{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Class 19: Monte Carlo simulations II\n", "\n", "---\n", "\n", "\n", "\n", "This notebook is licensed under a [Creative Commons Attribution-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-sa/4.0/)." ] }, { "cell_type": "markdown", "metadata": { "cell_style": "center", "slideshow": { "slide_type": "slide" } }, "source": [ "## Load packages" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "cell_style": "center", "slideshow": { "cell_style": "split", "slide_type": "-" } }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from pathlib import Path\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import seaborn as sns\n", "import scipy\n", "\n", "np.random.seed(1618027461)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Monte Carlo integration" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import mc_integration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At the end of last class, we were introduced to Monte Carlo integration. We used it to estimate the area under the curve defined by the function $y(x)=-1.75x^2+x^3+1.4$ within the bounds $0\\leq{}x\\leq{}2.0$ and $0\\leq{}y\\leq{}2.5$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(start=0, stop=2.0, num=200)\n", "df = pd.DataFrame({\"x\": x, \"y\": mc_integration.cubic_function(x)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function and area to find is visualized below:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.lineplot(x=\"x\", y=\"y\", data=df, ax=ax, color=\"black\")\n", "ax.fill_between(x=df[\"x\"], y1=df[\"y\"], color=\"tab:orange\", alpha=0.3)\n", "ax.set_xlim([0, 2.0])\n", "ax.set_ylim([0, 2.0]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To use a Monte Carlo simulation to calculate the area under the curve, we note that the area under the curve is approximately equal to\n", "\n", "\\begin{equation}\n", " \\text{area}\\approx{}\\left(\\text{area of enclosing rectangle}\\right)\\left(\\frac{\\text{number of darts below}}{\\text{number of darts}}\\right)\n", "\\end{equation}\n", "\n", "We implemented functions to compute this quantity, see the supplied file [mc\\_integration.py](mc_integration.py). We ran the simulation throwing 1,000 darts within the bounds and used this to compute the area under the curve." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "mc_results_df, mc_results_area = mc_integration.run(\n", " function=mc_integration.cubic_function,\n", " number_of_darts=1000,\n", " x_min=0,\n", " x_max=2,\n", " y_min=0,\n", " y_max=2.5\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visually, the integration looked as follows:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.lineplot(x=\"x\", y=\"y\", data=df, color=\"black\", ax=ax)\n", "ax.fill_between(x=df[\"x\"], y1=df[\"y\"], color=\"tab:orange\", alpha=0.3)\n", "sns.scatterplot(x=\"x\", y=\"y\", hue=\"hit\", data=mc_results_df, ax=ax)\n", "ax.set_xlim([0, 2.0])\n", "ax.set_ylim([0, 2.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimated area is:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "estimated area = 2.145\n" ] } ], "source": [ "print(f\"estimated area = {mc_results_area}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The exact area is:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "exact area = 2.1333333333333333\n" ] } ], "source": [ "exact_area_numerical = scipy.integrate.quad(\n", " func=mc_integration.cubic_function,\n", " a=0,\n", " b=2,\n", ")\n", "\n", "print(f\"exact area = {exact_area_numerical[0]}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Statistical variation of estimated area" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we re-run the computation for the estimated area using 1,000 darts, we find that the estimated area is different:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "estimated area = 2.29\n" ] } ], "source": [ "mc_results_df_run2, mc_results_area_run2 = mc_integration.run(\n", " function=mc_integration.cubic_function,\n", " number_of_darts=1000,\n", " x_min=0,\n", " x_max=2,\n", " y_min=0,\n", " y_max=2.5\n", ")\n", "print(f\"estimated area = {mc_results_area_run2}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a common feature of Monte Carlo simulations that is a direct consequence of using a random number generator. Even when all input variables are kept fixed, the numerical result will vary. Thus, we can apply the statistical methods we discussed during the data-driven modeling unit here. How to do this? First, we need a distribution of estimated areas when we perform 1,000 random dart throws. Here's how we'll obtain that:\n", "\n", "1. Initialize a list\n", "2. Fix the parameters for the `mc_integration.run()` simulation and run it.\n", "3. Append the estimated area to the list.\n", "4. Repeat the simulation multiple times, building up a distribution of estimated areas for the same number of random dart throws.\n", "\n", "In code, we use a `for` loop to do this:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "distribution_estimated_areas = {\n", " \"run\": [],\n", " \"area\": [],\n", "}\n", "\n", "for run in range(1000):\n", " tmp_df, tmp_estimated_area = mc_integration.run(\n", " function=mc_integration.cubic_function,\n", " number_of_darts=1000,\n", " x_min=0,\n", " x_max=2,\n", " y_min=0,\n", " y_max=2.5\n", " )\n", " distribution_estimated_areas[\"run\"].append(run)\n", " distribution_estimated_areas[\"area\"].append(tmp_estimated_area)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then convert the list of estimated areas into a data frame:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "distribution_estimated_areas_df = pd.DataFrame(distribution_estimated_areas)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the summary statistics, we get:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "count 1000.000000\n", "mean 2.133540\n", "std 0.080404\n", "min 1.855000\n", "25% 2.080000\n", "50% 2.135000\n", "75% 2.190000\n", "max 2.355000\n", "Name: area, dtype: float64" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "distribution_estimated_areas_df[\"area\"].describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the distribution of areas, we get:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jglasbr2/.conda/envs/cds411-dev/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.distplot(a=distribution_estimated_areas_df[\"area\"], bins=20, ax=ax)\n", "ax.set_xlim([1.8, 2.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use bootstrapping to estimate the standard error for the mean of the distribution:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "bootstrap_results = {\n", " \"sample\": [],\n", " \"mean\": [],\n", "}\n", "\n", "bootstrap_series = distribution_estimated_areas_df \\\n", " .sample(frac=1000, replace=True) \\\n", " .loc[:, \"area\"]\n", "bootstrap_df = pd.DataFrame(bootstrap_series) \\\n", " .assign(sample_id=[f\"{x}\" for x in range(1000) for _ in range(1000)])\n", "bootstrap_mean_samples = bootstrap_df \\\n", " .groupby([\"sample_id\"]) \\\n", " .mean() \\\n", " .loc[:, \"area\"] \\\n", " .values\n", "\n", "bootstrap_results[\"sample\"].extend(list(range(1000)))\n", "bootstrap_results[\"mean\"].extend(bootstrap_mean_samples)\n", "\n", "estimated_area_bootstrap_df = pd.DataFrame(bootstrap_results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll use the 95% confidence interval to define the lower and upper bounds of the error of the mean:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "estimated_areas_ci_95 = estimated_area_bootstrap_df \\\n", " .loc[:, [\"mean\"]] \\\n", " .quantile([0.025, 0.975]) \\\n", " .reset_index() \\\n", " .rename(columns={\"index\": \"quantile\"})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numerically, the mean is:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.13354" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "distribution_estimated_areas_df[\"area\"].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The upper and lower bounds for the error of the mean are:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "<div>\n", "<style scoped>\n", " .dataframe tbody tr th:only-of-type {\n", " vertical-align: middle;\n", " }\n", "\n", " .dataframe tbody tr th {\n", " vertical-align: top;\n", " }\n", "\n", " .dataframe thead th {\n", " text-align: right;\n", " }\n", "</style>\n", "<table border=\"1\" class=\"dataframe\">\n", " <thead>\n", " <tr style=\"text-align: right;\">\n", " <th></th>\n", " <th>quantile</th>\n", " <th>mean</th>\n", " </tr>\n", " </thead>\n", " <tbody>\n", " <tr>\n", " <th>0</th>\n", " <td>0.025</td>\n", " <td>2.128628</td>\n", " </tr>\n", " <tr>\n", " <th>1</th>\n", " <td>0.975</td>\n", " <td>2.138330</td>\n", " </tr>\n", " </tbody>\n", "</table>\n", "</div>" ], "text/plain": [ " quantile mean\n", "0 0.025 2.128628\n", "1 0.975 2.138330" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "estimated_areas_ci_95" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visually, we have:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jglasbr2/.conda/envs/cds411-dev/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.distplot(a=distribution_estimated_areas_df[\"area\"], bins=20, ax=ax)\n", "ax.axvline(x=distribution_estimated_areas_df[\"area\"].mean(), color=\"black\", linestyle=\"-\", linewidth=1)\n", "ax.axvline(x=estimated_areas_ci_95.loc[0, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.axvline(x=estimated_areas_ci_95.loc[1, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.set_xlim([1.8, 2.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Activity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the above code as a starting point, compute the area under the curve for increasing numbers of dart throws, starting from 1000 up until one million in powers of 10. So, 1,000, 10,000, 100,000, and 1,000,000. For each case, do the following:\n", "\n", "1. For a fixed number of dart throws, run the simulation 1000 times and obtain the distribution of estimated areas.\n", "2. Create histograms that summarize the range of outcomes for each amount of dart throws.\n", "3. Use bootstrapping to compute the standard error of the mean for each number of dart throws." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Activity work" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define functions to simplify how we run our simulations for different numbers of darts." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def multi_integration_sims(number_of_darts):\n", "\n", " distribution_estimated_areas = {\n", " \"run\": [],\n", " \"area\": [],\n", " }\n", " \n", " for run in range(1000):\n", " tmp_df, tmp_estimated_area = mc_integration.run(\n", " function=mc_integration.cubic_function,\n", " number_of_darts=number_of_darts,\n", " x_min=0,\n", " x_max=2,\n", " y_min=0,\n", " y_max=2.5\n", " )\n", " distribution_estimated_areas[\"run\"].append(run)\n", " distribution_estimated_areas[\"area\"].append(tmp_estimated_area)\n", " \n", " return pd.DataFrame(distribution_estimated_areas)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def darts_bootstrap(df):\n", " bootstrap_results = {\n", " \"sample\": [],\n", " \"mean\": [],\n", " }\n", " \n", " bootstrap_series = df \\\n", " .sample(frac=1000, replace=True) \\\n", " .loc[:, \"area\"]\n", " bootstrap_df = pd.DataFrame(bootstrap_series) \\\n", " .assign(sample_id=[f\"{x}\" for x in range(1000) for _ in range(1000)])\n", " bootstrap_mean_samples = bootstrap_df \\\n", " .groupby([\"sample_id\"]) \\\n", " .mean() \\\n", " .loc[:, \"area\"] \\\n", " .values\n", " \n", " bootstrap_results[\"sample\"].extend(list(range(1000)))\n", " bootstrap_results[\"mean\"].extend(bootstrap_mean_samples)\n", " \n", " return pd.DataFrame(bootstrap_results)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def confidence_intervals(df):\n", "\n", " return df \\\n", " .loc[:, [\"mean\"]] \\\n", " .quantile([0.025, 0.975]) \\\n", " .reset_index() \\\n", " .rename(columns={\"index\": \"quantile\"})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a dictionary to store our results" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "activity_results = {\n", " \"num_darts\": [],\n", " \"mean\": [],\n", " \"ci95_lower\": [],\n", " \"ci95_upper\": [],\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 100 darts" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "results_df = multi_integration_sims(100)\n", "bootstrap_df = darts_bootstrap(results_df)\n", "ci_df = confidence_intervals(bootstrap_df)\n", "\n", "activity_results[\"num_darts\"].append(100)\n", "activity_results[\"mean\"].append(results_df[\"area\"].mean())\n", "activity_results[\"ci95_lower\"].append(ci_df.loc[0, \"mean\"])\n", "activity_results[\"ci95_upper\"].append(ci_df.loc[1, \"mean\"])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jglasbr2/.conda/envs/cds411-dev/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.distplot(a=results_df[\"area\"], bins=20, ax=ax)\n", "ax.axvline(x=results_df[\"area\"].mean(), color=\"black\", linestyle=\"-\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[0, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[1, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.set_xlim([1.8, 2.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1,000 darts" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "results_df = multi_integration_sims(1000)\n", "bootstrap_df = darts_bootstrap(results_df)\n", "ci_df = confidence_intervals(bootstrap_df)\n", "\n", "activity_results[\"num_darts\"].append(1000)\n", "activity_results[\"mean\"].append(results_df[\"area\"].mean())\n", "activity_results[\"ci95_lower\"].append(ci_df.loc[0, \"mean\"])\n", "activity_results[\"ci95_upper\"].append(ci_df.loc[1, \"mean\"])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jglasbr2/.conda/envs/cds411-dev/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.distplot(a=results_df[\"area\"], bins=20, ax=ax)\n", "ax.axvline(x=results_df[\"area\"].mean(), color=\"black\", linestyle=\"-\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[0, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[1, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.set_xlim([1.8, 2.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10,000 darts" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "results_df = multi_integration_sims(10000)\n", "bootstrap_df = darts_bootstrap(results_df)\n", "ci_df = confidence_intervals(bootstrap_df)\n", "\n", "activity_results[\"num_darts\"].append(10000)\n", "activity_results[\"mean\"].append(results_df[\"area\"].mean())\n", "activity_results[\"ci95_lower\"].append(ci_df.loc[0, \"mean\"])\n", "activity_results[\"ci95_upper\"].append(ci_df.loc[1, \"mean\"])" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jglasbr2/.conda/envs/cds411-dev/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.distplot(a=results_df[\"area\"], bins=20, ax=ax)\n", "ax.axvline(x=results_df[\"area\"].mean(), color=\"black\", linestyle=\"-\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[0, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[1, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.set_xlim([1.8, 2.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 100,000 darts" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "results_df = multi_integration_sims(100000)\n", "bootstrap_df = darts_bootstrap(results_df)\n", "ci_df = confidence_intervals(bootstrap_df)\n", "\n", "activity_results[\"num_darts\"].append(100000)\n", "activity_results[\"mean\"].append(results_df[\"area\"].mean())\n", "activity_results[\"ci95_lower\"].append(ci_df.loc[0, \"mean\"])\n", "activity_results[\"ci95_upper\"].append(ci_df.loc[1, \"mean\"])" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jglasbr2/.conda/envs/cds411-dev/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.distplot(a=results_df[\"area\"], bins=20, ax=ax)\n", "ax.axvline(x=results_df[\"area\"].mean(), color=\"black\", linestyle=\"-\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[0, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[1, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.set_xlim([1.8, 2.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1,000,000 darts" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "results_df = multi_integration_sims(1000000)\n", "bootstrap_df = darts_bootstrap(results_df)\n", "ci_df = confidence_intervals(bootstrap_df)\n", "\n", "activity_results[\"num_darts\"].append(1000000)\n", "activity_results[\"mean\"].append(results_df[\"area\"].mean())\n", "activity_results[\"ci95_lower\"].append(ci_df.loc[0, \"mean\"])\n", "activity_results[\"ci95_upper\"].append(ci_df.loc[1, \"mean\"])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jglasbr2/.conda/envs/cds411-dev/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "sns.distplot(a=results_df[\"area\"], bins=20, ax=ax)\n", "ax.axvline(x=results_df[\"area\"].mean(), color=\"black\", linestyle=\"-\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[0, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.axvline(x=ci_df.loc[1, \"mean\"], color=\"tab:orange\", linestyle=\"--\", linewidth=1)\n", "ax.set_xlim([1.8, 2.5]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Summary of activity results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you complete this quickly, create a visualization that plots the mean estimated area for the different numbers of dart throws. Include error bars that represent the standard error of the mean. See the [class 19 Jupyter notebook](../class19/class19_notebook.ipynb) for a refresher on how to plot error bars." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "activity_results_df = pd.DataFrame(activity_results)\n", "activity_results_df[\"yerr_lower\"] = np.abs(activity_results_df[\"mean\"] - activity_results_df[\"ci95_lower\"])\n", "activity_results_df[\"yerr_upper\"] = np.abs(activity_results_df[\"mean\"] - activity_results_df[\"ci95_upper\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data frame summarizes the averages and standard errors for different number of dart throws." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "<div>\n", "<style scoped>\n", " .dataframe tbody tr th:only-of-type {\n", " vertical-align: middle;\n", " }\n", "\n", " .dataframe tbody tr th {\n", " vertical-align: top;\n", " }\n", "\n", " .dataframe thead th {\n", " text-align: right;\n", " }\n", "</style>\n", "<table border=\"1\" class=\"dataframe\">\n", " <thead>\n", " <tr style=\"text-align: right;\">\n", " <th></th>\n", " <th>num_darts</th>\n", " <th>mean</th>\n", " <th>ci95_lower</th>\n", " <th>ci95_upper</th>\n", " <th>yerr_lower</th>\n", " <th>yerr_upper</th>\n", " </tr>\n", " </thead>\n", " <tbody>\n", " <tr>\n", " <th>0</th>\n", " <td>100</td>\n", " <td>2.130150</td>\n", " <td>2.113849</td>\n", " <td>2.146050</td>\n", " <td>0.016301</td>\n", " <td>0.015900</td>\n", " </tr>\n", " <tr>\n", " <th>1</th>\n", " <td>1000</td>\n", " <td>2.131695</td>\n", " <td>2.126675</td>\n", " <td>2.136461</td>\n", " <td>0.005020</td>\n", " <td>0.004766</td>\n", " </tr>\n", " <tr>\n", " <th>2</th>\n", " <td>10000</td>\n", " <td>2.133681</td>\n", " <td>2.132144</td>\n", " <td>2.135266</td>\n", " <td>0.001537</td>\n", " <td>0.001584</td>\n", " </tr>\n", " <tr>\n", " <th>3</th>\n", " <td>100000</td>\n", " <td>2.133420</td>\n", " <td>2.132952</td>\n", " <td>2.133870</td>\n", " <td>0.000468</td>\n", " <td>0.000450</td>\n", " </tr>\n", " <tr>\n", " <th>4</th>\n", " <td>1000000</td>\n", " <td>2.133335</td>\n", " <td>2.133178</td>\n", " <td>2.133486</td>\n", " <td>0.000157</td>\n", " <td>0.000151</td>\n", " </tr>\n", " </tbody>\n", "</table>\n", "</div>" ], "text/plain": [ " num_darts mean ci95_lower ci95_upper yerr_lower yerr_upper\n", "0 100 2.130150 2.113849 2.146050 0.016301 0.015900\n", "1 1000 2.131695 2.126675 2.136461 0.005020 0.004766\n", "2 10000 2.133681 2.132144 2.135266 0.001537 0.001584\n", "3 100000 2.133420 2.132952 2.133870 0.000468 0.000450\n", "4 1000000 2.133335 2.133178 2.133486 0.000157 0.000151" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "activity_results_df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualizing the results for different numbers of dart throws:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "ax.set_xscale(\"log\", nonposx='clip')\n", "sns.scatterplot(x=\"num_darts\", y=\"mean\", data=activity_results_df, ax=ax)\n", "ax.errorbar(\n", " x=activity_results_df[\"num_darts\"],\n", " y=activity_results_df[\"mean\"],\n", " yerr=[activity_results_df[\"yerr_lower\"],\n", " activity_results_df[\"yerr_upper\"]],\n", ")\n", "ax.set_ylim([2.11, 2.150])\n", "ax.set_xlabel(\"number of darts\")\n", "ax.set_ylabel(\"area\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiplicative Linear Congruential Method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The textbook introduces the following simple linear congruential random number generator that generates values between 0 and 10, inclusive:\n", "\n", "\\begin{equation}\n", "r_{0}=10\n", "\\end{equation}\n", "\\begin{equation}\n", "r_{n}=\\left(7r_{n-1}+1\\right)\\text{ mod }11,\\text{ for }n>0\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "def my_random(seed, multiplier, increment, modulus):\n", " sequence = (multiplier * seed + increment) % modulus\n", " return sequence" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "my_random(10, 7, 1, 11)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "my_random(5, 7, 1, 11)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sequence 1" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "my_seed = 10\n", "my_multiplier = 2\n", "my_increment = 0\n", "my_modulus = 11\n", "\n", "save_sequence = []\n", "for i in range(20):\n", " random_out = my_random(my_seed, my_multiplier, my_increment, my_modulus)\n", " save_sequence.append(random_out)\n", " my_seed = random_out" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[9, 7, 3, 6, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 5, 10]\n" ] } ], "source": [ "print(save_sequence)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sequence 2" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "my_seed = 15\n", "my_multiplier = 16807\n", "my_increment = 0\n", "my_modulus = 2**31 - 1\n", "\n", "save_sequence = []\n", "for i in range(20):\n", " random_out = my_random(my_seed, my_multiplier, my_increment, my_modulus)\n", " save_sequence.append(random_out)\n", " my_seed = random_out" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[252105, 2089645088, 717430978, 1889252988, 2129248421, 610718139, 1515413160, 392926700, 406832375, 43794577, 1616048365, 1699186946, 997463616, 1113645630, 1722119805, 2030452016, 144398435, 247975935, 1613264365, 5655533]\n" ] } ], "source": [ "print(save_sequence)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sequence 3" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "my_seed = 200\n", "my_multiplier = 16807\n", "my_increment = 0\n", "my_modulus = 2**31 - 1\n", "generate_numbers = 1000000\n", "\n", "save_sequence = []\n", "for i in range(generate_numbers):\n", " random_out = my_random(my_seed, my_multiplier, my_increment, my_modulus)\n", " my_seed = random_out\n", " random_out = random_out / (2**31 - 2)\n", " save_sequence.append(random_out)\n", " \n", "save_sequence = np.array(save_sequence)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x480 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120)\n", "random_df = pd.DataFrame({\"random_numbers\": save_sequence})\n", "sns.distplot(a=random_df[\"random_numbers\"], bins=30, ax=ax, kde=False, hist_kws={\"alpha\": 1})\n", "ax.set_xlabel(\"random number\")\n", "ax.set_ylabel(\"count\")\n", "ax.set_title(\"Multiplicative Linear Congruential Method\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Random numbers from various distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Distribution of numbers\n", "\n", "* Description of portion of times each possible outcome or each possible range of outcomes occurs on the average over many trials" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Uniform distribution\n", "\n", "* Just as likely to return value in any interval\n", "\n", "* In list of many random numbers, on the average each interval contains same number of generated values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete distribution\n", "\n", "* Distribution with discrete values\n", "\n", "* **Probability function** (or **density function** or **probability density function**)\n", " * Returns probability of occurrence of particular argument value" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete distribution\n", "\n", "* **To Generate Random Numbers in Discrete Distribution with Equal Probabilities for Each of *n* Events**\n", " * Generate uniform random integer from a sequence of *n* integers, where each integer corresponds to an event" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using `numpy`\n", "\n", "There are two methods available in `numpy` for sampling integers from a uniform distribution.\n", "There is `np.random.randint`, which let's you specify the integer range directly, and works like so:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2, 1, 3, 4, 1, 1, 1, 1, 2, 3])" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.randint(low=1, high=5, size=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then there's `np.random.choice`, which is more general and allows you to randomly sample from an array-like list.\n", "To replicate the above behavior, you would use the following inputs like so:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 3, 3, 2, 1, 3, 1, 2, 4, 1])" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.choice(a=[1, 2, 3, 4], size=10, replace=True, p=None)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }