{ "cells": [ { "cell_type": "markdown", "id": "60829496", "metadata": {}, "source": [ "# Chapter 2: Information Criterions and Bootstrap Confidence Intervals" ] }, { "cell_type": "markdown", "id": "e8323d65", "metadata": {}, "source": [ "In this chapter, we'll cover the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for nested models, as well as the bootstrap method for confidence intervals. " ] }, { "cell_type": "markdown", "id": "0545c351", "metadata": {}, "source": [ "## Nested Models" ] }, { "cell_type": "markdown", "id": "a755c3f5", "metadata": {}, "source": [ "Let's say we have model A with variables $\\theta_1$, $\\theta_2$ and $\\theta_3$. Model B is nested in model A if model B contains a subset of the variables of model A, e.g. if model B has variables $\\theta_1$ and $\\theta_3$. We call model B a $\\textbf{nested model}$. \n", "Model B is $\\textbf{not}$ a nested model if it contains a variable that model A doesn't contain, e.g. if model B has variables $\\theta_1$, $\\theta_3$ and $\\theta_4$. \n", "\n", "Model A can be seen as the true model which describes the data. When researching, you don't know the true model, but you can construct a model B which is a nested model of model A. In order to check if model B doesn't include unnecessary parameters and that the model isn't overfitting the data, the Akaike Information Criterion and the Bayesian Information Criterion can be used. \n", "\n", "In this chapter we'll focus on the Akaike Information Criterion and Bayesian Information criterion specifically for nested models, as working with non-nested models would require to take the different normalisation constants of the likelihoods of the models into account. This can be done of course, but explaining this concept isn't the primary goal of this chapter and so we won't go into this any further. " ] }, { "cell_type": "markdown", "id": "f1bf12da", "metadata": { "jp-MarkdownHeadingCollapsed": true }, "source": [ "## Akaike Information Criterion (AIC)\n", "The $\\textbf{Akaike Information Criterion (AIC)}$ is an estimator of prediction error of statistical models. It is a method for evaluating how well a model fits the data it was generated from. AIC is used to compare different models and determine which model is the best fit. This best fit is the one that explains the greatest amount of variation and has the minimal amount of information loss, using the fewest amount of parameters. The equation for the AIC is as follows;\n", "\n", "\n", "$$\\mathrm{AIC} = - 2\\ln(\\hat{\\mathcal{L}}) + 2p_k \\tag{2.1}$$\n", "It combines the maximum likelihood $\\hat{\\mathcal{L}}$ and the number of parameters $p_k$. The best model will give the lowest value. From [Eq. 2.1](#eq:AIC) you can see that the AIC discourages overfitting. By adding more parameters, the AIC value will increase. The goodness of the fit, determined with the max-likelihood, will help decrease the AIC score.\n", "\n", "**Note**: The AIC gives a qualitative comparison between models, it *does not* say anything about the quality of the models themself. So after selecting a model with the AIC, you need to validate the quality of the model. This can be done for instance by checking the models residuals.\n", "\n", "### Simple usage of AIC values\n", "Let $\\mathrm{AIC}_{min}$ be the minimal AIC value. The following expression can be used to compare different AIC scores ($\\mathrm{AIC}_{i}$) with $\\mathrm{AIC}_{min}$.\n", "\n", "$$c = e^{\\frac{\\mathrm{AIC}_{min} - \\mathrm{AIC}_{i}}{2}} \\tag{2.2}$$\n", "This quantity $c$ is proportional to the probability of that the model $\\mathrm{AIC}_{i}$ minimizes the information loss.\n", "Say you have three models with the following values: $\\mathrm{AIC}_1 = 101$, $\\mathrm{AIC}_2 = 104$ and $\\mathrm{AIC}_3 = 111$.\n", "\n", "[//]: # \"'vo!!!!!!!\"\n", "\\begin{equation}\n", "c = \n", "\\begin{cases}\n", "e^{\\frac{101 - 104}{2}} \\approx 0.223 \\\\\n", "e^{\\frac{101 - 111}{2}} \\approx 0.007\\\\\n", "\\end{cases}\n", "\\end{equation}\n", "This means that model 2 is 0.223 times and model 3 is 0.007 times as probable as model 1 to minimize the information loss. Depending on the selection criteria, model 3 can probably be rejected. The quantity $c$ is known as the relative likelihood of model $i$ and it is closely related to the likelihood ratio used in the likelihood-ratio test.\n" ] }, { "cell_type": "markdown", "id": "e0110127-378a-473b-a39d-e303dd9cc40e", "metadata": {}, "source": [ "## Bayesian Information Criterion (BIC)\n" ] }, { "cell_type": "markdown", "id": "a095843e", "metadata": {}, "source": [ "The $\\textbf{Bayesian Information Criterion (BIC)}$ is another statistical measure used to evaluate how good of a fit a model is. As with the AIC, both unexplained variation and a higher number of variables increase the BIC value. However, in addition to the penalty for the number of parameters in the AIC, the BIC also penalises for the amount of data points n. The equation for the BIC is as follows:\n", "\n", "$$ \\mathrm{BIC} = -2\\ln(\\hat{\\mathcal{L}}) + \\ln(n)p_k \\tag{2.3}$$\n", "\n", "where $\\hat{\\mathcal{L}}$ is the maximum likelihood, $n$ is the number of data points and $p_k$ is the number of parameters.\n", "\n", "\n", "One of the advantages of using the Bayesian Information Criterion is that it's fairly simple and therefore easy to compute. Its penalty for the amount of parameters also helps preventing overfitting and using the BIC to compare models is very straightforward in general.\n", "Of course, the BIC also has its disadvantages. One important limitation to the BIC is that $n$ has to be much larger than $p_k$ for the expression to be valid. It also relies on assuming that the true model is one of the candidate models, and the same penalty for the number of parameters that helps prevent overfitting might also lead to oversimplification.\n", "\n", "Let's see a simple example of using the Bayesian Information Criterion below. We'll compare some model A and B for a dataset of 600 data points and we assume the maximum likelihood is 0.5 for model A and 0.3 for model B. Furthermore, model A uses 3 parameters while model B uses 4.\n", "$$\n", "\\begin{cases}\n", " \\text{BIC}_A = -2\\ln{0.5} + \\ln(600) * 3 \\approx 20.6\\\\\n", " \\text{BIC}_B = -2\\ln{0.3} + \\ln(600) * 4 \\approx 28.0\n", "\\end{cases}\n", "$$\n", "\n", "Since we want to minimalise the BIC value, the model with the lowest BIC (model A in the example) is assumed to be a better model than the one with a higher BIC. A little disclaimer: this does not necessarily mean that the model with the lowest BIC is a good fitting model objectively, it just means it explains the data better than the other model did. \n", "\n", "In the example above, we just assumed that the maximum likelihoods were equal to certain numbers, but normally you would need to calculate the likelihood yourself. [Chapter 1](https://bayesian-statistics-for-astrophysics-2024.readthedocs.io/en/latest/lecture_notes/group1/Chapter%201.html) contains more information about calculating the maximum likelihood. \n", "\n" ] }, { "cell_type": "markdown", "id": "36af75ab-c2f7-4c6f-a500-e3dfc2bdfd77", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## AIC vs BIC \n", "Though the Akaike Information Criterion and the Bayesian Information Criterion are pretty similar, they also have their differences. As mentioned above, the AIC assumes the true model isn't among the tested models, while the BIC assumes the true model $\\textit{is}$ among the tested models. Furthermore, the BIC penalises the complexity of the models more than the AIC does. Both of these differences lead towards the following; When $n \\rightarrow \\infty$ and $p_k < \\sqrt{n}$:\n", "\n", "+ AIC selects the best predictive model among a number of possibly misspecified models.\n", "+ BIC selects the true model (with minimal number of necessary parameters) if it is included in the candidate set.\n", "\n", "The example below shows the AIC plotted against the BIC. Random data is generated from the true model, in this case a polynomial with 4 parameters. For the maximum likelihood the Gaussian probability density function is used $\\hat{\\mathcal{L}}= \\frac{1}{\\sqrt{2\\pi}\\sigma} e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}}$. Taking the natural logarithm together with the definition of the log likelihood function given in [Chapter 1](https://bayesian-statistics-for-astrophysics-2024.readthedocs.io/en/latest/lecture_notes/group1/Chapter%201.html) gives the following equation for $\\ln(\\hat{\\mathcal{L}})$:\n", "\n", "\n", "$$ \\ln(\\hat{\\mathcal{L}}) = \\sum_i -\\frac{(x_i - \\mu)^2}{2\\sigma^2} \\tag{2.4}$$\n", "For simplicity the prefactor of the Gaussian function is left out in [Eq. 2.4](#eq:Gauss), because it is a constant.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "18f263b9-bf1d-48d9-aee3-b7c57b300a21", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "#IMPORTS AND FUNCTIONS\n", "import numpy as np\n", "from scipy.optimize import curve_fit\n", "import matplotlib.pyplot as plt\n", "from scipy.special import logsumexp\n", "\n", "#The true polynomial model\n", "true_values = [20, 3, 50, 101]\n", "def true_model(x, a=true_values[0], b=true_values[1], c=true_values[2], d=true_values[3]):\n", " return a*x**3 + b*x**2 + c*x + d\n", "\n", "#Function to generate different degrees of polynomial functions\n", "def poly_model(x, *p):\n", "\treturn np.polyval(p, x)\n", "\n", "#Function to simulate data using the true model\n", "def sim_data(x, uncertainty=0.2):\n", " y_true = model(x)\n", " y_unc_true = np.abs(y_true)*uncertainty\n", " y_sample = np.random.normal(y_true, y_unc_true, size=len(x))\n", " return y_sample, y_unc_true\n", "\n", "#The likelihood function assuming it is a Gaussian distribution\n", "def log_gaussian_likelihood(model, y, y_err):\n", " L = np.sum(-0.5*((model-y)**2)/y_err**2)\n", " return L\n", "\n", "#The functions for AIC & BIC\n", "def AIC(log_L_max, p_k):\n", " aic = -2*log_L_max + 2*p_k\n", " return aic\n", "\n", "def BIC(log_L_max, p_k, n):\n", " bic = -2*log_L_max + np.log(n)*p_k\n", " return bic\n" ] }, { "cell_type": "code", "execution_count": 3, "id": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Setting amount of data points\n", "xmin = 0\n", "xmax = 10\n", "npoints = 101\n", "xx = np.linspace(xmin, xmax, npoints)\n", "\n", "#Choosing the model & simulating the data\n", "model = true_model\n", "yy, y_err = sim_data(xx)\n", "\n", "#Setting maximum number of parameters\n", "max_params = 10\n", "params = np.arange(1, max_params+1, 1)\n", "model = poly_model\n", "\n", "#Plotting the simulated data and true model\n", "plt.figure()\n", "plt.errorbar(xx, yy, y_err, fmt='s', label='simulated data', zorder=1)\n", "plt.plot(xx, true_model(xx), label=\"true model\", zorder=2, color = '#de8f05')\n", "plt.xticks(params)\n", "plt.legend()\n", "plt.style.use(\"seaborn-v0_8-colorblind\")\n", "plt.show()\n", "\n", "#Calculating the likelihood and aic&bic the different amounts of parameters\n", "aic = []\n", "bic = []\n", "for i in params:\n", " p0 = np.zeros(i)\n", " popt, pcov = curve_fit(model, xx, yy, p0=p0, sigma=y_err, absolute_sigma = False)\n", " pcov = np.sqrt(np.diag(pcov))\n", " log_L = log_gaussian_likelihood(model(xx, *popt), yy, y_err)\n", " aic.append(AIC(log_L, len(popt)))\n", " bic.append(BIC(log_L, len(popt), npoints))\n", "\n", "#Plotting the results\n", "plt.figure()\n", "plt.subplot(1, 2, 1)\n", "plt.plot(params, aic, marker=\"o\", label=\"AIC\")\n", "plt.plot(params, bic, marker=\"o\", label=\"BIC\", color='#d55e00')\n", "plt.xlabel(\"Number of parameters\")\n", "plt.xticks(params)\n", "plt.title(\"AIC and BIC values\")\n", "plt.legend()\n", "plt.subplot(1, 2, 2)\n", "plt.plot(params[2:], aic[2:], marker=\"o\", label=\"AIC\")\n", "plt.plot(params[2:], bic[2:], marker=\"o\", label=\"BIC\", color='#d55e00')\n", "plt.xlabel(\"Number of parameters\")\n", "plt.xticks(params[2:])\n", "plt.title(\"Zoomed in AIC and BIC values\")\n", "plt.legend()\n", "plt.style.use(\"seaborn-v0_8-colorblind\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "35475b08-c17c-45f4-8213-d5a94a74a358", "metadata": {}, "source": [ "The resulting plot shows that the best fit model has 4 parameters, which of course is the right amount of parameters.\n", "\n", "For the above simulation, we only calculated the likelihood once. In order to get the maximum likelihood, we will simulate the calculations multiple times, of which the maximum likelihood will be selected and used." ] }, { "cell_type": "code", "execution_count": 23, "id": "be5a2797-814b-45d0-9bba-a99396e2b8d0", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Simulate maximum likelihood estimation 101 times to find the maximum likelihood\n", "N_sim = 101\n", "aic = []\n", "bic = []\n", "for i in params:\n", " p0 = np.zeros(i)\n", " L = []\n", " for t in range(N_sim):\n", " model = true_model\n", " y, yerr = sim_data(xx)\n", " model = poly_model\n", " popt, pcov = curve_fit(model, xx, y, p0=p0, sigma=yerr, absolute_sigma = False)\n", " log_L = log_gaussian_likelihood(model(xx, *popt), y, yerr)\n", " L.append(log_L)\n", " #np.min is used to find the maximum likelihood. The logarithm is taken of the likelikhood, so the least negative log likelihood corresponds to \n", " #the highest likelihood.\n", " aic.append(AIC(np.min(L), len(popt)))\n", " bic.append(BIC(np.min(L), len(popt), npoints))\n", "\n", "#Plotting the results\n", "plt.figure()\n", "plt.subplot(1, 2, 1)\n", "plt.plot(params, aic, marker=\"o\", label=\"AIC\")\n", "plt.plot(params, bic, marker=\"o\", label=\"BIC\", color='#d55e00')\n", "plt.xlabel(\"Number of parameters\")\n", "plt.xticks(params)\n", "plt.title(\"AIC and BIC values\")\n", "plt.legend()\n", "plt.subplot(1, 2, 2)\n", "plt.plot(params[2:], aic[2:], marker=\"o\", label=\"AIC\")\n", "plt.plot(params[2:], bic[2:], marker=\"o\", label=\"BIC\", color='#d55e00')\n", "plt.xlabel(\"Number of parameters\")\n", "plt.xticks(params[2:])\n", "plt.title(\"Zoomed in AIC and BIC values\")\n", "plt.legend()\n", "plt.style.use(\"seaborn-v0_8-colorblind\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7d917efd-c47c-46b5-a268-fbc82c9f9c31", "metadata": {}, "source": [ "The above plot also shows the right amount of parameters. If you try running the code, there is a good chance that the lowest AIC and BIC values won't be at 4 parameters, because of the likelihood function. Below the same calculation is done as for the plot above, but now multiple times to find the parameter which correspond to the lowest AIC and BIC values. " ] }, { "cell_type": "code", "execution_count": 31, "id": "91a71f64-4ebe-4da6-a343-b84646a0484b", "metadata": {}, "outputs": [], "source": [ "#Simulating the calculations 101 times. In every simulation, the values are calculated 101 times.\n", "#so if you run this code, it will take quite a long time\n", "\n", "sim = 101\n", "sim_range = np.arange(1, test+1, 1)\n", "min_aic = []\n", "min_bic = []\n", "\n", "for n in sim_range: \n", " N_sim = 101\n", " aic = []\n", " bic = []\n", " for i in params:\n", " p0 = np.zeros(i)\n", " L = []\n", " for t in range(N_sim):\n", " model = true_model\n", " y, yerr = sim_data(xx)\n", " model = poly_model\n", " popt, pcov = curve_fit(model, xx, y, p0=p0, sigma=yerr, absolute_sigma = False)\n", " log_L = log_gaussian_likelihood(model(xx, *popt), y, yerr)\n", " L.append(log_L)\n", " aic.append(AIC(np.min(L), len(popt)))\n", " bic.append(BIC(np.min(L), len(popt), npoints))\n", " min_aic.append(np.argmin(aic)+1)\n", " min_bic.append(np.argmin(bic)+1)" ] }, { "cell_type": "code", "execution_count": 32, "id": "ecf4f1c6-4057-4ab1-8d54-3b6a951f3612", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plotting the results\n", "plt.figure()\n", "plt.hist(min_aic, bins=params, align=\"left\", alpha=0.5, label=\"AIC\", edgecolor='#0173b2', hatch=\"///\")\n", "plt.hist(min_bic, bins=params, align=\"left\", alpha=0.5, color=\"#d55e00\", label=\"BIC\", edgecolor=\"#d55e00\")\n", "plt.axvline(x=4, label=\"True value\", color=\"black\", linestyle=\"--\")\n", "plt.xlabel(\"Number of parameters\")\n", "plt.ylabel(\"Frequency\")\n", "plt.xticks(params)\n", "plt.title(\"Outcomes multiple runs\")\n", "plt.legend()\n", "plt.style.use(\"seaborn-v0_8-colorblind\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8a252d10-2739-4b6c-99f7-18620cea2ac2", "metadata": {}, "source": [ "For this specific example, the BIC has a sharper peak in the frequency of finding the correct value than the AIC has. The plot also shows that both the AIC and BIC agree on 4 as the correct number of parameters most of the times. " ] }, { "cell_type": "markdown", "id": "bf65de41", "metadata": {}, "source": [ "## Bootstrap and confidence intervals" ] }, { "cell_type": "markdown", "id": "d0f379ed", "metadata": {}, "source": [ "The bootstrap method is a technique used to estimate a confidence interval ([Chapter 1](https://bayesian-statistics-for-astrophysics-2024.readthedocs.io/en/latest/lecture_notes/group1/Chapter%201.html)) for a parameter which inherently does not have a confidence interval. This is a powerful method since we do not need to know the distribution from which the data has been drawn." ] }, { "cell_type": "markdown", "id": "74fadb0d", "metadata": {}, "source": [ "### Bootstrap method" ] }, { "cell_type": "markdown", "id": "58702acf", "metadata": {}, "source": [ "Suppose you have a dataset with a large number of entries and you want to use Bayesian statistics to further develop a posterior likelihood. You need to have some distribution of your parameter which you can use later on, but you only have one dataset and thus one way to compute the parameter. The $\\textbf{bootstrap method}$ provides a way to develop a confidence interval for this parameter. It creates a new dataset from the original one with replacement, we do this by randomly selecting an entry from the dataset and putting it in our new dataset. In this way the new dataset is build up by a population of the original dataset. This specific bootstrap method is known as the $\\textbf{nonparametric bootstrap}$. The counterpart is the $\\textbf{parametric bootstrap}$, here we use the most likely parameter estimates from the original dataset to construct a new dataset. From there we find a most likely parameter and return this value. The parametric bootstrap fails if the original dataset is misspecified. However, the nonparametric bootstrap essentially always works!\n", "\n", "The bootstrap algorithm works as follows:\n", "\n", "- Step 1: Simulate $B \\in \\mathbb{N}$ independent datasets $Y_{1,b}, ..., Y_{n,b}$ from the true distribution, for $b = 1, ..., N$. Thus simulating $B$ bootstrap samples.\n", "- Step 2: For each $b$, compute the parameter $\\hat{\\theta_b}$\n", "- Step 3: Define your $\\gamma$-confidence interval with the quantiles $\\hat{q}_{\\alpha/2}$ and $\\hat{q}_{1-\\alpha/2}$ for each parameter $\\hat{\\theta_1}, ..., \\hat{\\theta_B}$\n", "- Step 4: Define your confidence intervals\n", "\n", "$$(\\hat{\\theta}_l, \\hat{\\theta}_u) = (\\hat{q}_{\\alpha/2}, \\hat{q}_{1-\\alpha/2})$$\n", "\n", "The next question we need to consider is the amount of bootstrap samples we need to use, thus how large does $B$ need to be to get the quantile estimates $\\hat{q}_{\\alpha/2},\\hat{q}_{1-\\alpha/2}$ to be stable. From multiple sources you can gather that finding a precise bootstrap sample size is not an exact science. Many say that 10.000 is a safe bet and thus this size. While many sources also mention that a sample size of 10.000 is also a very intense workload so for a quick test a sample size of 500 is all you need. So the question is how good you want your resolution to be, for a quick look into the confidence interval a sample of size of 500 is great and for an exact interval a sample size of 10.000 is recommend given your system can handle it. " ] }, { "cell_type": "code", "execution_count": 27, "id": "de8b22e2", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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3dZ6hQ4dCq9U+89xarVYeLtHr9bhz5w5yc3PRpEmTZ8bv6emJWrVqyfV58OBBaLVaTJo0CSkpKYiLiwPwqOemRYsWBQ41GetZ79fC3L59GwAMjn1c2bJlER0djW3btmHWrFkoX7680beLT5kyBVWrVsWQIUMKLaPRaDB8+HDs2rULERERiIuLw/Hjx9GrVy+597Uod2bevn0bM2bMwPTp0/O9d4tizZo1+OabbzBhwgTUqFHjuc5VpkwZPHz4MN8wzpMe783KyMjArVu3EBISAiEEYmJi8pV/9913DZ5v374dWq1W7iHMM2HCBAgh8Ouvvxb5NbzzzjsGz1u2bInbt2/Lf2d5nwtPXtuUnurRo0ejQ4cOaN++vcnxPXz4EPb29vm2Ozg4yPtLGg5LWVheN979+/eNKn/9+nVoNBpUr17dYHuFChXg4eGR78P2yUQAePTHfvfuXZNjzTv3k42Np6dnvsY6Li4Of//9d6EN3Y0bN54aZ9758uLM+9B42q2lN2/eRGpqKpYtW4Zly5YZdV1jPSu+pzG1LgICAvKVKV++PNq2bYv169fL3cXr1q2DjY0NevToIZfT6/VYuHAhvv76a1y9ehU6nU7eV65cuWfGaoybN2/iwYMHCAwMzLevdu3a0Ov1SEhIQJ06dZ76mgqzevVqzJ8/H+fPn0dOTo5J52jZsqXc0O/fvx9NmjRBkyZNULZsWezfvx/e3t44efIk+vbta3Q8BXme9wMAgzkYj7Ozs5Pn43Tu3Blt27ZF8+bN4eXlhc6dOxd6vj///BPff/89du3a9cz5KLNmzcKtW7fw2Wef4ZNPPgEAtG/fHoMHD8aSJUueOixdmGnTpqFs2bIYNWqUycc+af/+/Rg8eDDCw8Pl4ebnkVfXz0pm4+PjMWPGDPz3v//N93u8d++ewXMbG5t8c8euX78OX1/ffP+o1q5dW95fVE97v7m5ucmfC0/Osyrob7Qg69atw6FDh3D69Okixefo6FjgekKZmZny/pKGyY2Fubm5wdfX1+Q3lbH/dRb233Jhjau56PV6tGvXDpMnTy5wf82aNQ2emyPOvMm5b731Fvr3719gmfr16xt9vsc9T3ym1kVhDcEbb7yBgQMHIjY2Fg0bNsT69evRtm1bgzkJc+fOxfTp0zFo0CDMnj0bZcuWhUajwdixYw0mLxc3Yxu3H374AQMGDEC3bt0wadIkeHl5QavVIjIyEpcvX37m8S1atMDy5ctx5coV7N+/Hy1btoQkSWjRogX2798PX19f6PV6g97Moijq+yEvwbx79+5TJ1bnCQkJgY+PD3788cenJjeTJ09Gy5YtERAQIN8AkLc+SVJSEuLj4+UPSDs7O6xYsQIff/wxLl68CG9vb9SsWRN9+/Yt8B+nZ4mLi8OyZcsQFRWFf//9V96emZmJnJwcXLt2DW5ubihbtuwzz3Xy5Em8+uqrqFu3LjZu3Agbm+f/CLp79y6cnJye+h7U6XRo164d7ty5gylTpqBWrVpwdnZGYmIiBgwYkO9v5/EeUlMV1nY//o/Ikyzdjk+aNAk9e/aEnZ2d/P7Jm8SekJCA7Ozsp87X8/HxQWJiYr7tSUlJAGDSXL/iwuSmGHTu3BnLli3D4cOHERwc/NSyVapUgV6vR1xcnPwfAfBoIm1qaqp8d4sl5J07Li7OYDji5s2b+f7TqVatGtLT042+K+RZ8q73tCQw7y4BnU5ntuuaorBGy1x10a1bNwwfPlwemrp48SIiIiIMymzcuBFt2rTBN998Y7A9NTX1uSdm5vH09ISTkxMuXLiQb9/58+eh0WiKPHlw48aNqFq1KjZv3mxQn09OpC5MXtISHR2No0ePYurUqQAeTR5evHgxfH194ezsjMaNGz/1PM8zZPU0tWrVAgBcvXrV6Em3mZmZ+XoOnhQfH4/r168X2Lv16quvwt3dPd8dV97e3vKkd51Oh71796Jp06Ym99wkJiZCr9dj9OjR+YZFgEc9bmPGjHnmHVSXL1/GK6+8Ai8vL2zfvr1IPUgFuXr1qkFbWZBTp07h4sWLWL16Nfr16ydvN2URuipVquD333/H/fv3DXpvzp8/L+8H/tfr8uTv43l6dvI+Fy5fvmzQW1PQ32hBEhISsGbNGqxZsybfvkaNGqFBgwaIjY0t9PiGDRtiz549SEtLM5hUfOTIEXl/ScM5N8Vg8uTJcHZ2xpAhQ5CSkpJv/+XLl7Fw4UIAQMeOHQEgX0PxxRdfAIDJs+NNERYWBltbW3z55ZcG/zEU1Gj16tULhw8fxs6dO/PtS01NRW5urknX9vT0RKtWrfDtt98iPj7eYF9eLFqtFq+99ho2bdpUYBJUlJVeTeHs7FzgLbvmqgsPDw+Eh4dj/fr1WLt2Lezs7NCtWzeDMlqtNt9/cxs2bCjwv6qi0mq1aN++PX766SeDZQJSUlKwZs0atGjRIt9dE6acGzD8j/TIkSM4fPiwUccHBASgYsWKWLBgAXJyctC8eXMAj5Key5cvY+PGjWjWrNkzewScnZ0BGH8LtrEaN24MOzu7fKsGZ2RkFDgnZNOmTbh7967BqtA5OTk4f/68/F8x8Oi29C1bthj85A0RzZs3Dz/++ONT45o3bx6SkpLkuXumqFu3br5rb9myBXXq1EHlypWxZcsWDB48WC4fHx8vf+DnSU5ORvv27aHRaLBz506zzNvJc+LEiWfeiVrQ+04IIbe7xujYsSN0Op28LEOeBQsWQJIkdOjQAcCj3vry5cvnm2v39ddfG32tJ+Wd+/ElD4CC2+aCFPT7y5vL99133xnc6XXr1i2cP3/e4P36+uuvQ6fTGUwHyMrKwsqVK9G0adOSd6cU2HNTLKpVq4Y1a9agd+/eqF27Nvr164e6desiOzsbhw4dwoYNG+S1Vxo0aID+/ftj2bJlSE1NRWhoKP766y+sXr0a3bp1Q5s2bSwWp6enJyZOnIjIyEh07twZHTt2RExMDH799dd8vQKTJk3Cf//7X3Tu3Fm+9TwjIwOnTp3Cxo0bce3aNZN7Ev7v//4PLVq0QKNGjTBs2DC5C/6XX36R/6v45JNPsGfPHjRt2hRDhw5FUFAQ7ty5gxMnTuD333/HnTt3zFUd+TRu3BiLFy/GnDlzUL16dXh5eeHll182a1307t0bb731Fr7++muEh4fnW4uic+fOmDVrFgYOHIiQkBCcOnUKP/74o0FPmznMmTNHXsL/vffeg42NDZYuXYqsrCx89tlnRT5v586dsXnzZnTv3h2dOnXC1atXsWTJEgQFBRk9sbZly5ZYu3Yt6tWrJ/+X3KhRIzg7O+PixYtGzbfJ69kZPXo0wsPDodVq8cYbbxT5deVxcHBA+/bt8fvvv2PWrFny9ri4OISFhaF3796oVasWNBoNjh07hh9++AH+/v4G61wlJiaidu3a6N+/v7xWSkGTQPMSs9DQUIPk6IcffsCmTZvQqlUruLi44Pfff8f69esxZMgQvPbaawbnGDBgAFavXo2rV68arHH0uPLly+dLsoH/fbA+ua9fv374448/DBKJV155BVeuXMHkyZNx4MABHDhwQN7n7e2Ndu3ayc/37dsnJwY3b95ERkYG5syZA+BRD93jt/gfP34cd+7cQdeuXQuMPU+tWrVQrVo1TJw4EYmJiXBzc5MTS2N16dIFbdq0wQcffIBr166hQYMG+O233/DTTz9h7NixBvNhhgwZgk8++QRDhgxBkyZNsG/fPly8eNHoaz2pYcOG6NOnD77++mvcu3cPISEh2LVrFy5dumTU8QX9/vLa1A4dOhi0T4sWLcJHH32EPXv2yEsUNG3aFD179kRERARu3LiB6tWrY/Xq1bh27Vq+XuQSo7hvz1KzixcviqFDhwp/f39hZ2cnXF1dRfPmzcWXX34pMjMz5XI5OTnio48+EgEBAcLW1lb4+fmJiIgIgzJCPLqtuVOnTvmuExoaanD7pLG3ggvx6FbSjz76SPj4+AhHR0fRunVrcfr06QJXKL5//76IiIgQ1atXF3Z2dqJ8+fIiJCREzJs3T/6Kg6et+IoCbmE8ffq06N69u/Dw8BAODg4iMDBQTJ8+3aBMSkqKGDFihPDz8xO2traiQoUKom3btmLZsmX5rvGkwm4Ff3KV1z179ggABiurJicni06dOglXV1cBwKCOn7cu8qSlpQlHR0cBQPzwww/59mdmZooJEybIv5/mzZuLw4cPF/o7L+qt4EIIceLECREeHi5cXFyEk5OTaNOmjTh06JBBmcLqrzB6vV7MnTtXVKlSRdjb24sXXnhB/Pzzz6J///6iSpUqRp3jq6++EgDEu+++a7A9LCyswNVqC6qL3NxcMWrUKOHp6SkkSZJvCzf1/VqQzZs3C0mS5CUAhBDi5s2bYtiwYaJWrVrC2dlZ2NnZiRo1aoixY8fmuxU3L4ZnrQheWN0fOXJEtGrVSpQpU0Y4ODiIBg0aiCVLlhT4FQWvvfaacHR0FHfv3n3m63pSYbeCh4aG5rvNHo/d/v7kz5O3eufdolzQz5P1P2XKFFG5cmWjvn7h7NmzIiwsTLi4uIjy5cuLoUOHipMnT+Z7b/Tv3184OzsXeI779++LcePGCV9fX2Fraytq1KghPv/883zXf/DggRg8eLBwd3cXrq6uolevXvJSBgXdCv7ke6Cgtvnhw4di9OjRoly5csLZ2Vl06dJFJCQkmLxC8bOunbf9yVWlHz58KCZOnCgqVKgg7O3txYsvvih27Nhh8nWLiySEhWeeEhGpiE6nQ1BQEHr16mXSQmnW4O3tjX79+uHzzz+3digmy8rKgr+/P6ZOnWrQ80UEcM4NEZFZabVazJo1C1999ZXRQ23WcObMGTx8+BBTpkyxdihFsnLlStja2uZbI4YIANhzQ0RERIrCnhsiIiJSFCY3REREpChMboiIiEhRmNwQERGRoqhuET+9Xo9///0Xrq6uFluCnYiIiMxLCIH79+/D19f3md/9pbrk5t9//y2RS0UTERHRsyUkJDzzi2lVl9zkfeFZQkJCkb8fpzTSZevw99z9AID677eE1q7gb6ElIlICtnnKk5aWBj8/P4MvLi2M6pKbvKEoNzc31SU3LvaPvizQzc2Nf+hEpGhs85TLmCklnFBMREREisLkhoiIiBRFdcNSaiVpJJRr5CM/JiJSMrZ56sbkRiU0Nhr49wyydhhERMWCbZ66cViKiIiIFIU9NyohhIA+Rw8A0NhquIAhESka2zx1Y8+NSuhz9IiduRexM/fKf/BERErFNk/dmNwQERGRojC5ISIiIkVhckNERESKwuSGiIiIFIXJDRERESkKkxsiIiJSFK5zoxKSBHjU9ZIfExEpGds8dZOEEMLaQRSntLQ0uLu74969e3Bzc7N2OERERGQEUz6/2XNDpADShG0WOa+Y38Ui5yUisiTOuSEiIiJFYXKjErpsHY5H7MLxiF3QZeusHQ4RkUWxzVM3JjdERESkKExuiIiISFGY3BAREZGiMLkhIiIiRWFyQ0RERIrC5IaIiIgUhYv4qYQkAW6B5eTHRERKxjZP3ZjcqITGVosaAxpaOwwiomLBNk/dOCxFREREisLkhoiIiBSFw1IqocvW4e85+wAA9ae1gtZOa+WIiIgsh22eujG5URF9jt7aIRARFRu2eerFYSkiIiJSFCY3REREpChMboiIiEhRmNwQERGRojC5ISIiIkXh3VIqIUmAS4CH/JiISMnY5qkbkxuV0NhqETissbXDICIqFmzz1I3DUkRERKQoTG6IiIhIUTgspRK6bB1Of3YQAFB3cnMuRU5EisY2T92Y3KhIbkaOtUMgIio2bPPUi8NSREREpChMboiIiEhRmNwQERGRojC5ISIiIkXhhGIiKpQ0YZvFzi3md7HYuYlI3ZjcqIQkAU4VXeXHRERKxjZP3ZjcqITGVovaI1+ydhhERMWCbZ66cc4NERERKQqTGyIiIlIUDkuphD5bhzML/gQA1BnXDBouRU5ECsY2T92Y3KiEAJCdmik/JrI2S92JxbuwCGCbp3YcliIiIiJFYXJDREREisLkhoiIiBSFyQ0REREpCpMbIiIiUhTeLaUSEgAHL2f5MRGRkrHNUzcmNyqhsdOizrhm1g6DiKhYsM1TN6sOS0VGRuLFF1+Eq6srvLy80K1bN1y4cOGZx23YsAG1atWCg4MD6tWrh+3btxdDtERERFQaWDW5+eOPPzBixAj8+eefiI6ORk5ODtq3b4+MjIxCjzl06BD69OmDwYMHIyYmBt26dUO3bt1w+vTpYoyciIiISipJCFFiFm+8efMmvLy88Mcff6BVq1YFlunduzcyMjLw888/y9uaNWuGhg0bYsmSJc+8RlpaGtzd3XHv3j24ubmZLfaSTp+tw7mvjgIAao94kUuRK4ylVvstjbhCMQFs85TIlM/vEnW31L179wAAZcuWLbTM4cOHERYWZrAtPDwchw8fLrB8VlYW0tLSDH7USADIvJGBzBsZXIqciBSPbZ66lZjkRq/XY+zYsWjevDnq1q1baLnk5GR4e3sbbPP29kZycnKB5SMjI+Hu7i7/+Pn5mTVuIiIiKllKTHIzYsQInD59GmvXrjXreSMiInDv3j35JyEhwaznJyIiopKlRNwKPnLkSPz888/Yt28fKlWq9NSyFSpUQEpKisG2lJQUVKhQocDy9vb2sLe3N1usREREVLJZtedGCIGRI0diy5Yt2L17NwICAp55THBwMHbt2mWwLTo6GsHBwZYKk4iIiEoRq/bcjBgxAmvWrMFPP/0EV1dXed6Mu7s7HB0dAQD9+vVDxYoVERkZCQAYM2YMQkNDMX/+fHTq1Alr167FsWPHsGzZMqu9DiIiIio5rNpzs3jxYty7dw+tW7eGj4+P/LNu3Tq5THx8PJKSkuTnISEhWLNmDZYtW4YGDRpg48aN2Lp161MnIdOj5cftPBxg5+HApciJSPHY5qlbiVrnpjiodZ0bUjauc/M/XOeGSJlK7To3RERERM+LyQ0REREpSom4FZwsT5+jw4WlxwEAgcMbQ2PLpciJSLnY5qkbkxuVEAJ4kHhffkxEpGRs89SNyQ0RKYolJ1dzsjJR6cA5N0RERKQoTG6IiIhIUZjcEBERkaIwuSEiIiJF4YRiFbFxtrV2CERExYZtnnoxuVEJrZ0WDaa1snYYRETFgm2eunFYioiIiBSFyQ0REREpCoelVEKfo0PcylgAQI2BDbkUOREpGts8dWNyoxJCAOlXU+XHRERKxjZP3TgsRURERIrC5IaIiIgUhckNERERKQqTGyIiIlIUJjdERESkKLxbSkU0tsxliUg92OapF5MbldDaafHCrDbWDoOIqFiwzVM3JjdET5AmbLN2CERE9BzYZ0dERESKwp4bldDn6HD5x1MAgGpv1uNS5ESkaGzz1I3JjUoIAaRduC0/JiJSMrZ56sZhKSIiIlIUJjdERESkKExuiIiISFGY3BAREZGiMLkhIiIiRWFyQ0RERIrCW8FVQmunRePIttYOg4ioWLDNUzf23BAREZGiMLkhIiIiReGwlEroc3S4uv4sACCgVxCXIiciRWObp27suVEJIYDU0zeQevoGlyInIsVjm6duTG6IiIhIUZjcEBERkaIwuSEiIiJFYXJDREREisLkhoiIiBSFyQ0REREpCte5UQmNrQYNP2otPyYiUjK2eerG5EYlJEmC1o6LWBGROrDNUzems0RERKQo7LlRCX2uHvFbzgMAKnevBY0N81oiUi62eerG37ZKCL3A7RNJuH0iCULPtciJSNnY5qkbkxsiIiJSFCY3REREpChMboiIiEhRmNwQERGRojC5ISIiIkVhckNERESKwnVuVEJjq0H9D1rKj4mIlIxtnroxuVEJSZJg62Jn7TCIiIoF2zx1YzpLREREisKeG5XQ5+rxzy8XAQCVOtXkUuREpGhs89SNyY1KCL3AzT8TAQAVO9SwcjREpZM0YZtFzivmd7HIedWMbZ66MZUlIiIiRTFLcpOammqO0xARERE9N5OTm08//RTr1q2Tn/fq1QvlypVDxYoVcfLkSbMGR0RERGQqk5ObJUuWwM/PDwAQHR2N6Oho/Prrr+jQoQMmTZpk9gCJiIiITGHyhOLk5GQ5ufn555/Rq1cvtG/fHv7+/mjatKnZAyQiIiIyhck9N2XKlEFCQgIAYMeOHQgLCwMACCGg0+nMGx0RERGRiUxObnr06IG+ffuiXbt2uH37Njp06AAAiImJQfXq1U061759+9ClSxf4+vpCkiRs3br1qeX37t0LSZLy/SQnJ5v6MlRHY6NB3ckhqDs5hOs9EJHisc1TN5OHpRYsWAB/f38kJCTgs88+g4uLCwAgKSkJ7733nknnysjIQIMGDTBo0CD06NHD6OMuXLgANzc3+bmXl5dJ11UjSSPBvoyjtcMgIioWbPPUzeTk5vDhwxg7dixsbAwPHTVqFA4dOmTSuTp06CD3/JjCy8sLHh4eJh9HREREymdyX12bNm1w586dfNvv3buHNm3amCWoZ2nYsCF8fHzQrl07HDx48Klls7KykJaWZvCjRvpcPf7ZHod/tsdBn6u3djhERBbFNk/dTE5uhBCQJCnf9tu3b8PZ2dksQRXGx8cHS5YswaZNm7Bp0yb4+fmhdevWOHHiRKHHREZGwt3dXf7Ju9NLbYReIGV/PFL2x0PohbXDISKyKLZ56mb0sFTenBhJkjBgwADY29vL+3Q6Hf7++2+EhISYP8LHBAYGIjAwUH4eEhKCy5cvY8GCBfj+++8LPCYiIgLjx4+Xn6elpak2wSEiIlIDo5Mbd3d3AI96blxdXeHo+L+JWnZ2dmjWrBmGDh1q/gif4aWXXsKBAwcK3W9vb2+QiBEREZGyGZ3crFy5EgDg7++PiRMnWnwIylixsbHw8fGxdhhERERUQph8t9TMmTPNdvH09HRcunRJfn716lXExsaibNmyqFy5MiIiIpCYmIjvvvsOABAVFYWAgADUqVMHmZmZWLFiBXbv3o3ffvvNbDERERFR6WZycpOSkoKJEydi165duHHjBoQwnKhlyirFx44dM7jDKm9uTP/+/bFq1SokJSUhPj5e3p+dnY0JEyYgMTERTk5OqF+/Pn7//fdiu0uLiIiISj6Tk5sBAwYgPj4e06dPh4+PT4F3ThmrdevW+ZKjx61atcrg+eTJkzF58uQiX4+IiIiUz+Tk5sCBA9i/fz8aNmxogXDIUjQ2GgSNbSo/JiJSMrZ56mZycuPn5/fU3hYqmSSNBEdvF2uHQURULNjmqZvJ6WxUVBSmTp2Ka9euWSAcIiIioudjcs9N79698eDBA1SrVg1OTk6wtbU12F/QVzOQ9elz9Ujeew0AUKG1P7tpiUjR2Oapm8nJTVRUlAXCIEsTeoGkXVcBAN6tqlg5GiIiy2Kbp24mJzf9+/e3RBxEREREZmFycvP4ujMFqVy5cpGDISIiInpeJic3/v7+T13bxpRF/IiIiIjMzeTkJiYmxuB5Tk4OYmJi8MUXX+Djjz82W2BERERERWFyctOgQYN825o0aQJfX198/vnn6NGjh1kCIyIiIioKs90bFxgYiKNHj5rrdERERERFYnLPTVpamsFzIQSSkpLw4YcfokaNGmYLjMxLY6NBrfdelB8TESkZ2zx1Mzm58fDwyDehWAgBPz8/rF271myBkXlJGgnOfm7WDoOIqFiwzVM3k5ObPXv2GDzXaDTw9PRE9erVYWNj8umIiIiIzMrkbCQ0NNQScZCF6XP1uHEoAQDgFeLHbloiUjS2eepWpK6Wy5cvIyoqCufOnQMABAUFYcyYMahWrZpZgyPzEXqBxF8vAQA8m1WycjRERJbFNk/dTE5ld+7ciaCgIPz111+oX78+6tevjyNHjqBOnTqIjo62RIxERERERjO552bq1KkYN24cPvnkk3zbp0yZgnbt2pktOCIiIiJTmdxzc+7cOQwePDjf9kGDBuHs2bNmCYqIiIioqExObjw9PREbG5tve2xsLLy8vMwRExEREVGRmTwsNXToUAwbNgxXrlxBSEgIAODgwYP49NNPMX78eLMHSERERGQKk5Ob6dOnw9XVFfPnz0dERAQAwNfXFx9++CFGjx5t9gCJiIiITCEJIURRD75//z4AwNXV1WwBWVpaWhrc3d1x7949uLmpZ/VKoRdIv5YKAHDx94CkkZ5+gIpJE7ZZOwRSGTG/i7VDUBy2ecpjyue3yT03V69eRW5uLmrUqGGQ1MTFxcHW1hb+/v4mB0yWJ2kkuFYtY+0wiIiKBds8dTN5QvGAAQNw6NChfNuPHDmCAQMGmCMmIiIioiIzObmJiYlB8+bN821v1qxZgXdRUckgdHrcOJyAG4cTIHR6a4dDRGRRbPPUzeRhKUmS5Lk2j7t37x50Op1ZgiLz0+sEEv57EQBQrrEvtForB0REZEFs89TN5J6bVq1aITIy0iCR0el0iIyMRIsWLcwaHBEREZGpTO65+fTTT9GqVSsEBgaiZcuWAID9+/cjLS0Nu3fvNnuARERERKYwuecmKCgIf//9N3r16oUbN27g/v376NevH86fP4+6detaIkYiIiIio5nccwM8WrRv7ty55o6FiIiI6LmZ3HNDREREVJIxuSEiIiJFKdKwFJU+Gq2E6v0byI+JiJSMbZ66MblRCUmrgXut8tYOg4ioWLDNU7ciDUvl5ubi999/x9KlS+UF/f7991+kp6ebNTgiIiIiU5ncc3P9+nW88soriI+PR1ZWFtq1awdXV1d8+umnyMrKwpIlSywRJz0nodPjdmwyAKBcwwqQtJxuRUTKxTZP3Uz+bY8ZMwZNmjTB3bt34ejoKG/v3r07du3aZdbgyHz0OoHrG8/h+sZz0OuEtcMhIrIotnnqZnLPzf79+3Ho0CHY2dkZbPf390diYqLZAiMiIiIqCpN7bvR6fYFfkPnPP//A1dXVLEERERERFZXJyU379u0RFRUlP5ckCenp6Zg5cyY6duxoztiIiIiITGbysNT8+fMRHh6OoKAgZGZmom/fvoiLi0P58uXxn//8xxIxEhERERnN5OSmUqVKOHnyJNauXYu///4b6enpGDx4MN58802DCcZERERE1mBycpOZmQkHBwe89dZbloiHiIiI6LmYnNx4eXmhe/fueOutt9C2bVtoNFw7oDTQaCVU7VtXfkxEpGRs89TN5Mxk9erVePDgAbp27YqKFSti7NixOHbsmCViIzOStBqUqeeNMvW8uZgVESke2zx1M/k33r17d2zYsAEpKSmYO3cuzp49i2bNmqFmzZqYNWuWJWIkIiIiMlqR01lXV1cMHDgQv/32G/7++284Ozvjo48+MmdsZEZCp8fdUym4eyoFQqe3djhERBbFNk/dipzcZGZmYv369ejWrRsaNWqEO3fuYNKkSeaMjcxIrxO4suY0rqw5zaXIiUjx2Oapm8kTinfu3Ik1a9Zg69atsLGxweuvv47ffvsNrVq1skR8RERERCYxObnp3r07OnfujO+++w4dO3aEra2tJeIiIiIiKhKTk5uUlBR+hxQRERGVWEYlN2lpaXBzcwMACCGQlpZWaNm8ckRERETWYFRyU6ZMGSQlJcHLywseHh6QpPwLIgkhIElSgd8YTkRERFRcjEpudu/ejbJlywIA9uzZY9GAiIiIiJ6HUclNaGio/DggIAB+fn75em+EEEhISDBvdGQ2Gq2EKq/Xlh8TESkZ2zx1M3lCcUBAgDxE9bg7d+4gICCAw1IllKTVoHxjX2uHQURULNjmqZvJi/jlza15Unp6OhwcHMwSFBEREVFRGd1zM378eACAJEmYPn06nJyc5H06nQ5HjhxBw4YNzR4gmYfQ6ZEWdwcA4FajLL9IjogUjW2euhmd3MTExAB41HNz6tQp2NnZyfvs7OzQoEEDTJw40fwRklnodQKXVp8EADT8qDW0WuvGQ0RkSWzz1M3o5CbvLqmBAwdi4cKFXM+GiIiISiSTJxSvXLnSEnEQERERmYXJyQ0AHDt2DOvXr0d8fDyys7MN9m3evNksgREREREVhckzrNauXYuQkBCcO3cOW7ZsQU5ODs6cOYPdu3fD3d3dEjESERERGc3k5Gbu3LlYsGABtm3bBjs7OyxcuBDnz59Hr169ULlyZUvESERERGQ0k5Oby5cvo1OnTgAe3SWVkZEBSZIwbtw4LFu2zKRz7du3D126dIGvry8kScLWrVufeczevXvRqFEj2Nvbo3r16li1apWpL4GIiIgUzOTkpkyZMrh//z4AoGLFijh9+jQAIDU1FQ8ePDDpXBkZGWjQoAG++uoro8pfvXoVnTp1Qps2bRAbG4uxY8diyJAh2Llzp2kvQoU0Wgl+r9aE36s1uRQ5ESke2zx1M3lCcatWrRAdHY169eqhZ8+eGDNmDHbv3o3o6Gi0bdvWpHN16NABHTp0MLr8kiVLEBAQgPnz5wMAateujQMHDmDBggUIDw836dpqI2k18Ar2s3YYRETFgm2eupmc3CxatAiZmZkAgA8++AC2trY4dOgQXnvtNUybNs3sAT7u8OHDCAsLM9gWHh6OsWPHFnpMVlYWsrKy5OdpaWmWCo+IiIhKAJOTm7Jly8qPNRoNpk6dataAniY5ORne3t4G27y9vZGWloaHDx/C0dEx3zGRkZH46KOPiivEEkvoBdKvpQIAXPw9IGnYTUtEysU2T92MSm5M6e0oaSsXR0REyN+LBTx6LX5+6uuq1OfqcXH5CQD/fylyO65FTkTKxTZP3YxKbjw8PAr8JvDH5X1buE6nM0tgBalQoQJSUlIMtqWkpMDNza3AXhsAsLe3h729vcViIiIiopLFqOQm73ulrC04OBjbt2832BYdHY3g4GArRURE9PykCdssdm4xv4vFzk1UUhmV3ISGhlrk4unp6bh06ZL8/OrVq4iNjUXZsmVRuXJlREREIDExEd999x0A4J133sGiRYswefJkDBo0CLt378b69evxyy+/WCQ+IiIiKn1MXucGAPbv34+33noLISEhSExMBAB8//33OHDggEnnOXbsGF544QW88MILAIDx48fjhRdewIwZMwAASUlJiI+Pl8sHBATgl19+QXR0NBo0aID58+djxYoVvA2ciIiIZCbfLbVp0ya8/fbbePPNN3HixAn5Nut79+5h7ty5+YaNnqZ169YQQhS6v6DVh1u3bo2YmBhTwyYiIiKVMLnnZs6cOViyZAmWL18OW1tbeXvz5s1x4sQJswZHREREZCqTe24uXLiAVq1a5dvu7u6O1NRUc8REFiBpJFTsUF1+TESkZGzz1M3k5KZChQq4dOkS/P39DbYfOHAAVatWNVdcZGYaGw0qtKpi7TCIiIoF2zx1M3lYaujQoRgzZgyOHDkCSZLw77//4scff8TEiRPx7rvvWiJGIiIiIqOZ3HMzdepU6PV6tG3bFg8ePECrVq1gb2+PiRMnYtSoUZaIkcxA6AUeJD76Nneniq7spiUiRWObp24mJzeSJOGDDz7ApEmTcOnSJaSnpyMoKAguLi6Ffr8TWZ8+V4/zXx8FwKXIiUj52OapW5HWuQEAOzs7BAUF4aWXXoKtrS2++OILBAQEmDM2IiIiIpMZndxkZWUhIiICTZo0QUhICLZu3QoAWLlyJQICArBgwQKMGzfOUnESERERGcXoYakZM2Zg6dKlCAsLw6FDh9CzZ08MHDgQf/75J7744gv07NkTWi27/YiIShJLfW8Vv7OKSjKjk5sNGzbgu+++w6uvvorTp0+jfv36yM3NxcmTJ5/5jeFERERExcXoYal//vkHjRs3BgDUrVsX9vb2GDduHBMbIiIiKlGMTm50Oh3s7Ozk5zY2NnBxcbFIUERERERFZfSwlBACAwYMgL29PQAgMzMT77zzDpydnQ3Kbd682bwRkllIGgk+bQPkx0RESsY2T92MTm769+9v8Pytt94yezBkORobDXzD+PUYRKQObPPUzejkZuXKlZaMg4iIiMgsTF6hmEonoRfIvJkBAHDwdGY3LREpGts8dSvyCsVUuuhz9TgbdQRno45An6u3djhERBbFNk/dmNwQERGRojC5ISIiIkVhckNERESKwuSGiIiIFIXJDRERESkKkxsiIiJSFK5zoxKSRoJ3y8ryYyIiJWObp25MblRCY6NBpY41rB0GEVGxYJunbkxuqFSSJmyzdghERFRCMblRCaEXyL6XCQCwc3dgNy0RKRrbPHXjhGKV0OfqcfqzQzj92SEuRU5Eisc2T92Y3BAREZGiMLkhIiIiRWFyQ0RERIrC5IaIiIgUhckNERERKQqTGyIiIlIUrnOjEpJGgmezivJjIiIlY5unbkxuVEJjo0HlrrWsHQYRUbFgm6duHJYiIiIiRWHPjUoIIZCbkQMAsHG2hSSxm5aIlIttnrqx50Yl9Dl6/P3xfvz98X7oc7gUOREpG9s8dWNyQ0RERIrC5IaIiIgUhckNERERKQqTGyIiIlIU3i1FFiNN2GbtEIiISIXYc0NERESKwp4blZA0Eso18pEfExEpGds8dWNyoxIaGw38ewZZOwwiomLBNk/dOCxFREREisKeG5UQQsirdGpsNVyKnIgUjW2eujG5UQl9jh6xM/cCABp+1BpaO628j3c1EZHSPK3NI+XjsBQREREpCpMbIiIiUhQmN0RERKQoTG6IiIhIUZjcEBERkaIwuSEiIiJF4a3gKiFJgEddL/kxEZGSsc1TNyY3KqGx1aLam/WsHQYRUbFgm6duHJYiIiIiRWFyQ0RERIrC5EYldNk6HI/YheMRu6DL1lk7HCIii2Kbp26cc0NERCaz5HfSifldLHZuUgf23BAREZGiMLkhIiIiRWFyQ0RERIpSIpKbr776Cv7+/nBwcEDTpk3x119/FVp21apVkCTJ4MfBwaEYoyUiIqKSzOrJzbp16zB+/HjMnDkTJ06cQIMGDRAeHo4bN24UeoybmxuSkpLkn+vXrxdjxERERFSSWT25+eKLLzB06FAMHDgQQUFBWLJkCZycnPDtt98WeowkSahQoYL84+3tXYwRl06SBLgFloNbYDkuRU5Eisc2T92seit4dnY2jh8/joiICHmbRqNBWFgYDh8+XOhx6enpqFKlCvR6PRo1aoS5c+eiTp06BZbNyspCVlaW/DwtLc18L6AU0dhqUWNAQ2uHQURULNjmqZtVe25u3boFnU6Xr+fF29sbycnJBR4TGBiIb7/9Fj/99BN++OEH6PV6hISE4J9//imwfGRkJNzd3eUfPz8/s78OIiIiKjmsPixlquDgYPTr1w8NGzZEaGgoNm/eDE9PTyxdurTA8hEREbh37578k5CQUMwRExERUXGy6rBU+fLlodVqkZKSYrA9JSUFFSpUMOoctra2eOGFF3Dp0qUC99vb28Pe3v65Yy3tdNk6/D1nHwCg/rRW0NpprRwREZHlsM1TN6v23NjZ2aFx48bYtWuXvE2v12PXrl0IDg426hw6nQ6nTp2Cj4+PpcJUDH2OHvocvbXDICIqFmzz1Mvq3y01fvx49O/fH02aNMFLL72EqKgoZGRkYODAgQCAfv36oWLFioiMjAQAzJo1C82aNUP16tWRmpqKzz//HNevX8eQIUOs+TKIiIiohLB6ctO7d2/cvHkTM2bMQHJyMho2bIgdO3bIk4zj4+Oh0fyvg+nu3bsYOnQokpOTUaZMGTRu3BiHDh1CUFCQtV4CERERlSBWT24AYOTIkRg5cmSB+/bu3WvwfMGCBViwYEExREVERESlUam7W4qIiIjoaZjcEBERkaKUiGEpsjxJAlwCPOTHRERKxjZP3ZjcqITGVovAYY2tHQYRUbFgm6duHJYiIiIiRWFyQ0RERIrCYSmV0GXrcPqzgwCAupObcylyIlI0tnnqxuRGRXIzcqwdAhFRsWGbp14cliIiIiJFYXJDREREisLkhoiIiBSFyQ0REREpCpMbIiIiUhTeLaUSkgQ4VXSVHxMRKRnbPHVjcqMSGlstao98ydphEBEVC7Z56sbkhoiIShRpwjZrh2AyMb+LtUOgx3DODRERESkKe25UQp+tw5kFfwIA6oxrBg2XIiciBbMHsMHWAQDQMycTWdYNh4oZkxuVEACyUzPlx0RESiYB8JU08mNSFw5LERERkaIwuSEiIiJFYXJDREREisLkhoiIiBSFyQ0REREpCu+WUgkJgIOXs/yYiEjJBIDLer38mNSFyY1KaOy0qDOumbXDICIqFlkAeudmWjsMshIOSxEREZGisOemlCiN37VCRERkDey5UQl7AOtsHLDOxgH21g6GiMjC2OapG3tuVEICUE3DpciJSB3Y5qkbe26IiIhIUZjcEBERkaIwuSEiIiJFYXJDREREisLkhoiIiBSFd0uphADwr+BS5ESkDmzz1I3JjUpkAXg1h0uRE5E6sM1TNw5LERERkaIwuSEiIiJF4bCUmZXU74CyB7DM5tEi5MNys5Bl3XCIiCyquNs8S7b9Yn4Xi51bqZjcqIQEoI5GKz8mIlIytnnqxmEpIiIiUhQmN0RERKQoTG6IiIhIUZjcEBERkaIwuSEiIiJF4d1SKnJXcBFyIlIPtnnqxeRGJTIBtMt5aO0wiIiKBds8deOwFBERESkKkxsiIiJSFCY3KmEPYKmNPZba2MPe2sEQEVkY2zx145wblZAANOZS5ESkEmzz1I09N0RERKQoTG6IiIhIUZjcEBERkaIwuSEiIiJFYXJDREREisK7pVTkIZciJyIVYZv3dNKEbRY7t5jfxWLnNgaTG5XIBNCSS5ETkUqwzVM3DksRERGRojC5ISIiIkVhcqMSdgCibOwRZWMPO2sHQ0RkYWzz1I1zblRCA6DF/1+KnBktESkd2zx1Y3JDRERUglnyrialKhEJ7VdffQV/f384ODigadOm+Ouvv55afsOGDahVqxYcHBxQr149bN++vZgiJSIiopLO6snNunXrMH78eMycORMnTpxAgwYNEB4ejhs3bhRY/tChQ+jTpw8GDx6MmJgYdOvWDd26dcPp06eLOXIiIiIqiaye3HzxxRcYOnQoBg4ciKCgICxZsgROTk749ttvCyy/cOFCvPLKK5g0aRJq166N2bNno1GjRli0aFExR05EREQlkVWTm+zsbBw/fhxhYWHyNo1Gg7CwMBw+fLjAYw4fPmxQHgDCw8MLLU9ERETqYtUJxbdu3YJOp4O3t7fBdm9vb5w/f77AY5KTkwssn5ycXGD5rKwsZGVlyc/v3bsHAEhLS3ue0AuX9cAy531OAkD6/1+KXGRz1U4iUja2edZlic/YvHMKI75WQ/F3S0VGRuKjjz7Kt93Pz88K0VhPFoDW1g6CiKiYsM2zLvevLHfu+/fvw93d/allrJrclC9fHlqtFikpKQbbU1JSUKFChQKPqVChgknlIyIiMH78ePm5Xq/HnTt3UK5cOUiS9Jyv4JG0tDT4+fkhISEBbm5uZjknGWIdWx7r2LJYv5bHOrY8a9axEAL379+Hr6/vM8taNbmxs7ND48aNsWvXLnTr1g3Ao+Rj165dGDlyZIHHBAcHY9euXRg7dqy8LTo6GsHBwQWWt7e3h729vcE2Dw8Pc4Sfj5ubG/+gLIx1bHmsY8ti/Voe69jyrFXHz+qxyWP1Yanx48ejf//+aNKkCV566SVERUUhIyMDAwcOBAD069cPFStWRGRkJABgzJgxCA0Nxfz589GpUyesXbsWx44dw7Jly6z5MoiIiKiEsHpy07t3b9y8eRMzZsxAcnIyGjZsiB07dsiThuPj46HR/O+mrpCQEKxZswbTpk3D+++/jxo1amDr1q2oW7eutV4CERERlSBWT24AYOTIkYUOQ+3duzfftp49e6Jnz54Wjsp49vb2mDlzZr7hLzIf1rHlsY4ti/VreaxjyystdSwJY+6pIiIiIiolrL5CMREREZE5MbkhIiIiRWFyQ0RERIrC5IaIiIgUhcnNMyxevBj169eXFywKDg7Gr7/+atSxa9euhSRJ8gKFVLCi1HFqaipGjBgBHx8f2Nvbo2bNmti+fXsxRVz6FKWOo6KiEBgYCEdHR/j5+WHcuHHIzMwspohLt08++QSSJBksNlqQDRs2oFatWnBwcEC9evX4HjaBMXW8fPlytGzZEmXKlEGZMmUQFhaGv/76q/iCLOWMfR/nKUmfeUxunqFSpUr45JNPcPz4cRw7dgwvv/wyunbtijNnzjz1uGvXrmHixIlo2bJlMUVaeplax9nZ2WjXrh2uXbuGjRs34sKFC1i+fDkqVqxYzJGXHqbW8Zo1azB16lTMnDkT586dwzfffIN169bh/fffL+bIS5+jR49i6dKlqF+//lPLHTp0CH369MHgwYMRExODbt26oVu3bjh9+nQxRVp6GVvHe/fuRZ8+fbBnzx4cPnwYfn5+aN++PRITE4sp0tLL2DrOU+I+8wSZrEyZMmLFihWF7s/NzRUhISFixYoVon///qJr167FF5xCPK2OFy9eLKpWrSqys7OLOSpleVodjxgxQrz88ssG28aPHy+aN29eHKGVWvfv3xc1atQQ0dHRIjQ0VIwZM6bQsr169RKdOnUy2Na0aVMxfPhwC0dZuplSx0/Kzc0Vrq6uYvXq1ZYLUAFMreOS+JnHnhsT6HQ6rF27FhkZGYV+lxUAzJo1C15eXhg8eHAxRqcMxtTxf//7XwQHB2PEiBHw9vZG3bp1MXfuXOh0umKOtnQypo5DQkJw/PhxuQv/ypUr2L59Ozp27FicoZY6I0aMQKdOnRAWFvbMsocPH85XLjw8HIcPH7ZUeIpgSh0/6cGDB8jJyUHZsmUtEJlymFrHJfEzr0SsUFzSnTp1CsHBwcjMzISLiwu2bNmCoKCgAsseOHAA33zzDWJjY4s3yFLOlDq+cuUKdu/ejTfffBPbt2/HpUuX8N577yEnJwczZ84s5shLD1PquG/fvrh16xZatGgBIQRyc3PxzjvvcFjqKdauXYsTJ07g6NGjRpVPTk6Wv2Ymj7e3N5KTky0RniKYWsdPmjJlCnx9fYuUGKmFqXVcUj/z2HNjhMDAQMTGxuLIkSN499130b9/f5w9ezZfufv37+Ptt9/G8uXLUb58eStEWnoZW8fAo2+O9/LywrJly9C4cWP07t0bH3zwAZYsWVLMUZcuptTx3r17MXfuXHz99dc4ceIENm/ejF9++QWzZ88u5qhLh4SEBIwZMwY//vgjHBwcrB2OIj1vHX/yySdYu3YttmzZwt9RIUyt4xL9mWftcbHSqG3btmLYsGH5tsfExAgAQqvVyj+SJAlJkoRWqxWXLl2yQrSlU2F1LIQQrVq1Em3btjXYtn37dgFAZGVlFUd4ivC0Om7RooWYOHGiwbbvv/9eODo6Cp1OVxzhlSpbtmzJ97cPQP7bz83NzXeMn5+fWLBggcG2GTNmiPr16xdT1KVLUeo4z+effy7c3d3F0aNHizHi0sfUOi7Jn3kclioCvV6PrKysfNtr1aqFU6dOGWybNm0a7t+/j4ULF8LPz6+4Qiz1CqtjAGjevDnWrFkDvV4vf2P8xYsX4ePjAzs7u+IMs1R7Wh0/ePBArts8Wq0WACD4dXT5tG3bNt/f/sCBA1GrVi1MmTJFrrvHBQcHY9euXQa32UZHRz91Pp+aFaWOAeCzzz7Dxx9/jJ07d6JJkybFEWqpZWodl+TPPCY3zxAREYEOHTqgcuXKuH//PtasWYO9e/di586dAIB+/fqhYsWKiIyMhIODA+rWrWtwvIeHBwDk207/Y0odA8C7776LRYsWYcyYMRg1ahTi4uIwd+5cjB492povo0QztY67dOmCL774Ai+88AKaNm2KS5cuYfr06ejSpUuhHyJq5urqmu9v3NnZGeXKlZO3P1nHY8aMQWhoKObPn49OnTph7dq1OHbsGJYtW1bs8ZcGRanjTz/9FDNmzMCaNWvg7+8vz2dycXGBi4tL8b6AUsDUOi7Jn3lMbp7hxo0b6NevH5KSkuDu7o769etj586daNeuHQAgPj4+33+4ZBpT69jPzw87d+7EuHHjUL9+fVSsWBFjxozBlClTrPUSSjxT63jatGmQJAnTpk1DYmIiPD090aVLF3z88cfWegml3pN1HBISgjVr1mDatGl4//33UaNGDWzdutXqHwql2ZN1vHjxYmRnZ+P11183KDdz5kx8+OGHxRydMpSWzzxJsI+ZiIiIFKTkp19EREREJmByQ0RERIrC5IaIiIgUhckNERERKQqTGyIiIlIUJjdERESkKExuiIiISFGY3BCRUfz9/REVFWXtMJ5KCIFhw4ahbNmykCTJrN9UvHXrVlSvXh1ardbgKxOsYdWqVfJKsESUH1coJiLF2LFjB1atWoW9e/eiatWqZv2m4uHDh2PgwIEYPXo0XF1dzXZeIjI/JjdEpBiXL1+Gj48PQkJCzHre9PR03LhxA+Hh4fD19TXruYnI/DgsRaRwy5Ytg6+vL/R6vcH2rl27YtCgQQAeJQVdu3aFt7c3XFxc8OKLL+L3338v9JzXrl3LN+yTmpoKSZKwd+9eedvp06fRoUMHuLi4wNvbG2+//TZu3bol79+4cSPq1asHR0dHlCtXDmFhYcjIyCj0un/88Qdeeukl2Nvbw8fHB1OnTkVubi4AYMCAARg1ahTi4+MhSRL8/f0LPMft27fRp08fVKxYEU5OTqhXrx7+85//FHrNvXv3yj01L7/8ssFr3LRpE+rUqQN7e3v4+/tj/vz5BsdKkoStW7cabPPw8MCqVasM6nHz5s1o06YNnJyc0KBBAxw+fNjgmFWrVqFy5cpwcnJC9+7dcfv27ULjJSImN0SK17NnT9y+fRt79uyRt925cwc7duzAm2++CeBRz0THjh2xa9cuxMTE4JVXXkGXLl0QHx9f5Oumpqbi5ZdfxgsvvIBjx45hx44dSElJQa9evQAASUlJ6NOnDwYNGoRz585h79696NGjBwr7urvExER07NgRL774Ik6ePInFixfjm2++wZw5cwAACxcuxKxZs1CpUiUkJSXh6NGjBZ4nMzMTjRs3xi+//ILTp09j2LBhePvtt/HXX38VWD4kJAQXLlwA8CiZSUpKQkhICI4fP45evXrhjTfewKlTp/Dhhx9i+vTpcuJiig8++AATJ05EbGwsatasiT59+shJ25EjRzB48GCMHDkSsbGxaNOmjfyaiagQgogUr2vXrmLQoEHy86VLlwpfX1+h0+kKPaZOnTriyy+/lJ9XqVJFLFiwQAghxNWrVwUAERMTI++/e/euACD27NkjhBBi9uzZon379gbnTEhIEADEhQsXxPHjxwUAce3aNaNew/vvvy8CAwOFXq+Xt3311VfCxcVFfh0LFiwQVapUMep8j+vUqZOYMGFCofuffG1CCNG3b1/Rrl07g3KTJk0SQUFB8nMAYsuWLQZl3N3dxcqVK4UQ/6vHFStWyPvPnDkjAIhz584JIYTo06eP6Nixo8E5evfuLdzd3U14hUTqwp4bIhV48803sWnTJmRlZQEAfvzxR7zxxhvQaB41Aenp6Zg4cSJq164NDw8PuLi44Ny5c8/Vc3Py5Ens2bMHLi4u8k+tWrUAPBoGa9CgAdq2bYt69eqhZ8+eWL58Oe7evVvo+c6dO4fg4GBIkiRva968OdLT0/HPP/8YHZdOp8Ps2bNRr149lC1bFi4uLti5c6fJr/XcuXNo3ry5wbbmzZsjLi4OOp3OpHPVr19ffuzj4wMAuHHjhnydpk2bGpQPDg426fxEasMJxUQq0KVLFwgh8Msvv+DFF1/E/v37sWDBAnn/xIkTER0djXnz5qF69epwdHTE66+/juzs7ALPl5cUiceGkHJycgzKpKeno0uXLvj000/zHe/j4wOtVovo6GgcOnQIv/32G7788kt88MEHOHLkCAICAszxsgv0+eefY+HChYiKikK9evXg7OyMsWPHFvpan4ckSfmG2Z6sJwCwtbU1OAZAvjlSRGQ8JjdEKuDg4IAePXrgxx9/xKVLlxAYGIhGjRrJ+w8ePIgBAwage/fuAB4lJteuXSv0fJ6engAezZt54YUXACDfmjKNGjXCpk2b4O/vDxubgpsaSZLQvHlzNG/eHDNmzECVKlWwZcsWjB8/Pl/Z2rVrY9OmTRBCyAnAwYMH4erqikqVKhldFwcPHkTXrl3x1ltvAXiURFy8eBFBQUFGnyMvnoMHD+Y7d82aNaHVagE8qqekpCR5f1xcHB48eGDydY4cOWKw7c8//zTpHERqw2EpIpV488038csvv+Dbb7+VJxLnqVGjBjZv3ozY2FicPHkSffv2fWrPgaOjI5o1a4ZPPvkE586dwx9//IFp06YZlBkxYgTu3LmDPn364OjRo7h8+TJ27tyJgQMHQqfT4ciRI5g7dy6OHTuG+Ph4bN68GTdv3kTt2rULvOZ7772HhIQEjBo1CufPn8dPP/2EmTNnYvz48XJPkjFq1Kgh9xidO3cOw4cPR0pKitHH55kwYQJ27dqF2bNn4+LFi1i9ejUWLVqEiRMnymVefvllLFq0CDExMTh27Bjeeecdg14aY4wePRo7duzAvHnzEBcXh0WLFmHHjh0mx0ukKtad8kNExUWn0wkfHx8BQFy+fNlg39WrV0WbNm2Eo6Oj8PPzE4sWLRKhoaFizJgxcpnHJxQLIcTZs2dFcHCwcHR0FA0bNhS//fZbvkm3Fy9eFN27dxceHh7C0dFR1KpVS4wdO1bo9Xpx9uxZER4eLjw9PYW9vb2oWbOmwQTmguzdu1e8+OKLws7OTlSoUEFMmTJF5OTkyPuNmVB8+/Zt0bVrV+Hi4iK8vLzEtGnTRL9+/UTXrl0LPaagCcVCCLFx40YRFBQkbG1tReXKlcXnn39usD8xMVG0b99eODs7ixo1aojt27cXOKH4aROzhRDim2++EZUqVRKOjo6iS5cuYt68eZxQTPQUkhCF3HdJREREVApxWIqIiIgUhckNERERKQqTGyIiIlIUJjdERESkKExuiIiISFGY3BAREZGiMLkhIiIiRWFyQ0RERIrC5IaIiIgUhckNERERKQqTGyIiIlIUJjdERESkKP8P1mDTzGdChVoAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.optimize import curve_fit\n", "import random\n", "\n", "# Bootstrap exercise with sin(ax) as example\n", "a_true = 4\n", "b_true = 3\n", "\n", "x_min = 0\n", "x_max = 10\n", "N = 100\n", "x = np.linspace(x_min, x_max, N)\n", "\n", "def linear(x, a=a_true, b=b_true):\n", " return a*x + b\n", "\n", "model = linear\n", "y_samp, y_unc = sim_data(x)\n", "\n", "bootstrap_samples = 500\n", "\n", "a_s = []\n", "for i in range(bootstrap_samples):\n", " x_data = []\n", " y_data = []\n", " for i in range(N):\n", " temp = random.randint(0, (N-1))\n", " x_data.append(x[temp])\n", " y_data.append(y_samp[temp])\n", " popt, pcov = curve_fit(linear, x_data, y_data, absolute_sigma=True, maxfev=800)\n", " a_s.append(popt[0])\n", "\n", "# In our variable a_s we have a distribution of a's found by the bootstrap model.\n", "# Now we need to determine our gamma-confidence \n", "\n", "gamma = 95\n", "\n", "z = z_alpha(gamma)\n", "\n", "mean_a = np.mean(a_s)\n", "std_a = np.std(a_s)\n", "\n", "lower = mean_a - z*std_a\n", "higher = mean_a + z*std_a\n", "# Now that we have the confidence interval, all we need to do is plot it\n", "\n", "plt.hist(a_s, bins = 20, density=True)\n", "plt.axvline(lower, color='#cc78bc', linestyle=\"--\", label=f\"Lower limit {gamma}%\")\n", "plt.axvline(higher, color='#cc78bc', linestyle=\"--\", label=f\"Upper limit {gamma}%\")\n", "plt.title(f\"Confidence interval for a with ({lower.round(2)}, {higher.round(2)}) around {np.round(mean_a)}\")\n", "plt.ylabel(\"Relative counts\")\n", "plt.xlabel(\"values of a found\")\n", "plt.style.use(\"seaborn-v0_8-colorblind\")\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.19" } }, "nbformat": 4, "nbformat_minor": 5 }