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"cell_type": "markdown", + "id": "ed78ded5-0cd8-4b61-9866-c3b804ffcf9b", + "metadata": {}, + "source": [ + "## Random Samples\n", + "\n", + "Let's first randomly generate samples from a given distribution (normal or Gaussian, centered in zero with unit variance), then calculate summary statistics on these samples." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "cf7ba0e0-4068-42e7-8b5a-a871e9629e87", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "#number of samples\n", + "n = 1000\n", + "\n", + "# generate random samples\n", + "samples = stt.norm.rvs(size=n)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "ac6fd30c-8c07-48fa-859b-02b8b6e7b11a", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# variable range\n", + "vx = np.linspace(-3.0,3.0,50)\n", + "dx = np.diff(vx)[0]\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples, bins=vx)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx, stt.norm.pdf(x=vx)*n*dx)\n", + "\n", + "# show percentiles from samples, top and bottom 5%\n", + "if False:\n", + " top_lim = stt.scoreatpercentile(samples, 95.0)\n", + " bottom_lim = stt.scoreatpercentile(samples, 5.0)\n", + " l = max(stt.norm.pdf(x=vx)*n*dx)\n", + " plt.plot([top_lim]*2, [0,l], ls='--', c='gray')\n", + " plt.plot([bottom_lim]*2, [0,l], ls='--', c='gray')\n", + "\n", + "# show percentiles from samples, top and bottom 5%\n", + "if False:\n", + " top_lim_th = stt.norm.isf(0.05)\n", + " bottom_lim_th = stt.norm.isf(0.95)\n", + " l = max(stt.norm.pdf(x=vx)*n*dx)\n", + " plt.plot([top_lim_th]*2, [0,l], ls='--', c='k')\n", + " plt.plot([bottom_lim_th]*2, [0,l], ls='--', c='k')\n", + " \n", + "plt.tight_layout()\n", + "#plt.savefig('figs/ex_hist_norm_perc_th_n100000.png')" + ] + }, + { + "cell_type": "markdown", + "id": "1bfdb6a3-c880-41fa-9056-a2696ace2a9f", + "metadata": {}, + "source": [ + "With the cumulative density function" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "7c0a36c0-59a3-42ec-aec1-bb84e7d92bdc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(samples, bins=vx, cumulative=True)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx, stt.norm.cdf(x=vx)*n)\n", + "\n", + "# show percentiles, top and bottom 5%\n", + "top_lim = stt.norm.isf(0.05)\n", + "bottom_lim = stt.norm.isf(0.95)\n", + "plt.plot([top_lim]*2, [0,n], '--k')\n", + "plt.plot([bottom_lim]*2, [0,n], '--k')\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "id": "304a427a-c94b-4995-a24e-ff26c4f8b07f", + "metadata": {}, + "source": [ + "In this way, we can find boundaries for the probability of finding a random samples that follow the concerned distribution. This leads to the notion of statistical testing, which we will see in detail later." + ] + }, + { + "cell_type": "markdown", + "id": "b5be9b02-17d6-4407-aa71-53a31a6b224c", + "metadata": {}, + "source": [ + "## Summary statistics\n", + "\n", + "Let's now look at the summary statistics of the $n$ samples:\n", + "- mean: $\\mu = E[X] = \\frac{1}{n} \\sum_i x_i$\n", + "- variance: $\\sigma^2 = E[(X-\\mu)^2] \\simeq \\frac{1}{n-1} \\sum_i (x_i - \\mu)^2$\n", + "\n", + "Here $\\sigma$ is the standard deviation, whose square is the variance. Note that the denominator of the sample variance is $n-1$ and not $n$, to correct a bias.\n", + "\n", + "The skew and kurtosis measure deviations from normality:\n", + "- skew: $E[\\frac{(X-\\mu)^3}{\\sigma^3}] = \\frac{m_3}{\\sigma^3}$\n", + "- kurtosis: $E[\\frac{(X-\\mu)^4}{\\sigma^4}] = \\frac{m_4}{\\sigma^4}$\n", + "\n", + "They also correspond to standardized moments, including a normalization by $\\sigma$.\n", + "\n", + "In the previous definitions, we see some powers of the demeaned variables. This is generalized by moments, which have several variations. In scipy.stats they correspond by default to the central moments of samples (without removing the bias)\n", + "$$ m_k = \\frac{1}{n} \\sum_{i = 1}^n (x_i - \\bar{x})^k $$\n", + "where $\\bar{x} = \\mu$ is the mean. Note that this convention implies that the first centralized moment is 0.0.\n", + "\n", + "Scipy.stats has a large range of summary statistics ([link](https://docs.scipy.org/doc/scipy/reference/stats.html#summary-statistics)). For further details, check also the moment generation function and cumulants." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "9fa8b512-f6ba-4396-a0a3-9cc54646f6cc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean:\t\t 0.06369257912897128\n", + "variance:\t 0.9904037965124035\n", + "skew:\t\t 0.041740780051845346\n", + "kurtosis:\t -0.22248866205996043\n" + ] + } + ], + "source": [ + "print('mean:\\t\\t', np.mean(samples))\n", + "print('variance:\\t', np.var(samples))\n", + "print('skew:\\t\\t', stt.skew(samples))\n", + "print('kurtosis:\\t', stt.kurtosis(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "5812c419-861a-4733-97ff-e532deb2c3eb", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "central moments:\n", + "order 1: 0.0\n", + "order 2: 0.9904037965124035\n", + "order 3: 0.04114139425748412\n", + "order 4: 2.7244599829877796\n" + ] + } + ], + "source": [ + "print('central moments:')\n", + "for k in range(1,5):\n", + " print('order {0}:'.format(k), stt.moment(samples, moment=k))" + ] + }, + { + "cell_type": "markdown", + "id": "b6579e85-c7c4-47bf-81fd-24c94a104771", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Change the `loc` and `scale` parameters (see the doc of `norm`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm))" + ] + }, + { + "cell_type": "markdown", + "id": "1133965f-51e0-490e-984e-c917b4ef6583", + "metadata": {}, + "source": [ + "Let's not w try with another type of distribution, like lognormal (`lognorm`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html#scipy.stats.lognorm)). There is a shape argument $s$, so let's see its effect." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "53914dd6-b0ee-43ad-80b3-9533367d28d5", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean:\t\t 0.9994246665864521\n", + "variance:\t 0.009883960897972291\n", + "skew:\t\t 0.25496719930358314\n", + "kurtosis:\t 0.04524705934311646\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate random samples with shape s\n", + "s = 0.1\n", + "samples2 = stt.lognorm.rvs(s=s, size=n)\n", + "\n", + "# variable range\n", + "vx2 = np.linspace(0.0,3.0,50)\n", + "dx2 = np.diff(vx2)[0]\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples2, bins=vx2)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx2, stt.lognorm.pdf(x=vx2, s=s)*n*dx2)\n", + "\n", + "plt.tight_layout()\n", + "\n", + "print('mean:\\t\\t', np.mean(samples2))\n", + "print('variance:\\t', np.var(samples2))\n", + "print('skew:\\t\\t', stt.skew(samples2))\n", + "print('kurtosis:\\t', stt.kurtosis(samples2))" + ] + }, + { + "cell_type": "markdown", + "id": "22149ced-544b-49ea-9a1b-33773c523560", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Change the `s` shape parameter and see its effect on the skew and kurtosis" + ] + }, + { + "cell_type": "markdown", + "id": "83b5a55f-7889-49d2-8f85-42030e930018", + "metadata": {}, + "source": [ + "## Statistical test about the mean of a distribution\n", + "\n", + "We want to test whether observations could come from a distribution with a given mean.\n", + "\n", + "According to the law of large numbers, for independent random variables $X_i$ following a same distribution $P(X_i) = P(X)$, the sample mean is distributed normally with:\n", + "- a mean equal to the mean of $E[X]$\n", + "- a standard deviation equal to $\\sigma / \\sqrt{n}$ with $n$ the number of samples and the standard deviation $\\sigma = \\sqrt{E[(X-E[X])^2]}$.\n", + "\n", + "Student's t-test focuses on the following statistics that involves the sample mean $\\bar{x}$, tested against a given value $\\mu$, and the sample standard deviation $s$:\n", + "$$ t = \\frac{\\bar{x} - \\mu}{s / \\sqrt(n)} $$\n", + "According to what is said above, $t$ becomes normally distributed with unit variance when the number of samples increases." + ] + }, + { + "cell_type": "markdown", + "id": "4320932d-787a-4f9f-a489-7fb9ae38a8d8", + "metadata": {}, + "source": [ + "### *EXERCISE*\n", + "- Verify empirically the law of large number for a normal distribution, then for a lognormal distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "0aeebbcf-26d8-491a-aee4-787123cc38bc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# random samples to generate at each repetition\n", + "n = 100\n", + "\n", + "# repetition to evaluate the distirbution of sample mean\n", + "n_rep = 100\n", + "\n", + "# standard deviation of the normal distribution\n", + "sig = 1.0\n", + "\n", + "m_hat = np.zeros([n_rep])\n", + "for i_rep in range(n_rep):\n", + " samples = stt.norm.rvs(scale=sig, size=n)\n", + " m_hat[i_rep] = samples.mean()\n", + "\n", + "#sig = samples.std()\n", + " \n", + "vx = np.linspace(m_hat.min(), m_hat.max(), 50)\n", + "dx = np.diff(vx)[0]\n", + "plt.figure()\n", + "plt.hist(m_hat, bins=vx)\n", + "plt.plot(vx, stt.norm.pdf(x=vx, scale=sig/np.sqrt(n))*n_rep*dx)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "e9c978a7-b08e-4155-a4b7-b558049b92f5", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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yswPTgF7HR5eTk/T3M4uqAQNCXTi9HRi5hUl/TxHJXsMKPJdddhmXXXZZ4nFDQ8N+z/nnf/5nSkoGrtxaXFzM7bffzrp16/jggw/43e9+xw9/+MPhlCUih6Dc0zdDywoCyW9tMbx+jIJynI5G7JbtmAo8IpJEKRu0PFjYifP5fJx00kkAbNq0KVUlicheylM4YDlOM7VEJFWG1cKTDKFQCIDc3Nwhj9m+fTvf//732bFjB4FAgMmTJ3Peeecxc+bMFFUpkrnKPe1Aaqakx5nFY7C2rdBMLRFJulEReHp6enjllVcAmDVr1pDH1dXVUVdXl3j82muv8cADD3DhhRdy66237jMsHSivd2QbvTwes99HST+ZeA8H+1pSsejgR9/XVzaWCOC07Rzx773B3jeT7mG20T1Mb6Ph/o2KwPOLX/yCpqYmSktL+40NiissLGTevHmceeaZTJgwgaKiIurr63n22We5//77eeGFF7AsizvvvPOQ6jBNg5KS/EO6xlAKCw89jIm7Mv0elvUtOtiUxBaej/437B1/GN0AbTuS9r23r/eX9KN7mN7cvH+uB56FCxfy8MMPA3DLLbcQDA5c/eOcc87hnHPO6ffcpEmT+M53vsORRx7Jd77zHV566SXeffddZs+ePexabNuhvb172OcPxuMxKSzMpb29B8vSJonpKB3voWEYmObQA49N0yAYDOw5HpuyvhaexiS28Hz0v6HtiY3ti7bvpnlXM4YvObPD0vEeSn+6h+ktmfevsDD3gFqOXA08ixYt4vvf/z4A3/nOdwaEmgNxwQUX8NBDD7F8+XL+9Kc/HVLgAYhGk/ONZFl20q4tqZEu99A0DYqLD+wHQFyx2Y3XsIk6Jq12XtJqG/Df0JePESjA6e0g3FSPp3xi0t570PeXtKN7mN7cvH+uBZ533nmHq6++mkgkwoIFC/h//+//Dftaxx13HMuXL2fLli0jWKFIejJNA4/H5I5fL6GuoWPQY46fWsmXL5iWeByfodVkB3FSvOOMWTwGa2cHduuOpAceEclergSepUuXsmDBAnp6evjSl77E9ddff0jX8/l8AESj0ZEoTyQj1DV0sKG+bdDXaiv7dx2Xp2D8zlBigWe9dk0XkaRK+XDplStXMn/+fLq7u7nssstGZJHBDz74AIDq6upDvpZINtqzBk+yd9AaSGvxiEgqpDTwrFu3jq9//et0dHRw8cUXc8sttxzy/jlr167lr3/9KwCnnnrqSJQpknXKEqssu9HCs2dPLRGRZElZ4Nm8eTNXXHEFra2tzJ07l5/+9KeY5v7fvrOzk2uvvZb33nsPx3H6vfbXv/6V+fPnY1kWU6dO5dxzz01W+SIZzY1VluMSLTxtDTi2lfL3F5HsMKwxPDt27OCSSy5JPA6HwwC89957nHjiiYnn582bx/z584HYlPPdu3cDsRWTv/jFLw567YqKCu66667EY9u2efHFF3nxxRfJz89n3Lhx+P1+tm/fnrjelClT+O///m88Hs9wvhyRLOfsCTwutPAYBWXg8YEVweloxChS17SIjLxhBR7LsmhtbR3wfDQa7fd8b29v4vN4KAJYsWLFkNeuqanp9zg3N5fvfe97LFu2jPXr17N9+3a6u7sJBoOceOKJnHfeeVx22WXk5CR/d2eRTJRvhMg1IwA0uzCGxzBMzOJq7KZt2K07+nZRFxEZWcMKPLW1taxbt+6gznn00UeH81b4fD6+/vWvD+tcEdm/eOtOq51HxKWVKszisdhN27BaduCdcJwrNYhIZtOmJCJZLj4lvdGF7qw4zdQSkWRT4BHJcnsWHXQz8MRnamktHhFJDgUekSwXb+FxY8BynFp4RCTZFHhEspybiw7GmYWVsU/C3TihLtfqEJHMpcAjkuXcXHQwzvDlYOTEApfd2exaHSKSuRR4RLKY14lQZPYA7iw6uDcjWAaA09nkah0ikpkUeESyWJET21y0y/bT47i7lpUZLAXAVuARkSRQ4BHJYvHA4+YMrTijoBxQC4+IJIcCj0gWK7JjgcfN8TtxauERkWRS4BHJYvEWHrfH78CeMTwKPCKSDAo8Ilms2BlNLTzxQcuapSUiI0+BRySLjcYWHqe7BceOulyNiGQaBR6RLOVYUQoc91dZjjNyC8H0guPgdLW4XY6IZBgFHpEsFW3fjYlD2PHQ7uS6XQ6GYWIkBi6rW0tERpYCj0iWirTsBKDJCuJguFxNjKnFB0UkSRR4RLJUtC/wjIbxO3GaqSUiyaLAI5KlIi0NwOhYdDAu0cLTocAjIiNLgUckS8W7tEbDgOW4xBieLgUeERlZCjwiWSraOvq6tDSGR0SSRYFHJBs5TqJLazS18JjB2H5admczjuO4XI2IZBIFHpEsFLC6cCIhbAya7Xy3y0mId2kR6YVQl7vFiEhGUeARyUL50djCfh1GARYel6vZw/D6MQKxFifN1BKRkaTAI5KF4oGnzSh0uZKBDO2pJSJJoMAjkoXyo60AtBlF7hYyCFNr8YhIEijwiGSh/Ei8hWf0BZ49iw/udrkSEckkCjwiWSgYb+ExR1/gMdWlJSJJoMAjkoXy+gJP+6hs4YlvIKouLREZOV63CxCR1PIRJWB3A9BuFAChlL23x7Pvv7Fs29HigyKSFAo8Ilmm2IyFHcMfIEQOqQg8xQU52LZDYWHuPo+zLJvmngoAnO42HCuK4dGPKRE5dPpJIpJlSsxOALyF5dBlpOQ9g7k+TNPgjl8voa6hY9BjaqsKuOELs/DkFYLHC1YUp6sZo7AyJTWKSGZT4BHJMiVmbAVjb2EFpHgx47qGDjbUt+3zGMMwMIJlOG0N2J1NmAo8IjICNGhZJMuUePoCT1G5y5UMTTO1RGSkKfCIZJmSvjE83sLRH3g0U0tERooCj0iW2dOlNXoDz57tJbT4oIiMDAUekSxTbKZPl5atLi0RGSEKPCJZxUmzFh51aYnIyFDgEcki+UYIv2HhAN6CMrfLGZK512rLjuO4XI2IZAIFHpEsEm/d6fUEMbw+l6sZmpEfCzxEwzihTneLEZGMoMAjkkVK+wJPj6fQ5Ur2zfD6MXJjNapbS0RGwrAWHmxsbGTRokWsXLmS999/nzVr1hAKhZgzZw6PPvroPs+NRCI8/PDDPP/882zduhWfz8fUqVP50pe+xLnnnrvPc1evXs3//u//8s4779De3k5lZSVnnnkmV111FaWlpcP5UkSySnzAcrd3dAceiI3jcXrasTub8JRPdLscEUlzwwo8L7zwArfddttBnxcKhfja177GkiVL8Hg8HH744fT09PD222/z9ttvM3/+fG644YZBz/3jH//IddddRyQSoaysjClTprBp0yYeffRRXnrpJX7zm98wbty44Xw5IlmjJE1aeCA2U8tu3KTFB0VkRAyrSysYDHLKKafwjW98g1/+8pdcddVVB3Tez372M5YsWUJtbS0LFy7k+eef509/+hP33HMPfr+f++67j1dffXXAeQ0NDXzve98jEolw1VVX8cYbb/D000/zxhtvcNppp9HY2Mi1116rwY0i+1GSZi08AHaH1uIRkUM3rMBz2WWX8eCDD3LdddfxiU98grKy/c/22L17N48//jgAt956K5MnT068dvbZZzNv3jwAfvnLXw449/7776enp4cTTjiBb3/723i9sYapgoICfv7zn1NQUMDKlSv5y1/+MpwvRyRrxLeV6EmDwGNqarqIjKCUDVp+9dVXiUQiTJw4kZNOOmnA65/73OcAWLVqFVu3bu332ssvvwzAZz7zmQHnFRUVMXfuXABefPHFkS5bJKMkWnjSoEvL0OKDIjKCUhZ4li1bBsCsWbMGfb2qqora2tp+xwLs2LGDhoYGAE444YRBz509ezYAy5cvH6FqRTKPB4sCoweAbm+Ry9Xsn1p4RGQkDWvQ8nBs3rwZgPHjxw95zPjx46mrq2PTpk0DzvP5fFRXVw96Xnyw8rZt24hEIvh8w19fxOsd2Qzo8Zj9Pkr6Sbd7OFSdRWY3pgFhx0PYzE1xVQcuXr9ZXAGA09OGx7AwPMP/vk63eygD6R6mt9Fw/1IWeNra2oBYF9RQ4q+1t7cnnmttbU28ZhjGoOcVFxcDYNs2nZ2dlJSUDKtG0zQoKckf1rn7U1g4en/ByIFJ93sY785qtfNgiO+l0SD+39kpzqPd68eJhikwe/CVFI/YtSV96R6mNzfvX8oCTygUAthn64vf7wegt7d3WOftffxw2LZDe3v3sM8fjMdjUliYS3t7D5Zlj+i1JTXS7R7G6/2oeOBpsZMT6kfK3v+djWAZTusOWurr8BnDH3eUbvdQBtI9TG/JvH+FhbkH1HKUssCTk5MDxBYeHEo4HAYgEAgM67y9jx+uaDQ530iWZSft2pIa6X4P0yXw7P3f2cgvhdYdRNsaMaoP/b99ut9D0T1Md27ev5R1phUWxv46i3dtDSb+WvxY2NPN1dbWNuQ6O/FuL9M0CQaDI1GuSMZJl8CzN7NAM7VEZGSkLPBMnDgRgC1btgx5THw6evzYvT+PRCLs2LFj0PO2bdsGQG1t7SENWBbJZInAY6VP4DESM7W0+KCIHJqUBZ6ZM2cC8N577w36ekNDA3V1df2OBRg7diyVlZUAvPvuu4OeG39+7/NEpL+0bOHRWjwiMkJSFnjOPvtsfD4fmzdvZvHixQNej6/CPG3aNCZMmNDvtfPOOw+AJ598csB5bW1tvPTSSwCJBQhF5KOcxCrLrWkUePYsPqi1eETk0KQs8JSXl/PZz34WgB/+8Ids3Lgx8dqrr77K/fffD8DVV1894Nyvf/3rBAIB3nnnHe68804sywKgo6OD66+/no6ODqZNm8ZZZ52Vgq9EJP3kGhECRhRIzxYep7NJe+WJyCEZ1iytHTt2cMkllyQex2dJvffee5x44omJ5+fNm8f8+fMTj7/73e+yatUqli5dykUXXcSUKVPo7u5OjN254oorOOeccwa835gxY/jpT3/K9ddfzz333MMTTzxBdXU1mzZtoru7m/Lycv7zP/9zyHV6RLJdvDur084hkrrJmYfMyC8BDLAiOL0dGLmjf0sMERmdhvWTz7KsxMyovUWj0X7P772eDsSmmz/yyCM89NBD/P73v2fz5s34fD7mzJnDF7/4xUTX1WDmzp3LuHHjuPfee3n33XdZv349lZWVXHrppVx11VUHtIGpSLZKx/E7AIbHh5FXhNPdGttiQoFHRIZpWIGntraWdevWDesN/X4/CxYsYMGCBQd97vTp07nrrruG9b4i2azE7ATSL/AAGMFSnO5W7M4mPBWT3C5HRNKUNiURyQLp2sID2kRUREaGAo9IFig2Y1umpGPgSczU6lDgEZHhU+ARyQJq4RGRbKfAI5IF0nGV5bhEC0+XFh8UkeFT4BHJcCY2RWncpaUWHhEZCQo8Ihmu0OzBYzhEHZMOJ9ftcg5aIvD0tONEwy5XIyLpSoFHJMPFu7Na7Twc0nBxzpx88OYA4GhPLREZJgUekQyXzgOWAQzD2GsTUXVricjwKPCIZLhiM/02Df0oI1gKaByPiAyfAo9Ihkv3Fh5ALTwicsgUeEQyXCYEHkOBR0QOkQKPSIbLhMCjqekicqgUeEQyXCYEnj0tPJqlJSLDo8AjksH8RMg3Y2vXtFh5LlczfIkWnq4mHMd2uRoRSUcKPCIZLN660237CeF3uZrhM4IlgAFWFKen3e1yRCQNKfCIZLASz55FB9OFx2Pi9fb/5/P7MfKLYwdoTy0RGQav2wWISPKk0/id4oIcbNuhsHDw7S+6iysJdbWQ63QSMQ1s20lxhSKSzhR4RDJYOgWeYK4P0zS449dLqGvoGPD63LDNEcSmppsKPCJykBR4RDJYOgWeuLqGDjbUtw14fmuunyNyIdq2G48LdYlIetMYHpEMlo6BZyjxryHa1uhyJSKSjhR4RDJYRgae9t0uVyIi6UiBRyRTOQ7FZjegwCMiosAjkqHy6MZr2NiOQVsaTUsfSosdBMDubseJhFyuRkTSjQKPSIYqcGIzndrsXOwM+FbvcXyE8QHaRFREDl76/xQUkUEVOJ1AZnRnxRi0G4UA2B3q1hKRg6PAI5KhCuxYC0/mBB7oMAoABR4ROXgKPCIZKuhkXuBJtPBo4LKIHCQFHpEMlXldWtDe18JjqYVHRA6SAo9IhooPWm7NpMBjxsfwaPFBETk4CjwiGaogA7u0NIZHRIZLgUckA9mREHn0AJkVeOJjeJzuNpxo2OVqRCSdKPCIZCCrI7ZOTcjx0u34Xa5m5PQSwPAFAHA6m12uRkTSiQKPSAaKtsW6fGKtO4a7xYwkw8BbXAGA3aluLRE5cAo8Ihkovt9Ui5U53VlxvqJKQON4ROTgKPCIZKBE4Mmg8Ttx3qJYC4+jwCMiB0GBRyQD9e/SyizeYrXwiMjBU+ARyUCZ3cLTF3g0hkdEDoICj0gGirbHFubLzMCjLi0ROXjeVL1RXV0dZ5999gEde+mll3LbbbclHp911lnU19fv85wVK1aQk5NzSDWKZALHcTK6S8sXDzzdrThWBMPjc7kiEUkHKQs8OTk5HH/88UO+HgqFWLVqFQDHHXfcoMccccQRBIPBQV8zjAyaeityCJzezsSifK12nsvVjDwzrxC8foiGcTqbMIqq3S5JRNJAygJPRUUFv/nNb4Z8/ZlnnuH73/8+gUCACy64YNBjbrzxRk488cRklSiSEezO2KKDXeRh4XG5mpFnGAZmQQV2Sz12x25MBR4ROQCjZgzP008/DcAnPvGJIVtxRGT/4oGnw8jc7yOzoBzQTC0ROXCjIvDU1dXxzjvvALHxOyIyfHbfthKdfRttZiJPYSzwaOCyiByolHVp7cuzzz6L4ziMHTuWk046acjjHn/8cR544AF6e3spLy9n9uzZXHzxxWoREtnLnhaezA08iRYeTU0XkQPkeuBxHIdnnnkGgE9+8pOY5tCNTn/4wx/6PV64cCF33nknP//5zzn11FNHpB6vd2QbvTwes99HST/pdg9DfZtqdpiZG3h8JVWxveC7msjJGfhjzLYdHMdJPE63eygD6R6mt9Fw/1wPPG+//TZ1dXXA0N1Zc+bM4aSTTmLGjBmMHTuWSCTCkiVLuOuuu1i9ejVXXnklv/nNb5g+ffoh1WKaBiUlyZnGW1iYm5TrSuqkyz3s7mkBMnMMT3FBDrbtEKyqoR1wOpoGvS+27WCaA2dupss9lKHpHqY3N++f64En3roze/Zsxo8fP+gxt99+e7/Hubm5nHnmmZx88slcfvnlrFq1ip/97Gc89NBDh1SLbTu0t3cf0jU+yuMxKSzMpb29B8uyR/Takhrpdg8jrbFFBzOxSyuY68M0De7783YuBKKdzVz/81ewjD2z0WqrCrjhC7P63a90u4cykO5hekvm/SsszD2gliNXA09XVxcvv/wyAJ/61KcO+vxAIMC1117L/Pnzeeutt2hra6OoqOiQaopGk/ONZFl20q4tqZEO99Cxo9hdrUA88ERcrSdZNjRahB0PfsOieed2dtuFA44Z7H6lwz2UfdM9TG9u3j9XO0Nffvlluru7yc3NZe7cucO6RnwxQ9u22bZt20iWJ5J2nM4WwMHw+Oghg5v+DYNmO9ZlV2p2ulyMiKQDVwNPvDvrvPPOG/ZMK59vz7LylmWNSF0i6cruiHVneYsrIcNXH2+2+gKPp8vlSkQkHbgWeLZt25ZYe2c43Vlx69evT3xeXa0VVyW72e27APAWV7lcSfI19+0TphYeETkQrgWe+No7NTU1h7RdxH333QfA4YcfTlVV5v+QF9kXp6+Fx1eS+d8LTX1dWmUKPCJyAFwZtOw4Ds8++ywQa93Z18afv/rVr/D7/Vx00UWUlJQknm9paeEXv/hFYtDzt771raTWLJIO7PZ4l1bmBx6N4RGRg+FK4ImvvWMYBpdccsk+j925cyePPPIIt956KzU1NZSWltLb28vGjRuJRqOYpsl1113Heeedl5riRUaxeJeWr6QayOyxLRrDIyIHw5XAEx+sfMIJJzBu3Lh9HnvhhRcCsGLFCrZv387atWvxeDzU1tYyZ84cLr/8co466qik1yySDuKDln3FVcBGd4tJspa+MTyFRjcerIzcGV5ERo4rgef2228fsJjgUGbOnMnMmTOTW5BIBnBCXRCKtXZ4iyvJ9MDT4QQSa/EUm9002Zm30KKIjBxtSiKSIeKtO0ZuEaY/4HI1qbBnLR4NXBaR/VHgEckQ8QHLZmGFy5WkTrOlqekicmAUeEQyRDzweAorXa4kdRIztTwKPCKybwo8IhnC6YjN0DKLsqiFJzE1XTO1RGTfFHhEMsSeLq1sauFRl5aIHBgFHpEMEV+DJ6sCj6XFB0XkwCjwiGQAx7ZwOpsA8GTToOW+Lq0iswcP2jxYRIamwCOSAZzOZnBs8Hgx8ovdLidl4mvxmIZDsdntdjkiMoop8IhkgPgaPGZBBYaRTd/WRmLFZXVrici+ZNNPRpGMFR+/YxRkT3dWnMbxiMiBUOARyQBOR/YtOhi3Zy0eTU0XkaEp8IhkgMQMrYLsmaEVp6npInIgFHhEMkA2rsET12SrS0tE9k+BRyQDJDYOzcYuLUsbiIrI/inwiKQ5J9QFodj4FTMbBy3vtRaPie1yNSIyWinwiKS5ROtObiGGL8flalKv0wkQccy+tXg0cFlEBqfAI5Lm4uN3jCwcvwPgYGgTURHZLwUekTSXGLCchd1ZcfGZWhrHIyJDUeARSXNOYtPQLA488cUHPQo8IjI4BR6RNJfYViJLu7Rgr8UH1cIjIkNQ4BFJc9m8rUScxvCIyP4o8IikMce2cDqbALXwgFp4RGRoCjwiaczpbAbHBo8XI6/I7XJc02zFBi0Xmd0YjtbiEZGBFHhE0lhi/E5BBYaRvd/OHU4uUcfEYzgEHbXyiMhA2fsTUiQDaPxOTGwtnlgrT6HT7nI1IjIaKfCIpDFNSd8jPo6n0OlwuRIRGY0UeETS2J4urewdsBwXX4tHLTwiMhgFHpE0llhlOYtnaMXFW3gKFHhEZBAKPCJpLLFxqLq09hrDoy4tERlIgUckTTmhLgjFFtrL5n204ppsdWmJyNAUeETSVKJ1J7cQw5fjcjXui4/hCTqdOLblcjUiMtoo8Iikqfj4HUPjd4A9a/GYOEQ7mtwuR0RGGQUekTQVX4NH3VkxDgYtfeN4oq2NLlcjIqONAo9ImnISM7QUeOLiM7WibbtcrkRERhsFHpE0lViDR11aCU2WWnhEZHAKPCJpSttKDBRv4YmohUdEPkKBRyQNObaF0xkbmKsWnj3UpSUiQ/G6XYCkXm80xAetGwhbYSzHJmpbWE6076OFZVtEHQsTg2MrjmZssNrtkuUjnM5mcGzweDHyitwuZ9RIBB51aYnIRyjwZJnm3hbuWvq/NPYc2LTdhZv+yNFlUzln/BkcXjwJwzCSXKEciD17aFVgGGqojYuvxRPtaOpbi0f/v4pITEoDz913380vf/nLfR7zL//yL3z+858f8HwkEuHhhx/m+eefZ+vWrfh8PqZOncqXvvQlzj333GSVnFEau5u4c+m9tIRaKfAHqc6rxGt68RgmHtOL1/BgGh68pgeP6aEt1MbK3WtZ2RT7N7FwPOeM/zjHVkzH1C9ZV2n8zuDanVwsTDy2hdPVArmlbpckIqOEKy08ZWVlTJgwYdDXKioG/gAPhUJ87WtfY8mSJXg8Hg4//HB6enp4++23efvtt5k/fz433HBDsstOazu7Grhr6f/SFu6gMq+cb81cQEmgeL/n7epu5JWtb7B45xI2t2/l/pWPUpFbxtnjP86J1bPwe3zJL14GcOJr8GhKej8OBh1GAcVOG1bHbgwFHhHp40rgOf3007n99tsP+Pif/exnLFmyhNraWu677z4mT54MwCuvvMK1117Lfffdx/HHH89ZZ52VrJLTWl3Hdu5edh+dkS7G5lfzzZnzKcopOKBzK/Mq+PzUT3Ph5HN5fdsiXq9/k8aeJh5f9zQvbPwjZ4w7lY/XnkKuNzfJX4XsbU+XlgYsf1R7X+Cx2xvxVB7hdjkiMkqM+n6J3bt38/jjjwNw6623JsIOwNlnn828efMA9ttVlq02t2/lP5feS2eki3EFNXz7+G8ccNjZW6G/gIsPm8u/nvLPXDblHyjJKaYj0snvN77Mv771H6xt/iAJ1ctQ7HatwTOUVqMEAKtlu8uViMhoMuoDz6uvvkokEmHixImcdNJJA17/3Oc+B8CqVavYunVrqssb1T5s3cTdS++jJ9rDpMIJfGvmAoK+/EO6ZsCbw5njPsbNJ/8TX5n2OSpyy2gNtXH3svt4cv1zhK3wCFUvQzFNA6evhcdXUoXXa/b75/GM+m/rpGoyY91YdnO9y5WIyGjiSpfW2rVruf7662lsbCQ/P58jjzySCy+8kClTpgw4dtmyZQDMmjVr0GtVVVVRW1tLXV0dy5YtY/z48cksPW2saV7PvSseJmJHOKL4ML5xzFcJeEduR22P6WFO9fEcW3E0z3z4An+tf5PX6xaxtvkDvjLts0woHDdi7yV7mKZBQcCmLdQFQOn4CZj+gMtVjS7NRizwWC0KPCKyhyuBZ82aNaxZsybx+NVXX+V//ud/+PKXv8w//dM/4fF4Eq9t3rwZYJ9BZvz48dTV1bFp06ZDrs3rHdm/juN/bafyr+7lu1bxv8sfIepYHF0+lW8c+5WkDS72egN8cfqnmVk1nUdWPUlD9y7uWPJfXDT5E8yddBYe07P/i4xybtzDoXg8ZmLAchd5XPfLxQOOOX5qJV++YFqqSxs1ms0yAOz23XicCIYvZ1TdQxke3cP0NhruX0oDT2VlJd/61rc47bTTqK2tJRgMsmnTJh577DEef/xxHn74YbxeL9/73vcS57S1tQFQVDT04mrx19rb2w+pPtM0KCk5tC6foRQWpmZQ7+Jt73Hv8oexHJs5NTP59slX4EvBTKrTSmYxc/yR3LfkNyze9h7Pb3iZNS3ruPqkrzK2oCrp758KqbqH+9NZ3wDArkg+G5rbBrxeWxlMdUmjSo+Ri5lXiN3dTr7VQk7lYYnXRss9lOHTPUxvbt6/lAaez372swOeO/LII7n55pupra3ljjvu4OGHH+byyy+ntrYWiE1JB/D5hv6l7ff7Aejt7T2k+mzbob29+5Cu8VEej0lhYS7t7T1Ylj2i1/6o3miI/3rrkVjYqT6Orx71OTrbw0CqxtUYfHXq55lWPJXfrHmaD5o3872XbuWyIy/m9NqT03bRwlTewwOpxW7ZCUCTnd3BZl/85ePo3bqKli0byAlUj6p7KMOje5jeknn/CgtzD6jlaNSstHzFFVfwyCOPsGvXLl599VW+/OUvA5CTExt3EolEhjw3HI79Qg8EDn0sQzSanG8ky7KTdu24d3csJ2SFqMgt40tHfRbHNojaqf/BMKtiJpMLJvLImidZ3/Ihj615mhW7VvPlaZ8j35eX8npGSiru4YGItsZaeHbbBz/bLlv4K2KBJ7p7G57D9tyz0XIPZfh0D9Obm/dv1HSGejwejj32WAC2bNmSeL6wsBDY07U1mPhr8WOz1eId7wJw0pjZrq+EXBIo5pqZ87hsyj/gM72sbFrLT9+5i7oOTRU+VInAYynwDMVXHmsh1sBlEYkbNYEH9nRbRaPRxHMTJ04E+oegj4pPR48fm4129zTzQetGDAzmVB/vdjkAmIbJmeM+xvWzvklZoJSm3mbuWPJfvL3zPbdLS2uRlljgUZfW0PwVsVmCttbiEZE+oyrwfPBBbPG66uo9u3PPnDkTgPfeG/yXZENDA3V1df2OzUZv71wCwJElh1MaKHG5mv7GFYzln074FtNKjyRiR3h49eM8uf45LNtyu7S049gW0bbYGjxNauEZkr88Fnicjt040ZDL1YjIaDBqAs9rr72WCDynnnpq4vmzzz4bn8/H5s2bWbx44BTc+CrM06ZNG3J/rkxnOzaLd8QCz4ljBl+vyG35vjyuPPZrnD/xbABer1vEnUvvpS10aDPrso3d2QyOTRQP7Y5mqwzFk1+EESgAHOyWHW6XIyKjQMoCzwcffMCPfvQj1q5d2+9527ZZuHAh119/PQBnnnkmxxxzTOL18vLyxOyuH/7wh2zcuDHx2quvvsr9998PwNVXX53sL2HU2tC6mabeZgKeHGZWHO12OUMyDZOLJp/HN2Z8hYAnwIa2zdz+zp1saN3sdmlpI75LertRiEN6znpLFU9pDQC2xvGICCmcpRWNRnniiSd44oknKC4uZuzYsXg8HrZu3ZoYdDx79mz+/d//fcC53/3ud1m1ahVLly7loosuYsqUKXR3dyfG7lxxxRWcc845qfpSRp3FO2ODlY+vPAa/x+9yNft3TMV0vnfCNdz3/iPs6GrgP5f+D5+ecjEfrzklbaeup4rdFgs8bUZ2D9A/EJ6SsUS3r1XgEREghYGnpqaGa6+9lmXLlrFhwwa2bNlCOBymqKiI008/nYsuuoiLLrqo3yrLcYFAgEceeYSHHnqI3//+92zevBmfz8ecOXP44he/yHnnnZeqL2PU6Y2GeG/XCgBOHDPb5WoOXFVeBTfM+iaPrf0dS3Yt57frn2NL+zY+f+Snk7YqdCawEi08Qy/EKTFmaXymlgYui0gKA09hYSFXXnnlsM/3+/0sWLCABQsWjGBV6W9540rCVpjy3DIOK5rodjkHJeDN4WvTL2dC4Tie3fAH3t75Hju6Glgw48ujbuD1aBHfJb3NVAvP/qhLS0T2NmoGLcvwLO6bnXVS9ey07A4yDIOzx5/ONTPnke/LY1tHPT995y4+bD30fdEyUXwMT5taePbLUxILPE7HbpyIZmqJZDsFnjTW1NPC+pYPMTA4cczoWHtnuI4oOZx/mv0taoJj6Ix0cefSe3mj7k0cx3G7tFEl0cKjwLNfZl5hYqaW1aqZWiLZToEnjcXX3plSclhGdAGV5ZZyw6yrmVV5LLZj88T6Z/jNuqeI2NH9n5wFnFAXTqgLiM3Skv0zS8YCYDWrW0sk2ynwpCnHcfZsJVE9OtfeGQ6/x8/Xpl/OJw87HwODRdvf5i6t1wOA3RFr3fHkFxM1NLD7QJh93Vq2Ao9I1lPgSVMb2jazu7eZHI+fmZUz3C5nRBmGwbkTzuTKY68g1xtgY9sWfvrOXWxu3+p2aa6yW2O7pHuLq1yuJH0kWng0cFkk6ynwpKl4687xlceSkwZr7wzH9LIj+d7sa6jOq6Qt3M4v3vsf3uz7urOR3RQLfP7K7FxRfDjiLTzq0hIRBZ40FLLCLO1be+ekNFp7Zzgq8yq4YfY3mVE+jagd5f/WPMkT654lmoXjeqy+wJNTPcnlStJHokurvRFbM7VEspoCTxpa3riSXitEeaA07dbeGY5cb4AFM77MBRNjq2m/Uf937lx6L62hNpcrSx3HcbB3bwHAX6XAc6CMQAFGThBwiOxWK49INlPgSUPx7qwTx8xKy7V3hsM0TC6cfC7/75iv9hvXky3r9TjdrTi9HWAY+CvHu11O2jAMA7NvAcLw7uweAyaS7RR40kxs7Z0NAJyYQbOzDtSM8ml8b/a3GJtfTXu4gzuX3stftv0t49frsZtirTtm8VhMX47L1aSXeLdWZHedy5WIiJsUeNLM2zvfw8HhiOLDKMstdbscV1TmlXPD7G8yu2omtmPzuw+e56HVvyFshd0uLWmsvtYJb7kGLB8sszg2UyvcuM3lSkTETQo8acRxHN7q2xk90wcr70+Ox89Xp32eT0+5GNMwebdhGXcs+S8au5vcLi0p4jO0POXqzjpYe7q01MIjks0UeNLIxrYtNPY04ff4ObbiaLfLcZ1hGJw17jS+NXMBBf4g9Z07+Om7d7Fy9xq3SxtxVt+AZU+FWngOVrxLK9rSoD21RLKYAk8aSay9U3EMAa/GccRNKZnM90/4NpMKx9MT7eF/VjzE7ze+jGVbbpc2IpxwN058lWV1aR0wj8fE6zXxBYswArGZWrTvxOs1E/9MMzsG/YuIAk/aCFsR3tu1HICTxmTfYOX9Kc4p4trj/x+n15yMg8NLm1/hrmX/mxFT162m2NgTI1iGGQi6XM3oV1yQg207FBbmUlKST2lpkJy+mW2+nkZKSvIT/4qL8xR6RLKE1+0C5MBs7aij1wpR5C/gsGKtwzIYr+nls0d+isOKJ/HY2t/xYesmbnv7P/nKtM8xrexIt8sbtvj6O54yjd85EMFcH6ZpcMevl1DX0AHAGWGTY4AX/7CIv/8pNqOvtqqAG74wC9M0sO3MnuUnIgo8aWNbR2zRtPGFtZiGGub2ZXbVTMYX1PCrlb+mrnM7/7X8V5w74UwumnQuHtPjdnkHzYpPSVfgOSh1DR1sqI+18I3NyeOYfMjpbmBDZ/q3+onIwdNvzjRR17kdgNrgWJcrSQ+VeRXcMOtqTq85GYA/bvkL/7n0Xlp6W90tbBjsvinppsbvDNsOqxiAao/Cjki2UuBJE3UdfYGnoMblStKHz+Pjs0d+iq8f/UUCngAb2zZz29v/mVazuBwrgt0Su/fq0hq+BqsIgDKzAx/Ztw+biCjwpIWoHWVHVwMA49TCc9COrzyG75/wbcYX1NAV7ea/VzzI0x8uTItZXHZLPTgW5ORjBMvcLidtdTgBOu0cTAMq1cojkpUUeNLAjq5dWI5FrjeX0kCJ2+WkpYq8Mq6bdTUfrz0VgFe2vsHPl9xDQ9culyvbN2uvAcvZsm9achjs7GvlGaPAI5KVFHjSQF3fgOXa4Bj90jsEPtPLZ474JPNnfJlcby5bOrZx2zt38kbd30ftXlzxFZY1YPnQ7UyM42l1tQ4RcYcCTxrY1jdgeZzG74yImRVH88M53+HIksOJ2BGeWP8s9yx/gLZQu9ulDRAfsKwFBw+dAo9IdlPgSQOJAcsavzNiSgLFfHPmPC6b8g/4TC+rm9dx61v/wdJd77tdWoLj2FjNsUUHzTIFnkMV79LSTC2R7KTAM8rZjk19fEp6gQLPSDINkzPHfYx/OuHbjAuOpSvazf0rH+WR1U/QE+1xuzyc9l0Q6QWPD7O42u1y0l68hUcztUSykwLPKLe7p5leK4TX9FKdV+l2ORlpTH4VN8z+JnMnnIWBwVs7l3DrW7/gg5YNrtZlxdffKa3FSMMFE0ebDidAl+3XTC2RLKXAM8rFFxwcm1+VlqsEpwuv6eXiw+byneOvpDxQSkuolTuX/i9Pf7CQsBV2pSa7KT5DS91ZI8NILEComVoi2UeBZ5TbM35HA5ZT4bDiifxgzrWcMmYODg6vbHuDm//+c95vWJvyWuJT0s1yzdAaKRq4LJK9FHhGuW2dsSnp4zR+J2UC3gBfOOoyrjzmaxTnFLG7p4lbXruTR1Y9SXekO2V1xKeka4XlkbNn4HKru4WISMop8Ixy9R0asOyWo8uP4sYTr+eMcacAsKj+bX7y1h28t2tF0tftsbtbcXrawTAwy8Yl9b2yyU7tqSWStRR4RrH2cAdt4Q4MDMbmj3G7nKyU6w3w+aMu5Sdn3UB1fiUd4U5+tfL/uO/9R2gNJe+Xph3vzioag+HNSdr7ZJu9Z2p5HM3UEskmCjyj2La+1p3KvHIC+qXnqqkVh3Hjyddx/sSzMQ2T5btXccvin/O3+sXYjj3i72dpheWk2HumVqnT4nY5IpJCCjyjWL0WHBxVfKaXiyafx/dP+DYTCsfRa/Xym3VPc+fSe6nv3DGi7xVv4fFowPII2zNTq9RudrcUEUkpBZ5RLD5gWeN3Rpea4BhumHU1l035B/ymjw9bN3H7O3fy5Prn6I6MzIKFe1p4NCV9pDXEA4/T5G4hIpJSCjyjWHxK+jhNSR914qs033jiDcysmIHt2Lxet4ibF/87i7a/dUjdXE64J7bKMpqSngw7+mZqqYVHJLso8IxSvdFeGntif4GqhWf0KsstYf6ML3HNzPlU51XSGenisbVPcce7/8Wmtq3Duma8dcfIL8UMFIxkucJeA5cdBR6RbKLAM0rVd+7EwaHIX0iBP+h2ObIfU0un8M9zvsOnD7+IgCfAlo5t3LHklzy6+knawx0HdS1bA5aTKh54ipw27EjI3WJEJGUUeEYpLTiYfjymh7PGn86PTvouJ1XPBmDxzne5+c2f8erWN4jaBzYN2koMWNb4nWSIz9QygEjTdrfLEZEUUeAZpfYsOKjxO+mmKKeAL037DDfMuprxBTX0Wr089eFCbll8B+82LNvv+B618CSbkWjlCe/e5m4pIpIy3lS9keM4LF26lFdffZUlS5awceNGOjs7KSgoYNq0aVxyySVcfPHFGIYx4Nwjjzxyn9cuLy9n0aJFySrdFds6NSU93U0qmsB3Z1/Dm9vf4febXmZ3bzMPrnqMP299nUsOu4CppVMGnONYUeyWWOuepqQnz06rmMN8u4g0bsWomeV2OSKSAikLPIsXL+arX/1q4vG4ceOoqamhvr6eRYsWsWjRIl544QXuvvtu/H7/oNc4+uijB32tuLg4SVW7w7ItdnTuBNSlle5Mw+TUmhOZVTWTv2z7G3/e+hrbOuq5e9l9HFV6BJ887HzG7dWKZ7fUg22BPw8jWO5i5Zltm1UKQM/WNeTN/JTL1YhIKqS0hae2tpavfOUrXHjhhZSVlSVee/bZZ7npppt47bXXuPPOO/nud7876DXuvPNOamtrU1Wya3Z27yLqWAQ8AcoCpW6XIyMg4M3h/Eln87GaE3lp8yv8tX4xa5rXs6Z5PbOrZnLx5LmU55b22zB0sNZOGRnrIrGtWkL168kN94CplcxFMl3KxvAcc8wxvPTSS3z5y1/uF3YALrnkEq6++moAfve732HbI79UfzrZ1hFfcHCMfullmAJ/kH884pP86KQbmF01E4B3G5bxk8U/43frn6e18UMATA1YTqpmu4BWowgcm0j9arfLEZEUSFngCQaD+Hy+IV8//fTTAWhtbaW5ObvXx9CCg5mvPLeMr02/nO+f8G2OKj0Cy7H4S93fuDW0hoXlQTqLK90uMeNtNWNjpKLbVrlciYikQsq6tPant7c38XkgEBj0mHvuuYddu3ZhWRZVVVWcdNJJXHDBBUOO+UlXdfEByxq/k/HGFdTwzZnzWNv8Ab/f+BKb27fxt+I8Fu/8M6d6OvnE+I9TEih2u8yMtNUzjmOs94nUrSSzfoKIyGBGTeB54YUXAJg6dSrB4OAL7T311FP9Hj/zzDPcdddd3H333UyfPn1E6vB6R7bRy+Mx+33cH8dxEoFnQnHtiNcjB+9g7+FwHF15JFP9RSx55kZeKQuyJQCv1y1iUf1iTq2Zw9xJZ1GaW5LUGrJNnVkLhonduhOjpxlPgQaJj2ap+D6U5BkN929UBJ6VK1fy+OOPA7BgwYIBr5999tl88pOfZOrUqVRXV9PV1cWbb77JL37xC7Zt28YVV1zBs88+y5gxYw6pDtM0KCnJP6RrDKWwMPeAjmvobKQn2ovX9DKtdjJe05OUeuTgHeg9HK7OnQ0c0RPmaKuY1jO+zm9X/YE1jR/wet2b/G3725wx8WQ+ddR5FJLcOrJF2MghZ+wUQvXr8Dd9QOF4jZtKB8n+PpTkcvP+uR54du/ezTXXXEM0GuUTn/gEF1544YBj7rnnnn6Pc3JyuPDCCzn55JP59Kc/zfbt2/nlL3/Jrbfeeki12LZDe3v3IV3jozwek8LCXNrbe7Cs/Q/GXtmwAYCx+VV0tPXu52hJhYO9h8PVs3l97JOS8dT4x3Htcd9gffMGFm78E+uaP+SVjX/jL5v+zsfGn0DEW4TWDT10uZOPJVS/jrZ1S7Amnux2ObIPqfo+lORI5v0rLMw9oJYjVwNPR0cH8+fPZ/v27UyfPp3bb7/9oM4vLS1lwYIF/Mu//At//vOf+dd//ddDntUUjSbnG8my7AO69pa2OgBqgmOTVosMz4Hew+GKNMa2lDBKxiXeZ3LhJL41cwEftm7ipc2vsKZ5PW9seQuqwB8oI7pzInZbOaDZfMORN+lYWv/6JJG6VUTCUQxTIXK0S/b3oSSXm/fPtcDT1dXFvHnzWL16NVOmTOFXv/rVkGN39uW4444DYrO7WltbKSkpGelSU6ouMSVdA5azjb2PPbQOL57EN2fOo66rjte3L+LvW9/DU9SEp6gJuztIdOdErKYx4KgL9GDkjD0c/LkQ6sLevRlP5WS3SxKRJHHlz5menh6+8Y1vsGzZMiZOnMiDDz447KCy91R3y7JGqkTX1HXuADQlPdvY3a04PW2AgVk6bsjjJhaN59pT5lHZcCHRnRNwLA9mXif+ySsJzHwd79gPiaCu0ANleLz4ao4CIFqv6ekimSzlgScUCnHllVfyzjvvUFNTw0MPPURFRcWwr/fBBx8AsXE96b7FREe4k9ZQGwYGNcFqt8uRFEpsGFpUheHb/6q/XiufyNaj6F12BpGtR2KHAhi+ML7aD1nmfZx73/k1EV9LssvOCN5xRwNg1SnwiGSylHZpRSIRrrnmGt58802qqqp4+OGHD2lmVTQa5cEHHwTgpJNOwut1fQz2IYkvOFiRW0bAO/haRJKZrMbNwDBWWLZ8RHdOItowAU/pTrzVmzHz23ll49+gEnLyiog2jMdqrlZ31xB8tUfTA1gNH+BEejF8+t4TyUQpa+GxLIvrr7+e119/nYqKCh5++GHGjRu66T7ujjvu4JlnnqGzs7Pf8zt27OBb3/oWy5Ytw+v1JramSGdacDB7RbcsA8Az5sjhXcAxsZrGElp1MlOjF3DKuFngmJjBNvyHvU/guNfwjluLkdM1ckVnCLOoCqOgHGwLa8c6t8sRkSRJWZPIiy++yMsvvwyA3+/nn//5n4c89qabbmLatGkAbNy4kfvuu48f/vCHjBs3jqKiIjo6Oti0aROO45CTk8O//uu/cuyxx6bk60imxB5aQQWebGJ37MZu3AgY+CfP3udik/ufemlQ6Izh2lMuZsPbL1EXXY2nchtmTi++MZvxjdmM1VZGsxEhah83ol9HujIMA2/NdCJrXydatxLv+PT/WSIiA6Us8ITD4cTn9fX11NfXD3lsR0dH4vPPf/7zlJeXs3LlSnbt2kV9fT0+n48pU6Zw8skn88UvfpHx48cntfZU2dPCowHL2SS66V0g1rpTOnbMiK1E6rEDRHccRnTHZMziRryV2zCLGvEUNfEhr3D1798lXDgGo7kMp6dgRN4zXXlqY4HH0sBlkYyVssBz6aWXcumllx70eaeddhqnnXZaEioaXUJWmF3duwEYpy6trBLpCzz+w0/A4zG549dLqGvoGPTY46dW8uULph3kOxjYrZWEWysx/N14KuvIHbOdlt42KGgjMAPszkKiu2uwmsdANPt2lvKOnQYY2C3bsbtaMPPTe3kLERkovUf5ZpD6zh04OBT6Cyj0Z/df29nE7mzGbvgQAP/k2QDUNXSwob5t0ONrKw9+raq9OeE8onVHMLPidM44I4df/nkhPTnbMYPt+IPtOOPXYrdWEt1dg82hbdWSToxAELNiInbjJqy6lZhHZv4fWSLZRoFnlNCCg9kpunkJAJ6qKSltVTDxMKd2JqXNrWxo2IWnbAfe8nrM/A48pQ14ShtY5qzm4aVbCfsMwEOmr+bsrT2acOMmovWr8CnwiGQcBZ5RYlvflHQtOJhdohvfAcA7+QQXi8jBapiI1TARI7cdb0U9nrIdRH29vLD+ldj09sJcrOYxWE3VfeN9Mi/8eGqmw9LfY9WtwnFsDEPbTIhkEgWeUUJT0rOP3d2KtTO2cKZ30iyXq4lxegqJbC0ksu1IjjnOoWJSM29uWYYZ6MEcuxHf2I3YPflYzdVYTWNweg+ti2008VQdDt4cnN4O7KZtg27xISLpS3/CjAKWbbG9ayegKenZJLppCeBgVh6GGSxzu5z+HJMSJ7aNRdXOSwh/eCxWcxWObWLmduGr2UDgmL+Rc/Tf2G4uo759p9sVHzLD48UzdioAUa26LJJx1MIzCuzs3kXUjhLw5FCeW+p2OZIi8e4sX99g5dHKdLyx7qzmMWBG8ZQ04CnbiVm4GzOvkzqW8J0Xl+CpLMBrlGO3VmJ3FpOO3V7e2qOxti6PTU+feYHb5YjICFLgGQW29g1YrgmOwdS4gaxgd7dh7Yyt6uudNLoDTz+2F6upBqupBjwRPCUNVExspcu7k6ivA9/YDhi7CSfsx2qtxGqpxG4fZa1X++CpmQ6AtXMdTjSM4c2+KfoimUq/XUeBja2bAZhcNNHVOiR1opvfA8fBrJiEWTD8zXNdZfmwdtdypHUe91/y75Q0n0y0aQxO1IvhD+OtrCPnyPcIHP8qH3he4bVNb2KZPW5XvU9m8RiM/BKwolg717tdjoiMILXwjAIb2jYDcFjxRFfrkNSJr66cVq07+5DnyyW3ZzyR+iIiho1Z0IynZBeekgYMf4gWNnPP25thDOQUFmK1lWO3lvd1fbn7d9dHV7b2jTua8Nq/Ym9fhXfiMdi2g207LlUnIiNFgcdlHeFOGrp3ATCpSLNCsoHd24G1fQ0AvgwJPP04JnZ7OXZ7OZEtR2HktzN5ag+B8mY2tmzFzG/HzG+HsRtxol7s9jKs1grCFKe0zOKCHGzbobAwt9/zvqmz2LX2rzjbV1NSko9l2bS2div0iKQ5BR6XbWzbAkB1fhVBX77L1UgqxLqzbMyy8ZhFVW6Xk2QGTlcRtfY0bjh3Ntf850ts696IWbwbT9FuDG9kz0KHrOT6l96grSgfs6sAu6MELF/SKgvm+jBNY8BWHrlOD/OB8K4t3P3w61zzlY9jmoYCj0iaU+Bx2Ya2TQAcpvE7WSPTurMOhscOJAY9R3Aw8tvwFDfiKdqNmd/GtrbtEIScI8BxwOkqwmovw24vw+4oTkpNg23lsa2wlHHeZrwNa4CPJ+V9RSS1FHhcFh+wrMCTHZxQF1bdagB8bq6uPCoYOF3FRLuKidZP4ZTjyjjj47nc+6e/0OnZgRnoxgi2YQbbYt1ftskaqvjdql2E/J1geMHxJKWydZExjPM2M97elpTri0jqKfC4KGyFE1PSDyue5HI1kgqx7iwLs6QWszh7Nuc8ED4CnDxuFk+0dtBU34bh78EsbMIsbMZT2IThD9HBDp5c+XuogECZgd1VhN1REvvXOXJdYOsiYzkndxXjrG04jrqyRDKBAo+LtrRvw3IsivyFlAVSt3GkuCcS787K+tad/XPCuVi7a7F218a6vwJdHDndYuzEMG9tXoXt6cVT0IqnoBXYFOsC6ylgs1nLoq0OUU8X4DCcBRA3RisJOx6CRheRxm3gS5+1hERkcAo8Ltp7OrphpN+qtHJwnHA3Vt1KALyjfHXl0cfA6Q1SZdfwnVNm8+3Ff2HT7p2YBc2YBS2xf4FujLwOdrGGO99cA9UQKM3B7izC7irG7izG7ioEe/8/9qJ42BCp4ij/dro3LYcjzkrB1ygiyaTA46INifE76s7KBtEty8C2MIvH4impcbuctGZg4ITysEJ5WLtrY0/6QpjBFsZPDpNf3snG5m0Y/hCe0l14SmNLPziOgdMdxO4sptHoZlvbWBzsQd9jXXRMLPB88C65CjwiaU+BxyW2YyempGvBwewQ3ztLrTtJEsnBbqlmgl3DDefO5tv/8Wc2t9VhBlsxg60Y+W2YOb0Y+R2Y+R1sYhvXv/QGxhgv/sIgTlcRdlchdlcRTm8+y8Pj+Ye89+jdshLfjnVQMcXtr1BEDoECj0u2d+6k1+ol4MlhbH612+VIkjnhHqJ17wPgnaTxO6lg4MXu7BvMHOfrTQSgkqoeIv5WQtFQbBxQQWviMMfy0NldyMP2eI7pbaD2rd8w4fwf4PMkb10gEUkuBR6XxMfvTCqagMdMztRaGT2iW5eDFcUoqsIsrXW7nOwVCWC3VGO3VDOtvIbrPnU81/xyIfWddZj57bFWoLwODI+Fp6CFdcC6okKgE8/rN1EdrKImOIba4NjEx6BfC4aKpAMFHpdsaNWCg9kkvtigb9IJGqA+ipimiS9auGcHeIC+GWFmfhslVb2MLd7JtlAbvR6o79xBfecO3ua9xDWK/IXUBMcwJljFmPxqxuZXUZ1fRY5HO62LjCYKPC5wHEcbhmYRJxIiunUFoPE76SE2I8zqDVIUKOInl89iyy+vosXupWn2RewoKKC+cwd1nTvY3dNEW7idtuZ2Vjev2+sKBqWBEsb2haAx+VWMya+iKq8Cv4KQiCsUeFzQ3NtKa6gN0zCZUDje7XIkyaLbloMVxiiowCzTBrHpxpNbQGDmBZS8/TtKVy9m5mf+DcOM/ejsjfayvWsn9Z072dHVwI6+jx2RTpp6m2nqbeb93Wv6Xa80UEJVXgXVeZVU5VdSnVdBVX4lBb6gWv9EkkiBxwXx/bPGFdSo2TvDOY5DZO0bQGzvLP1CS0+BY88l9P4fcdp3EVn7Bv5psWnqAW+AyUUTmfyRrumOcCc7uhrY3rUnCO3s2kVXtJvm3haae1tY07y+3zm53lyq8yqoyCunMre838dcbyBVX6pIxlLgcUGiO0vjdzJe9INFscUGTQ+50z+Ox2sOeazHM/Rr4i5vII/A7E/S89dHCb/3PLlHnYbhy0m8bttOv93UC/xBCvxBjig5rN91OsNd7OzeRUP3Lhq6Gmno3sXO7kaaeprpifawqX0rm9q3Dnj/Al+wXwCqyC2lPLeMstxS8r15CtIiB0CBxwWJDUO1f1ZGszub6f37rwEoPu2zlE7WOi7pprggB9t2KCzMpeDUC9m24mWibbswP3yd4lM+lTjOsmxaW7v7hZ7BBP35HO6fxOEf+d6PWBF29eymobuRxu7d7OrZnfjYEe6kI9JJR1snG/v+WNpbwBOgvC8AxT6WUh4ooyy3hJJACT5TP+ZFQIEn5boj3Wzv2gmohSeTOY5D7xsPQLgHT+VkSk65hDt+vYS6ho4hzzl+aiVfvmBaCquU/Qnm+jBNI3HvpkaP4Vz+zPa//Jbb3swlZASorSrghi/MwjSN/Qaeofg8PmqCY6gJDtxQtifaS2M8AHU30dizm909TezuaaYt3E6v1Utd53bqOrcPeu0ifwGlgVJKA8WU5cY+lgZKKQuUUBoo1iBqyRoKPCkWX125Mq+cAn/Q5WokWSJrX491ZXl85J+9AMP0UNfQwYb6tiHPqa3U/w+jVfzebaSaGYXFjPG2MrnlTRb2HJ/09871BhhfUMv4goHrN4WtCM29zTT2BaCmnmZ29zbR2NNMc28LYStMW7iDtnAHm9q3DHr9fF8eJTnFlASK+j4W7/WxiOKcIq0VJhlBgSfF9ozfUXdWprLbGwktfhyAnBMuw1My1uWKZKQ4mCzsmcn8gtc4PbCWN3qnAkWu1eP3+KjuW/fnoxzHoSvSTVNvM829rYmPzfHHPc30WiG6It10RbqHbCEyMAj68ynJKaKoLwAV5xT2fV6YeD7gydFYIhnVFHhSTAsOZjbHsel9/X6I9OKpPgLfjE+4XZKMsJWRcWyKljPJu5tzc99nKbFuqP0NOv/owOZkM4xYUAn685lQOG7QY3qiPTT3ttLS20pLqK3v457Hrb2tRB0rNo4o3Akd9UO+n9/0UZhTSJG/gKKcQor8hRTmFFDkL6Qop5BCfwGFOQXkeXMxDQ3Ql9RT4EmhiBVhS/s2QAsOZqrIqlewdqwDr5/AGfMw9IM9Axks7D6eawr/yCk562nMOy0xsHlfDnRgcyrlenOpCeYOOnYIYpscd0W6aQ217fWvndZQG219H1tD7fREewjbkb6xRU37fE/TMCnwBSnMKaDAH4wFIf+ezwt8wcQst3xfnsKRjBgFnhTa2lFP1LFiU0xzy90uR0aY3bqT0Fu/BSDnxM9iFla6XJEky4fRatZExnCUbweze9/ENM/f56D0kRjY7AbTMBPhY1xBzZDHha0wbaGO2KrToXbawx20hdppC7fTvtfz3dEebMeOPQ637/f9DQzyfXl9YShIabCYHALke/MI+oKxFixf7PN8X+xzjTeSoSjwpFB8wcHDiieqrzvDOLZNz+v3gxXGUzMN37Qz3S5Jkmxh9/EcVfQC47pWEd61Zb+D0jOZ3+OnIq+MiryyfR4XtaN0hDtpD3f0fYx/3rHn+UgXneFOuiLdODh0RrrojHSxo6sBWvZfS643ty8E5ZPvyyPfl0+eL5d8b/xxXuL5oC+PPF8eftOnn8lZQIEnhTbE19/R+J2ME3n/JeyGD8EXIPDxr6srKwvUWWUsDU3guJwtNL3yMKZzqtsljXpe0xub/RUo3u+xlm3RFe1OjB/qtrqxvGEaWptpD3XSFemiI9xFV18gigeknmgPPdEeGvfTtbY3j+HpC0V55Plyyev7mO/NI9eXS563758vl9yPfK6wlD4UeFLEduzEomFacDCzWC31hN59GoDAyZdjBvf9V65kjj/0zOTYnG30bFzOJeZu7jFOpcvRNhAjwWN6EuN7ALxek5KSfFpauohG7QHH245Nd7SHrnAXHZFYEIrPQIv9iz3ujHTTFd3z2HZsrL0HZh9snYaHPG8uud4AuYmPgX6PA94Aed5cAt4Aud4cAt4AAU8g8ZoWh0wN/VdOkZ1du+iO9uA3fdQGNU05Uzi2Re9r94MVxTPuGLxHnuZ2SZJCu+wi3qq4lFPaFlIbrue6wj9wf+eZ7LBK3C4t65iGSdCXT9CXz8BJ+oNzHIeQFaYn2kNXpJvuaDfdkR66+j529z3fE+2hO9JDT7SX7mh338eePWEpElsNe7i8ppeAJycRgAKeHALeHHI8OXseewIEvDkEPDnkxD/ufZwnhxyPH6/pVYvTEBR4UuTDltj4nYlFEzSoLkM4jk343WewGzdh5OQTPOvrmL6B91Z7ZGW2HXlTqLnkNlbd/2PKPe18p/BFHu38GO9HxrtdmuyHYRixEOHNOaButr3tHZa6o7Ew1BPtSYSh3n4fe+mJ9NBrheiJ9tIb7aXX6iVkhYHY2KZOO0pnpOuQvybTMBNhKMcbC0E5nvjHgZ/7+z5PfDT9idf3fs2bAa1Q6f8VpIkPtf5ORrGatxH626NYO2M7XpfPnUdB7cCVcCU7+CvH80TOZzijYyFH+HYyr+A1XuieyR97ZwD6azsT9QtLFA/rGrZj0xvtC0FWbyIMhawQvdEQvVaoLxzFHoesED1WL6G+10JWOPF5xI4krtndF8IIjdzXaxomftOP3+PD7/HjN33kePz4PH5yPD78ph9f30e/x4ff9PV7HPDlMC5SRbV38CUQUkGBJ0XiLTxafye9OeEeQkueJbLyT+DY4PVTesbl3Lssj7o/vjboOdojKzv0Grn8d8c5fCrvHU4PrOPCvGWM9bTwWNcpbpcmo5RpmLFB0r59r+F0ICzbImyHE8Go1woRtsKJUBSy45+HCcXD0t7HWGHCdrj/YyuM5VhAXzizYsHsUHzj2K9wTNn0Q/56hyPtAs/ixYt58MEHWb58Od3d3YwdO5a5c+eyYMEC8vLy3C5vUE3dLTT1tmBgMKlQzdzpyHEcwh++Rffffo3T3QqAd9Js8j/2BYrHj6du0WtDTknWHlnZw8bkqe4T2W6VcFne2xyXs4UKTzt/tD/pdmmS4Tymh1wzNnNsJFm21S8Mha1I3+cRQlaYiBUm1Pc4stdrYbv/44gTIRjIZWLR4Kt+p0JaBZ5HH32UW2+9FcdxqK6uZsyYMXz44Yf893//N3/84x957LHHKC4udrvMAdbt3gBAbcFYAl7N4Eg3VusOdr74GD2blgNgFFYSOOWLeMcfg+nV+BwZ6M3QETRYRVwRfJ1abwufCz1Bz9bJUDDR7dJEDorH9JBn5pLHoQWp/c2yS4W0CTwrV67k3/7t3wD4yU9+wmc+8xkMw6ChoYErr7ySVatWcdNNN3H33Xe7XOlAaxtjgUfjd9KLEw0TXraQ8LI/gB0Fjw//zAvxH3sBhtfvdnkyym2MVvHz9guYF/wLtd4Wdjz6I8zSGrzjZ+IdPxOz8jAMU4FZJFXSJvDcc8892LbNJZdcwmc/+9nE81VVVfzHf/wH559/Pn/84x9Zu3YtU6dOdbHSgdbu/hDQ+jujnRPqwmrchLVrI9auDdgNG3BCsammuZOPw3fy5Tj5FS5XKemkxQ5yZ/tcrqhYylH2euzmesLN9YSXvYARKMAz/li8E2birT0aw6fWX5FkSovA09XVxV//+lcAPvOZzwx4feLEiZx00kn8/e9/56WXXhpVgacn0sOWttgOw5OLJrhcjcQ5VgS7aVss3DRuxNq1Eadt54DjjPxS8j72BSpnfZzW1m7XmmIlfYXx8Sf/J5h75Q9oXvUWvRveI7p1BU5vB9H1fyO6/m9gevHWTsM3bgZmYTlmXjFmXhFGXhGGxzfgmiO187ppGpjmvmeRpXqXd5FkSYvAs2bNGsLhMH6/n2OOOWbQY2bNmsXf//53li9fnuLq9m1D6xYcx6HcX0CwpYEoDW6XNLKcEfxB6DiA0/+6H33OccCxcGwbHAtsG2wLHBvHtmKf21GccA9OqBsn3A2hLpxw7HMnFPtHpGfQEozCSjyVk/FUTMZTORmzfCK+HL8W8pJDUlyQg5GTT8Xss2H22ThWlN5ta+j+4F26PniXaMtOoltXEN26YsC5ZiCIJ1iMJ1iCN78YT34RjtdPOOzgmF4M0wue2L9+n2OCYfTNijdjHw0TMMAwME2TvGAA07P3/9vGgE9ty6GzKzQyoedQvo88Br2duUQ7eohaCmBpx2MQtirB496inIbjjORvrOT47W9/y4033sjEiRN5+eWXBz3m+eef57vf/S5jxozhtddeG9b7OM7I/yXTHeqg247gt22C+iYdXQwj9tezx9v30YcxxF+7pmli24O37pimSWtHiKg1+Os5fg8Fef59HnOgx422Y0ZjTaO57s7uMNYgP2NMx8JnWHixsKwohmNjjP4fzSIHzcwrghEeA2maxgH9UZoWLTxtbbHpvkVFRUMeE38tfuxwGIaBxzOyf8kX5BVRMKJXFLeY+xhgWlyQs9/zD+SYkbxWKo8ZjTWNxrqDefv/QZ8WP5RF0lBaTBEIhWLLRfp8A/uy4/x+f79jRUREROLSIvDk5MT+copEIkMeEw6H+x0rIiIiEpcWgedAuqsOpNtLREREslNaBJ6JEycCsH379iFbebZu3drvWBEREZG4tAg8Rx11FD6fj3A4zIoVA6dtAixZsgSAmTNnprAyERERSQdpEXiCwSAf+9jHAHjyyScHvL5582YWL14MwNy5c1Nam4iIiIx+aRF4AK666ioMw+C5557jiSeeIL580K5du7juuuuwbZtzzjlnVK2yLCIiIqNDWiw8GPfQQw9x++234zgOY8aMoaSkhA8//JBwOMykSZN47LHHKC0tdbtMERERGWXSKvAAvPnmmzzwwAOsWLGC7u5uxo4dy9y5c1mwYAH5+flulyciIiKjUNoFHhEREZGDlTZjeERERESGS4FHREREMp4Cj4iIiGQ8BR4RERHJeF63C8hkixcv5sEHH2T58uUDZpTl5eW5XZ4MobGxkUWLFrFy5Uref/991qxZQygUYs6cOTz66KNulyf74TgOS5cu5dVXX2XJkiVs3LiRzs5OCgoKmDZtGpdccgkXX3wxhmG4Xarsw4svvsjf//53Vq1axa5du2htbcXn8zFx4kQ+/vGP85WvfIWSkhK3y5SD8Prrr7NgwQIAampqePXVV1P6/pqllSSPPvoot956K47jUF1dTWlpaWLNoMMOO4zHHnuM4uJit8uUQTz00EPcdtttA55X4EkPb775Jl/96lcTj8eNG0dhYSH19fW0trYCcMYZZ3D33Xfj9/vdKVL265Of/CRr167F7/dTUVFBSUkJzc3NbN++HYCysjIeeOABLTabJrq6urjooosS98+NwKMWniRYuXIl//Zv/wbAT37yEz7zmc9gGAYNDQ1ceeWVrFq1iptuuom7777b5UplMMFgkFNOOYUZM2YwY8YMVq9ezT333ON2WXKAHMehtraWr3zlK1x44YWUlZUlXnv22We56aabeO2117jzzjv57ne/62Klsi9f+MIXmDRpEjNnzsTn8yWeX7duHTfccAPr16/n+uuv54UXXnCxSjlQv/jFL9i+fTtnn302r7zyiis1qIUnCa666ipeeeUVLrnkEn7605/2e23z5s2cf/752LbNc889p79O0sD//d//ccstt6iFJ010dnaSk5PT75fk3v7nf/6HX/ziFxQXF/Pmm29imhrKmG5WrFjBP/7jPwLwhz/8gcMOO8zlimRfli1bxuc//3nOPPNMzjnnHH7wgx+40sKj7/QR1tXVxV//+lcAPvOZzwx4feLEiZx00kkAvPTSSymtTSQbBIPBIcMOwOmnnw5Aa2srzc3NqSpLRtDkyZMTn/f09LhYiexPJBLhpptuIhAI8KMf/cjVWhR4RtiaNWsIh8P4/X6OOeaYQY+ZNWsWAMuXL09laSIC9Pb2Jj4PBAIuViLDtWTJEgDy8vKYNGmSy9XIvtx7772sX7+eb3/721RXV7tai8bwjLBNmzYBMHbs2CH/yhw/fny/Y0UkdeJjPqZOnUowGHS5GjlQtm0nZlDecccdANxwww3aQ3EU27BhA/feey/Tp0/nS1/6ktvlKPCMtLa2NgCKioqGPCb+WvxYEUmNlStX8vjjjwMkpsfK6DbYrMljjjmG22+/PdE9KaOP4zjceOONRKNRbr75Zjwej9slqUtrpIVCIYB9jiGIT4WNHysiybd7926uueYaotEon/jEJ7jwwgvdLkkOQFVVFccffzzHHnssFRUVGIbBmjVreO6552hvb3e7PBnCY489xnvvvccXvvAFZsyY4XY5gFp4RlxOTg4QG6g1lHA43O9YEUmujo4O5s+fz/bt25k+fTq333672yXJATr//PM5//zzE4/Xrl3LLbfcwsKFC9mwYQNPPfXUqGg9kD0aGhr4j//4D6qqqrj22mvdLidBLTwj7EC6qw6k20tERkZXVxfz5s1j9erVTJkyhV/96lcau5PGpk6dyr333ktJSQlr1qzROjyj0C233EJnZyc33njjqPpeUwvPCJs4cSIA27dvJxKJDNq1tXXr1n7Hikhy9PT08I1vfINly5YxceJEHnzwQW1HkAGCwSBz5szh5ZdfZtWqVfzDP/yD2yXJXlavXg3AzTffzM0339zvtfgsyR07dnDqqacCcPfdd3P88ccnvS4FnhF21FFH4fP5CIfDrFixIjEFfW/xKZUzZ85McXUi2SMUCnHllVfyzjvvUFNTw0MPPURFRYXbZckIiUajAFiW5XIlMpTdu3cP+Zpt24nX9zUEZCQp8IywYDDIxz72Mf7yl7/w5JNPDgg8mzdvZvHixQDMnTvXjRJFMl4kEuGaa67hzTffpKqqiocffpgxY8a4XZaMkNbWVt5++20g9kemjC77WkH56aef1krLmeSqq67CMAyee+45nnjiCeK7d+zatYvrrrsO27Y555xztK2ESBJYlsX111/P66+/TkVFBQ8//DDjxo1zuyw5CG+//Tb33HMPdXV1A15btWoVX//61+no6KCqqkp/OMoB015aSfLQQw9x++234zgOY8aMoaSkJLFb+qRJk3jssccoLS11u0wZxI4dO7jkkksSj8PhMN3d3Xi93n4D8ObNm8f8+fNdqFD2ZeHChVx//fVAbEfmqqqqIY+96aabmDZtWqpKkwP05z//mauvvhqAiooKKisr8Xg87Nixg8bGRiA2Xf3ee+9VC0+acbOFR11aSfLVr36VI488kgceeIAVK1bQ1NTE2LFjmTt3LgsWLNDqoKOYZVm0trYOeD4ajfZ7fu8tCmT0iC/7AFBfX099ff2Qx3Z0dKSiJDlIxx13HD/4wQ946623+PDDD9m8eTPhcJjCwkJOPPFEzjrrLC677LJRNQNIRj+18IiIiEjG0xgeERERyXgKPCIiIpLxFHhEREQk4ynwiIiISMZT4BEREZGMp8AjIiIiGU+BR0RERDKeAo+IiIhkPAUeERERyXgKPCIiIpLxFHhEREQk4ynwiIiISMZT4BEREZGM9/8BZN7+poIAJYMAAAAASUVORK5CYII=", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# random samples to generate at each repetition\n", + "n = 100\n", + "\n", + "# repetition to evaluate the distirbution of sample mean\n", + "n_rep = 1000\n", + "\n", + "# standard deviation of the normal distribution\n", + "s = 1.0\n", + "\n", + "m_hat = np.zeros([n_rep])\n", + "for i_rep in range(n_rep):\n", + " samples = stt.lognorm.rvs(s=s, size=n)\n", + " m_hat[i_rep] = samples.mean()\n", + "\n", + "vx = np.linspace(m_hat.min(), m_hat.max(), 50)\n", + "vx = np.linspace(0, 4, 50)\n", + "dx = np.diff(vx)[0]\n", + "plt.figure()\n", + "plt.hist(m_hat, bins=vx)\n", + "plt.plot(vx, stt.norm.pdf(x=vx,\n", + " loc=np.mean(m_hat), # here we use the actual mean of m_hat\n", + " scale=np.std(samples)/np.sqrt(n))*n_rep*dx) # but here we use the std of a single batch of samples\n", + "plt.plot(vx, stt.lognorm.pdf(x=vx,s=s)*n_rep*dx)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5404b927-e644-41fd-805d-4b9fb5a59310", + "metadata": {}, + "source": [ + "We can use Student's test to check whether observations come from a distribution away from 0 (i.e. there is some effect)." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "4d970957-a64b-4dd8-9d58-53d818b00fa0", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t statistics: 0.4147384100014492\n", + "p value: 0.6783334109743193\n", + "TtestResult(statistic=0.40423699891771864, pvalue=0.6905525245190809, df=19)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# generate random samples\n", + "n = 20\n", + "samples = stt.norm.rvs(loc=0.3, scale=1.0, size=n)\n", + "\n", + "# t statistics\n", + "t = np.mean(samples) * np.sqrt(n) / np.std(samples) # n should be replaced by n-1 for unbiased estimate\n", + "print('t statistics:', t)\n", + "print('p value:', 1.0 - np.abs(0.5 - stt.norm.cdf(t))*2)\n", + "print(stt.ttest_1samp(samples, popmean=0.0))\n", + "\n", + "plt.figure()\n", + "plt.hist(samples, bins=50)\n", + "plt.title('sample mean {:.4f}'.format(samples.mean())) \n", + "\n", + "vx = np.linspace(-4.0,4.0,100)\n", + "plt.figure()\n", + "plt.plot(vx, stt.norm.cdf(x=vx))\n", + "plt.plot(t, 1.0, 'x')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c6f9c939-ba4e-474e-89bb-a3cae4c6fe46", + "metadata": {}, + "source": [ + "## Statistical testing: is a distribution normal?\n", + "\n", + "Several tests exists to compare distributions:\n", + "- D’Agostino-Pearson (`normaltest`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html#scipy.stats.normaltest))\n", + "- Shapiro-Wilk (`shapiro`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html#scipy.stats.shapiro))\n", + "- Anderson-Darling (`anderson`, [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html#scipy.stats.anderson))\n", + "\n", + "For example, the `normaltest` rely on the combined `kurtosistest` and `skewtest` that check how close to zero these statistics are (to match a normal distribution).\n", + "\n", + "From the doc: If the p-value is “small”, there is a low probability of sampling data from a normally distributed population. In other words, this may be taken as evidence against the null hypothesis in favor of the alternative: the weights were not drawn from a normal distribution.\n", + "\n", + "*Importantly:* The inverse is not true; that is, these tests are not used to provide evidence for the null hypothesis.\n", + "\n", + "In contrast, the `anderson` test fits to a given distribution and evaluates the goodness of fit. In this way, you get an estimation of the mean and variance of the estimated distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "d4f3f64e-cfa8-4b58-b27c-3ac289ffb5c3", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SkewtestResult(statistic=-1.013576502919708, pvalue=0.3107848743910204)\n", + "KurtosistestResult(statistic=-0.7866552414262014, pvalue=0.431483711987908)\n" + ] + } + ], + "source": [ + "print(stt.skewtest(samples))\n", + "print(stt.kurtosistest(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "395d152c-becb-4fed-b755-e5af7c94983e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NormaltestResult(statistic=1.64616379613426, pvalue=0.43907637852519876)\n" + ] + } + ], + "source": [ + "print(stt.normaltest(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "bf09163c-0c14-434a-bc20-3fa5d3ab34e8", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ShapiroResult(statistic=0.9387915134429932, pvalue=0.22747208178043365)\n" + ] + } + ], + "source": [ + "print(stt.shapiro(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "6b57ebfd-4cea-4143-8348-cf849531c4ab", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AndersonResult(statistic=0.5029750226521976, critical_values=array([0.506, 0.577, 0.692, 0.807, 0.96 ]), significance_level=array([15. , 10. , 5. , 2.5, 1. ]), fit_result= params: FitParams(loc=0.1138781533994346, scale=1.259851487296024)\n", + " success: True\n", + " message: '`anderson` successfully fit the distribution to the data.')\n" + ] + } + ], + "source": [ + "print(stt.anderson(samples, dist='norm'))" + ] + }, + { + "cell_type": "markdown", + "id": "0e840030-3d48-4313-9ef9-c543c6c25fe6", + "metadata": {}, + "source": [ + "### *EXERCISES*\n", + "- Apply these tests for various sample sizes and check the robustness of these tests\n", + "- Redo these steps with the lognormal distribution, playing with the shape $s$\n", + "- Try to fit the data *NeuroCog* (cognitive scores from patients and controls, see below), using the `fit` method of distributions (e.g. `norm.fit(...)`, `lognorm.fit(...)`, etc.)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "5d42fe82-e5d6-44f4-915e-a46f21f83a96", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 10\n", + "skew:\t\t 0.3593711385019305\n", + "kurtosis:\t -1.4244540959463516\n", + "NormaltestResult(statistic=2.559075324979261, pvalue=0.27816587724712266)\n", + "ShapiroResult(statistic=0.8652520179748535, pvalue=0.08797058463096619)\n", + "\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/INT/gilson.m/.local/lib/python3.10/site-packages/scipy/stats/_stats_py.py:1736: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10\n", + " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 100\n", + "skew:\t\t -0.48429086917433944\n", + "kurtosis:\t 0.6186676615520206\n", + "NormaltestResult(statistic=6.069805193567676, pvalue=0.04807934573043403)\n", + "ShapiroResult(statistic=0.9765862226486206, pvalue=0.071839839220047)\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 1000\n", + "skew:\t\t -0.0040079668918747416\n", + "kurtosis:\t -0.16531861298315453\n", + "NormaltestResult(statistic=1.1261373621525286, pvalue=0.569458892136816)\n", + "ShapiroResult(statistic=0.9985209107398987, pvalue=0.5683215856552124)\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 10000\n", + "skew:\t\t -0.0350430206764161\n", + "kurtosis:\t -0.039132344764211346\n", + "NormaltestResult(statistic=2.6552149714653597, pvalue=0.2651107844752864)\n", + "ShapiroResult(statistic=0.999798059463501, pvalue=0.49420076608657837)\n", + "\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/INT/gilson.m/.local/lib/python3.10/site-packages/scipy/stats/_morestats.py:1816: UserWarning: p-value may not be accurate for N > 5000.\n", + " warnings.warn(\"p-value may not be accurate for N > 5000.\")\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample size: 100000\n", + "skew:\t\t 0.002944283697641588\n", + "kurtosis:\t -0.005260165299323827\n", + "NormaltestResult(statistic=0.25264791128513453, pvalue=0.8813292889357649)\n", + "ShapiroResult(statistic=0.9999809265136719, pvalue=0.934694230556488)\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# loop to generate samples with various sizes\n", + "v_n = [10,100,1000,10000,100000]\n", + "\n", + "for n in v_n:\n", + " print('sample size:', n)\n", + " samples2 = stt.norm.rvs(size=n)\n", + "# samples2 = stt.lognorm.rvs(s=0.1, size=n)\n", + "# samples2 = stt.lognorm.rvs(s=0.5, size=n)\n", + "\n", + " # variable range\n", + " vx2 = np.linspace(-3.0,3.0,50)\n", + " dx2 = np.diff(vx2)[0]\n", + "\n", + " # comparison between sample histogram and ground truth (probability density function)\n", + " plt.figure()\n", + " plt.hist(samples2, bins=vx2)\n", + " plt.xlabel('value')\n", + " plt.ylabel('sample count')\n", + " plt.tight_layout()\n", + "\n", + " # summary statistics\n", + " print('skew:\\t\\t', stt.skew(samples2))\n", + " print('kurtosis:\\t', stt.kurtosis(samples2))\n", + " \n", + " # tests for normality\n", + " print(stt.normaltest(samples2))\n", + " print(stt.shapiro(samples2))\n", + " \n", + " print()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "3239e1ef-7c45-47a6-b1aa-0573fa2214f6", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# load NeuroCog data \n", + "import pandas as pd\n", + "df = pd.read_csv('../../data/ex_stats/NeuroCog_dataset.csv', sep=',')\n", + "\n", + "# select memory scores for control subjects\n", + "sel_df = df['Dx']=='Control'\n", + "samples = np.array(df[sel_df]['Memory'])\n", + "n = samples.size" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "3a3e6bfe-2508-4b64-a3ca-3d64a7099b11", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# range of values\n", + "vx = np.linspace(samples.min(),samples.max(),50)\n", + "dx = np.diff(vx)[0]\n", + "\n", + "plt.hist(samples, bins=vx)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "# show percentiles from samples, top and bottom 5%\n", + "if True:\n", + " top_lim = stt.scoreatpercentile(samples, 95.0)\n", + " bottom_lim = stt.scoreatpercentile(samples, 5.0)\n", + " l = 10\n", + " plt.plot([top_lim]*2, [0,l], ls='--', c='gray')\n", + " plt.plot([bottom_lim]*2, [0,l], ls='--', c='gray')" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "8cd1d6fd-f2ca-4f27-a4f8-420fa9c03013", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SkewtestResult(statistic=-3.093498102795657, pvalue=0.0019781181783180414)\n", + "KurtosistestResult(statistic=1.47635115293601, pvalue=0.13984964859269813)\n", + "NormaltestResult(statistic=11.749343238775817, pvalue=0.002809716699540441)\n", + "ShapiroResult(statistic=0.967986524105072, pvalue=0.0018053010571748018)\n" + ] + } + ], + "source": [ + "print(stt.skewtest(samples))\n", + "print(stt.kurtosistest(samples))\n", + "print(stt.normaltest(samples))\n", + "print(stt.shapiro(samples))" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "a2eaebb2-3ce1-4c2e-b78a-1cd9237c986d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AndersonResult(statistic=1.4625728239705609, critical_values=array([0.561, 0.639, 0.767, 0.894, 1.064]), significance_level=array([15. , 10. , 5. , 2.5, 1. ]), fit_result= params: FitParams(loc=45.66206896551724, scale=11.182340175507374)\n", + " success: True\n", + " message: '`anderson` successfully fit the distribution to the data.')\n", + "AndersonResult(statistic=38.501451395049344, critical_values=array([0.918, 1.074, 1.335, 1.599, 1.949]), significance_level=array([15. , 10. , 5. , 2.5, 1. ]), fit_result= params: FitParams(loc=0.0, scale=45.66206896551724)\n", + " success: True\n", + " message: '`anderson` successfully fit the distribution to the data.')\n" + ] + } + ], + "source": [ + "for dist_type in ['norm', 'expon']:\n", + " print(stt.anderson(samples, dist=dist_type))" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "fd2f6d0e-22ac-44c2-99dc-911a8a6712b9", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[<matplotlib.lines.Line2D at 0x74134048abf0>]" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# fit a normal distribution to the empirical data\n", + "fitted_loc, fitted_scale = stt.norm.fit(data=samples)\n", + "\n", + "plt.hist(samples, bins=vx)\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "\n", + "plt.plot(vx, stt.norm.pdf(x=vx, loc=fitted_loc, scale=fitted_scale)*n*dx)" + ] + }, + { + "cell_type": "markdown", + "id": "12cd9759-5bf4-4ab7-a75b-5cba2122f1df", + "metadata": {}, + "source": [ + "## Statistical testing to compare two distributions\n", + "\n", + "We can now consider the distributions of real data across several conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "a83ce97d-6fc3-46d0-906c-d0eec135e514", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sb.violinplot(data=df, y='Memory', x='Dx', hue='Dx', order=('Control','Schizophrenia','Schizoaffective'), palette=['blue','green','orange'])\n", + "plt.xticks(fontsize=14)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "3d8e7686-8ae6-404c-886e-669873077ac6", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# get memory scores for controls and schizophrenia patients\n", + "score_measure = 'Memory'\n", + "sel_df = df['Dx']=='Control'\n", + "samples_ctrl = np.array(df[sel_df][score_measure])\n", + "sel_df = df['Dx']=='Schizophrenia'\n", + "samples_pat = np.array(df[sel_df][score_measure])\n", + "n_ctrl = samples_ctrl.size\n", + "n_pat = samples_pat.size\n", + "\n", + "# range of values\n", + "samples = np.concatenate((samples_ctrl, samples_pat))\n", + "vx = np.linspace(samples.min(),samples.max(),50)\n", + "dx = np.diff(vx)[0]\n", + "\n", + "plt.hist(samples_ctrl, bins=vx, histtype='step', label='ctrl', color='orange')\n", + "plt.hist(samples_pat, bins=vx, histtype='step', label='pat', color='blue')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "336eb4c9-ea1a-4e9a-8a8b-da9ada5aa639", + "metadata": {}, + "source": [ + "\n", + "\n", + "https://en.wikipedia.org/wiki/Student%27s_t-test\n", + "\n", + "$\\chi$2 distibution [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html#scipy.stats.chi2)" + ] + }, + { + "cell_type": "markdown", + "id": "e0bfb221-6a9e-4905-a6bf-a3c5c7b5ba0e", + "metadata": {}, + "source": [ + "\n", + "\n", + "$$ f(x, k) = \\frac{1}{2^{k/2} \\Gamma \\left( k/2 \\right)}\n", + " x^{k/2-1} \\exp \\left( -x/2 \\right)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "2cb261b3-1444-44f6-ad28-d4177628c3d4", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ttest_indResult(statistic=4.707384156121897, pvalue=4.667384543620185e-06)\n" + ] + } + ], + "source": [ + "# Student's t-test (parametric: normal distributions with equal variances)\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat))" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "3418daca-4220-4b81-82ce-d8bc59bc691e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "variances\n", + "controls: 124.18235434007134\n", + "patients: 139.59958382877525\n" + ] + } + ], + "source": [ + "print('variances')\n", + "print('controls:', np.var(samples_ctrl))\n", + "print('patients:', np.var(samples_pat))" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "f63fc195-1845-4eb0-86c7-1fbcb1650f76", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ttest_indResult(statistic=4.580013245897252, pvalue=1.3509339537040669e-05)\n" + ] + } + ], + "source": [ + "# Welch's t-test (parametric: normal distributions with unequal variances)\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat, equal_var=False))" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "0818927a-7d17-41b3-b21f-fac1e7cb5113", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MannwhitneyuResult(statistic=5934.5, pvalue=4.707083559908631e-06)\n" + ] + } + ], + "source": [ + "# Mann-whitney test or Wilcoxon unsigned test (non-parametric)\n", + "print(stt.mannwhitneyu(samples_ctrl, samples_pat))" + ] + }, + { + "cell_type": "markdown", + "id": "d4508eb8-e3b6-489c-9890-3ff65d7470ea", + "metadata": {}, + "source": [ + "### Exercise\n", + "- Redo the comparison of statistical tests for other cognitive scores\n", + "- Redo the comparison of statistical tests for normal and lognormal distributions (playing with the shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "9fd0d37b-f800-48dd-9586-70e5bc6a412f", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ttest_indResult(statistic=6.413417601062506, pvalue=9.972764687201873e-10)\n", + "Ttest_indResult(statistic=6.523279590300689, pvalue=2.2290120236851023e-09)\n", + "MannwhitneyuResult(statistic=6530.0, pvalue=7.415691530325375e-10)\n" + ] + } + ], + "source": [ + "# get memory scores for controls and patients\n", + "score_measure = 'Verbal' # 'Attention', 'Memory', 'Verbal', 'Visual'\n", + "sel_df = df['Dx']=='Control'\n", + "samples_ctrl = np.array(df[sel_df][score_measure])\n", + "sel_df = df['Dx']=='Schizophrenia'\n", + "samples_pat = np.array(df[sel_df][score_measure])\n", + "n_ctrl = samples_ctrl.size\n", + "n_pat = samples_pat.size\n", + "\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat))\n", + "print(stt.ttest_ind(samples_ctrl, samples_pat, equal_var=False))\n", + "print(stt.mannwhitneyu(samples_ctrl, samples_pat))" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "c573b539-9003-414d-9d84-88743206b8e4", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sample mean and variance:\n", + "sample1: -0.24394829443971383 0.9331152425376638\n", + "sample2: 0.4135405943157268 2.6407966394867928\n", + "\n", + "theoretical t-statistics: -2.836446653297359\n", + "Ttest_indResult(statistic=-4.365216965963432, pvalue=1.753499521201049e-05)\n", + "Ttest_indResult(statistic=-3.712568974733387, pvalue=0.0002992774787276999)\n", + "MannwhitneyuResult(statistic=7356.0, pvalue=0.00018977075897167549)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create 2 normal distribution with variances sig1 and sig2, and mean separation of d_mu\n", + "d_mu = 0.5\n", + "sig1 = 1.0\n", + "sig2 = 1.5\n", + "n1 = 200\n", + "samples1 = stt.norm.rvs(loc=-0.5*d_mu, scale=sig1, size=n1)\n", + "n2 = 100\n", + "samples2 = stt.norm.rvs(loc=0.5*d_mu, scale=sig2, size=n2)\n", + "\n", + "print('sample mean and variance:')\n", + "print('sample1:', np.mean(samples1), np.var(samples1))\n", + "print('sample2:', np.mean(samples2), np.var(samples2))\n", + "\n", + "vx = np.linspace(-5.0,5.0,50)\n", + "plt.hist(samples1, bins=vx, histtype='step', label='norm1')\n", + "plt.hist(samples2, bins=vx, histtype='step', label='norm2')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()\n", + "\n", + "print()\n", + "print('theoretical t-statistics:', -d_mu / np.sqrt(np.var(samples1)/n1 + np.var(samples2)/n2))\n", + "print(stt.ttest_ind(samples1, samples2))\n", + "print(stt.ttest_ind(samples1, samples2, equal_var=False))\n", + "print(stt.mannwhitneyu(samples1, samples2))" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "9f6440ed-d77d-46f5-a1a9-caf16a6c75ce", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean, variance:\n", + "sample1: -0.07346716950949936 0.8913283013990926\n", + "sample2: -3.9968028886505634e-17 1.0\n", + "Ttest_indResult(statistic=-0.7535921841490139, pvalue=0.45153970767842466)\n", + "Ttest_indResult(statistic=-0.7535921841490139, pvalue=0.45154117793644255)\n", + "MannwhitneyuResult(statistic=20934.0, pvalue=0.41942105683228625)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create \n", + "n1 = 200\n", + "samples1 = stt.norm.rvs(loc=0.0, scale=1.0, size=n1)\n", + "n2 = 200\n", + "samples2 = stt.lognorm.rvs(s=0.5, size=n2)\n", + "# z-score to center and get standard deviation equal to 1\n", + "samples2 -= samples2.mean()\n", + "samples2 /= samples2.std()\n", + "\n", + "print('mean, variance:')\n", + "print('sample1:', np.mean(samples1), np.var(samples1))\n", + "print('sample2:', np.mean(samples2), np.var(samples2))\n", + "\n", + "vx = np.linspace(-5.0,10.0,50)\n", + "plt.hist(samples1, bins=vx, histtype='step', label='lognorm')\n", + "plt.hist(samples2, bins=vx, histtype='step', label='norm')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()\n", + "\n", + "print(stt.ttest_ind(samples1, samples2))\n", + "print(stt.ttest_ind(samples1, samples2, equal_var=False))\n", + "print(stt.mannwhitneyu(samples1, samples2))" + ] + }, + { + "cell_type": "markdown", + "id": "55084553-673a-48f5-874f-58351613107f", + "metadata": {}, + "source": [ + "## Miscellanous\n", + "\n", + "We can also generate a random variable from empirical observations ([link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_histogram.html#scipy-stats-rv-histogram)). But this method doesn't generalize well in the sense of smoothing the histogram for small number of observed samples..." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "0cfe8571-012e-4ab2-8ea1-861aea6a17df", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "<matplotlib.legend.Legend at 0x74134072df00>" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# create a generator of random variables from the empirical samples\n", + "hist = np.histogram(samples, bins=100)\n", + "emp_rv = stt.rv_histogram(hist)\n", + "\n", + "# generate surrogate samples\n", + "surr_samples = emp_rv.rvs(size=100000)\n", + "\n", + "# comparison between sample histogram and ground truth (probability density function)\n", + "plt.hist(samples, bins=vx, density=True, label='orig')\n", + "plt.hist(surr_samples, bins=vx, histtype='step', density=True, label='surr')\n", + "plt.xlabel('value')\n", + "plt.ylabel('sample count')\n", + "plt.legend()" + ] + } + ], + "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": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} -- GitLab