bar b)\n",
" \\left[\n",
" \\frac{3(-\\bar a + 2\\bar b)}{\\bar c}\\operatorname{Var}[c]+\n",
" \\operatorname{Cov}[a,c]-2\\operatorname{Cov}[b,c]\n",
" \\right]\n",
" \\right)\n",
" \\quad,\n",
"\\end{align*}\n",
" \n",
"which we can calculate directly on the data"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:18.362291Z",
"iopub.status.busy": "2021-11-16T10:25:18.361031Z",
"iopub.status.idle": "2021-11-16T10:25:18.382130Z",
"shell.execute_reply": "2021-11-16T10:25:18.383259Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Direct 0.33046 +/- 0.00884\n"
]
}
],
"source": [
"n = len(data)\n",
"meana, vara = meanVar([aa for aa,_,_ in data])\n",
"meanb, varb = meanVar([bb for _,bb,_ in data])\n",
"meanc, varc = meanVar([cc for _,_,cc in data])\n",
"covab = sum([(aa - meana)*(bb - meanb) for aa,bb,_ in data])/n\n",
"covac = sum([(aa - meana)*(cc - meanc) for aa,_,cc in data])/n\n",
"covbc = sum([(bb - meanb)*(cc - meanc) for _,bb,cc in data])/n\n",
"tmp = 3*(-meana + 2*meanb)/meanc\n",
"dvar = 1/meanc**6/n * (vara + 4*(varb+covab) + tmp*(tmp*varc+covac-2*covbc))\n",
"dstd = math.sqrt(dvar)\n",
"print('{:10s} {:.5f} +/- {:.5f}'.format('Direct',theta,dstd))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We perform the bootstrap and jackknife analyses"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:25:18.455539Z",
"iopub.status.busy": "2021-11-16T10:25:18.420089Z",
"iopub.status.idle": "2021-11-16T10:25:19.315206Z",
"shell.execute_reply": "2021-11-16T10:25:19.315773Z"
}
},
"outputs": [],
"source": [
"boot = list(bootstrap(events,est))\n",
"jack = list(jackknife(events,est))\n",
"bmean, bvar = meanVar(boot)\n",
"jmean, jvar = meanVar(jack)\n",
"bstd = math.sqrt(bvar)\n",
"jstd = math.sqrt(jvar * (len(events)-1))"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"caption": "Estimates of uncertainty $\\widehat{se}(\\hat\\theta)$ with samples from full event data. Left: Bootstrap, right: Jackknife",
"execution": {
"iopub.execute_input": "2021-11-16T10:25:19.326430Z",
"iopub.status.busy": "2021-11-16T10:25:19.324265Z",
"iopub.status.idle": "2021-11-16T10:25:22.366407Z",
"shell.execute_reply": "2021-11-16T10:25:22.365305Z"
},
"label": "fig:data:compare_all",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Direct 0.33046 +/- 0.00884\n",
"Bootstrap 0.33046 +/- 0.01103\n",
"Jackknife 0.33046 +/- 0.01103\n"
]
},
{
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\n",
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\n",
"text/plain": [
""
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"source": [
"fig, ax = plt.subplots(ncols=2,sharex=True,figsize=(10,6))\n",
"print('{:10s} {:.5f} +/- {:.5f}'.format('Direct',theta,dstd))\n",
"plot1(ax[0],boot,theta,bstd,'Bootstrap')\n",
"plot1(ax[1],jack,theta,jstd,'Jackknife')\n",
"fig.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The 3 estimates all agree to one significant digit, and we see that even in this case we do better by evaluating the uncertainties directly. "
]
},
{
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"slideshow": {
"slide_type": "slide"
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},
"source": [
"# Summary\n",
"\n",
"The bootstrap and jackknife methods for estimating the variance of an estimator are powerful tools, but are _not_ generally applicable. Here are some key take-aways \n",
"\n",
"- Bootstrap should be preferred over jackknife \n",
"- Bootstrap and jackknife should _only_ be applied if it is not possible to estimate the estimator variance through regular propagation of uncertainties or the like \n",
"- If bootstrapping is used, one best save the variables that go into the final calculation of the estimator, so that one can reliably perform the simulations. "
]
}
],
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