├── .DS_Store ├── Ch5 ├── .DS_Store ├── Central_Limit_Theorem.ipynb ├── Quantiles_Chebyshev_inequality.ipynb └── Lévy_alpha-stable_distribution.ipynb ├── Ch6 ├── .DS_Store ├── Covariance_matrix_vs_Scale_Matrix.ipynb ├── Marginal_vs_conditional_distribution_functions..ipynb └── Stress_Testing.ipynb ├── .gitignore ├── requirements.txt ├── README.md └── Ch8 └── Least_squares_solution.ipynb /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FinancialComputingUCL/DataDrivenModeling/HEAD/.DS_Store -------------------------------------------------------------------------------- /Ch5/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FinancialComputingUCL/DataDrivenModeling/HEAD/Ch5/.DS_Store -------------------------------------------------------------------------------- /Ch6/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FinancialComputingUCL/DataDrivenModeling/HEAD/Ch6/.DS_Store -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Created by https://www.toptal.com/developers/gitignore/api/macos,windows,linux 2 | # Edit at https://www.toptal.com/developers/gitignore?templates=macos,windows,linux 3 | 4 | ### Linux ### 5 | *~ 6 | 7 | # temporary files which can be created if a process still has a handle open of a deleted file 8 | .fuse_hidden* 9 | 10 | # KDE directory preferences 11 | .directory 12 | 13 | # Linux trash folder which might appear on any partition or disk 14 | .Trash-* 15 | 16 | # .nfs files are created when an open file is removed but is still being accessed 17 | .nfs* 18 | 19 | ### macOS ### 20 | # General 21 | .DS_Store 22 | .AppleDouble 23 | .LSOverride 24 | 25 | # Icon must end with two \r 26 | Icon 27 | 28 | 29 | # Thumbnails 30 | ._* 31 | 32 | # Files that might appear in the root of a volume 33 | .DocumentRevisions-V100 34 | .fseventsd 35 | .Spotlight-V100 36 | .TemporaryItems 37 | .Trashes 38 | .VolumeIcon.icns 39 | .com.apple.timemachine.donotpresent 40 | 41 | # Directories potentially created on remote AFP share 42 | .AppleDB 43 | .AppleDesktop 44 | Network Trash Folder 45 | Temporary Items 46 | .apdisk 47 | 48 | ### macOS Patch ### 49 | # iCloud generated files 50 | *.icloud 51 | 52 | ### Windows ### 53 | # Windows thumbnail cache files 54 | Thumbs.db 55 | Thumbs.db:encryptable 56 | ehthumbs.db 57 | ehthumbs_vista.db 58 | 59 | # Dump file 60 | *.stackdump 61 | 62 | # Folder config file 63 | [Dd]esktop.ini 64 | 65 | # Recycle Bin used on file shares 66 | $RECYCLE.BIN/ 67 | 68 | # Windows Installer files 69 | *.cab 70 | *.msi 71 | *.msix 72 | *.msm 73 | *.msp 74 | 75 | # Windows shortcuts 76 | *.lnk 77 | 78 | .ipynb_checkpoints 79 | 80 | # End of https://www.toptal.com/developers/gitignore/api/macos,windows,linux -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | anyio==3.7.1 2 | appnope==0.1.3 3 | argon2-cffi==21.3.0 4 | argon2-cffi-bindings==21.2.0 5 | arrow==1.2.3 6 | asttokens==2.2.1 7 | async-lru==2.0.4 8 | attrs==23.1.0 9 | Babel==2.12.1 10 | backcall==0.2.0 11 | beautifulsoup4==4.12.2 12 | bleach==6.0.0 13 | certifi==2023.7.22 14 | cffi==1.15.1 15 | charset-normalizer==3.2.0 16 | comm==0.1.3 17 | contourpy==1.1.0 18 | cycler==0.11.0 19 | debugpy==1.6.7 20 | decorator==5.1.1 21 | defusedxml==0.7.1 22 | exceptiongroup==1.1.2 23 | executing==1.2.0 24 | fastjsonschema==2.18.0 25 | fonttools==4.41.1 26 | fqdn==1.5.1 27 | idna==3.4 28 | importlib-metadata==6.8.0 29 | importlib-resources==6.0.0 30 | ipykernel==6.25.0 31 | ipython==8.14.0 32 | isoduration==20.11.0 33 | jedi==0.19.0 34 | Jinja2==3.1.2 35 | json5==0.9.14 36 | jsonpointer==2.4 37 | jsonschema==4.18.4 38 | jsonschema-specifications==2023.7.1 39 | jupyter-events==0.7.0 40 | jupyter-lsp==2.2.0 41 | jupyter_client==8.3.0 42 | jupyter_core==5.3.1 43 | jupyter_server==2.7.0 44 | jupyter_server_terminals==0.4.4 45 | jupyterlab==4.0.3 46 | jupyterlab-pygments==0.2.2 47 | jupyterlab_server==2.24.0 48 | kiwisolver==1.4.4 49 | MarkupSafe==2.1.3 50 | matplotlib==3.7.2 51 | matplotlib-inline==0.1.6 52 | mistune==3.0.1 53 | nbclient==0.8.0 54 | nbconvert==7.7.3 55 | nbformat==5.9.2 56 | nest-asyncio==1.5.7 57 | notebook==7.0.1 58 | notebook_shim==0.2.3 59 | numpy==1.25.2 60 | overrides==7.3.1 61 | packaging==23.1 62 | pandas==2.0.3 63 | pandocfilters==1.5.0 64 | parso==0.8.3 65 | pexpect==4.8.0 66 | pickleshare==0.7.5 67 | Pillow==10.0.0 68 | platformdirs==3.10.0 69 | prometheus-client==0.17.1 70 | prompt-toolkit==3.0.39 71 | psutil==5.9.5 72 | ptyprocess==0.7.0 73 | pure-eval==0.2.2 74 | pycparser==2.21 75 | Pygments==2.15.1 76 | pyparsing==3.0.9 77 | python-dateutil==2.8.2 78 | python-json-logger==2.0.7 79 | pytz==2023.3 80 | PyYAML==6.0.1 81 | pyzmq==25.1.0 82 | referencing==0.30.0 83 | requests==2.31.0 84 | rfc3339-validator==0.1.4 85 | rfc3986-validator==0.1.1 86 | rpds-py==0.9.2 87 | scipy==1.11.1 88 | Send2Trash==1.8.2 89 | six==1.16.0 90 | sniffio==1.3.0 91 | soupsieve==2.4.1 92 | stack-data==0.6.2 93 | terminado==0.17.1 94 | tinycss2==1.2.1 95 | tomli==2.0.1 96 | tornado==6.3.2 97 | traitlets==5.9.0 98 | typing_extensions==4.7.1 99 | tzdata==2023.3 100 | uri-template==1.3.0 101 | urllib3==2.0.4 102 | wcwidth==0.2.6 103 | webcolors==1.13 104 | webencodings==0.5.1 105 | websocket-client==1.6.1 106 | zipp==3.16.2 107 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Probabilistic data-driven modeling 2 | 3 | This repo contains the code related to the book titled __Probabilistic data-driven modeling__, written by Tomaso Aste, professor of Complexity Science at University College London. The book introduces and guides the reader through a selection of methodologies and approaches to construct models from data. These data-driven approaches have been originally developed in different fields from statistics to complexity science. They are general procedures and tools that apply to any domain where models must be built from observational data. The code in the current repository is organised by Chapters and presents an applied perspective on modeling of real complex systems. 4 | 5 | ## How to 6 | 7 | In the following lines, we report the main steps to download, access and run the code provided in the current GitHub repo. 8 | 9 | #### Cloning the GitHub repository 10 | In order to clone the current GitHub repository, the user is required to have Git locally installed. If this is not the case, follow the instructions at https://github.com/git-guides/install-git. 11 | 12 | Once you have Git locally installed and correctly set up, clone the following repository typing `git clone https://github.com/FinancialComputingUCL/DataDrivenModeling.git`. 13 | 14 | #### Python installation 15 | All the provided code is written using the Python programming language. The user is required to have a Python version installed locally. If this is not the case, follow the following steps to obtain it. 16 | - Access the URL: https://www.python.org/downloads/. 17 | - Download the latest stable version of the language (`3.11.4` at the writing time). 18 | - Follow the prompted installation steps to correctly finalise the process. 19 | - Double check everything was correctly installed typing `python --version` in a new Terminal. The prompted Python's version should coincide with the one you previously decided to download. 20 | 21 | #### Required packages' installation 22 | Using Python, packages can be managed in many different ways. We advise the user to use `virtualenv` to easily manage project' specific dependencies (i.e. packages). 23 | 24 | To create a new virtual environment, open a new Terminal in the chosen directory and follow these steps: 25 | - Type `which virtualenv` 26 | - _if_ `virtualenv not found` message is prompted: 27 | - Install `virtualnv` typing `pip3 install virtualenv`. 28 | - Double check everything was correctly installed typing `which virtualenv` command. 29 | - _else_: 30 | - Skip to the next step. 31 | - Create a new virtual environment typing `virtualenv `. If you have multiple Python versions installed locally, be sure to specify the Python's version to be used to create the new virtual environment (e.g. `virtualenv -p /usr/bin/python3.11.4 `). 32 | - Source the newly created virtual environment typing `source /bin/activate`. 33 | - Install the packages required to run the code provided in the current GitHub repo typing `pip3 install -r requirements.txt`. 34 | 35 | To temporarily deactivate your environment, type `deactivate`. 36 | To permanently delete your environment, type `sudo rm -rf `. 37 | 38 | #### Running the code 39 | The majority of the code provided in the current GitHub repo is in the form of Jupyter Notebooks. Once you run all the previously listed steps, you can run each Notebook in the following way: 40 | - Access the Chapter's folder you are interested in (e.g., `cd ./Chapter_5`). 41 | - Type `juyter notebook`. 42 | - Choose the `.ipynb` you are interested in and use the graphical interface to run all or specific cells. -------------------------------------------------------------------------------- /Ch6/Covariance_matrix_vs_Scale_Matrix.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "baf1360e", 6 | "metadata": {}, 7 | "source": [ 8 | "# Covaraince matrix vs Scale matrix\n", 9 | "\n", 10 | "In linear algebra and statistics, the covariance matrix and the scale matrix (also known as variance-covariance matrix or dispersion matrix) are closely related concepts. The covariance matrix represents the covariance between multiple random variables, while the scale matrix contains the variances of individual variables along the diagonal and covariances between them in off-diagonal elements.\n", 11 | "\n", 12 | "The `covariance_matrix` function calculates the covariance matrix. To do this, we first center the data by subtracting the mean of each column from the corresponding column elements. Then we compute the covariance matrix by multiplying the transposed centered data by itself and dividing by `(num_samples - 1)` to obtain an unbiased estimator.\n", 13 | "\n", 14 | "The `scale_matrix` function calculates the scale matrix, which is equivalent to the variance-covariance matrix. We use NumPy's cov function with `rowvar=False` to compute the variance-covariance matrix for the given data.\n", 15 | "\n", 16 | "Finally, we print both matrices and check if they are equal within a small tolerance using `np.allclose`. The equality check is necessary because covariance matrices and scale matrices should be identical in practice. However, due to floating-point precision, exact equality may not hold, so we use the `np.allclose` function to verify their similarity." 17 | ] 18 | }, 19 | { 20 | "cell_type": "code", 21 | "execution_count": 4, 22 | "id": "5098098d", 23 | "metadata": {}, 24 | "outputs": [], 25 | "source": [ 26 | "import numpy as np" 27 | ] 28 | }, 29 | { 30 | "cell_type": "code", 31 | "execution_count": 7, 32 | "id": "6f5f43a7", 33 | "metadata": {}, 34 | "outputs": [ 35 | { 36 | "name": "stdout", 37 | "output_type": "stream", 38 | "text": [ 39 | "Covariance Matrix:\n", 40 | "[[ 1.07152674 -0.01672361 0.04491799 0.03792043 0.04564139]\n", 41 | " [-0.01672361 1.01288579 0.00360372 0.00975283 0.06587266]\n", 42 | " [ 0.04491799 0.00360372 1.00234635 -0.03316989 -0.00862546]\n", 43 | " [ 0.03792043 0.00975283 -0.03316989 0.9391796 -0.01612904]\n", 44 | " [ 0.04564139 0.06587266 -0.00862546 -0.01612904 0.94788399]]\n", 45 | "\n", 46 | "Scale Matrix (Variance-Covariance Matrix):\n", 47 | "[[ 1.07045521 -0.01670689 0.04487308 0.0378825 0.04559575]\n", 48 | " [-0.01670689 1.0118729 0.00360011 0.00974308 0.06580679]\n", 49 | " [ 0.04487308 0.00360011 1.00134401 -0.03313672 -0.00861683]\n", 50 | " [ 0.0378825 0.00974308 -0.03313672 0.93824042 -0.01611291]\n", 51 | " [ 0.04559575 0.06580679 -0.00861683 -0.01611291 0.94693611]]\n", 52 | "\n", 53 | "Are the Covariance Matrix and Scale Matrix equal? False\n" 54 | ] 55 | } 56 | ], 57 | "source": [ 58 | "def generate_data(num_samples, num_features):\n", 59 | " # Generate random data with mean 0 and variance 1\n", 60 | " return np.random.randn(num_samples, num_features)\n", 61 | "\n", 62 | "def covariance_matrix(data):\n", 63 | " # Calculate the covariance matrix\n", 64 | " mean_centered_data = data - np.mean(data, axis=0)\n", 65 | " return np.dot(mean_centered_data.T, mean_centered_data) / (data.shape[0] - 1)\n", 66 | "\n", 67 | "def scale_matrix(data):\n", 68 | " # Calculate the scale matrix (variance-covariance matrix)\n", 69 | " return np.cov(data, rowvar=False, bias=True)\n", 70 | "\n", 71 | "def main():\n", 72 | " # Define the dimensions of the data\n", 73 | " num_samples = 1000\n", 74 | " num_features = 5\n", 75 | "\n", 76 | " # Generate random data\n", 77 | " data = generate_data(num_samples, num_features)\n", 78 | "\n", 79 | " # Calculate the covariance matrix and scale matrix\n", 80 | " cov_matrix = covariance_matrix(data)\n", 81 | " scale_matrix_result = scale_matrix(data)\n", 82 | "\n", 83 | " # Output the covariance matrix and scale matrix\n", 84 | " print(\"Covariance Matrix:\")\n", 85 | " print(cov_matrix)\n", 86 | "\n", 87 | " print(\"\\nScale Matrix (Variance-Covariance Matrix):\")\n", 88 | " print(scale_matrix_result)\n", 89 | "\n", 90 | " # Check if both matrices are equal (within a small tolerance). Try to tune rtol and atol to see the difference.\n", 91 | " matrices_equal = np.allclose(cov_matrix, scale_matrix_result, rtol=1e-05, atol=1e-08)\n", 92 | " print(\"\\nAre the Covariance Matrix and Scale Matrix equal?\", matrices_equal)\n", 93 | "\n", 94 | "if __name__ == \"__main__\":\n", 95 | " main()" 96 | ] 97 | } 98 | ], 99 | "metadata": { 100 | "kernelspec": { 101 | "display_name": "Python 3 (ipykernel)", 102 | "language": "python", 103 | "name": "python3" 104 | }, 105 | "language_info": { 106 | "codemirror_mode": { 107 | "name": "ipython", 108 | "version": 3 109 | }, 110 | "file_extension": ".py", 111 | "mimetype": "text/x-python", 112 | "name": "python", 113 | "nbconvert_exporter": "python", 114 | "pygments_lexer": "ipython3", 115 | "version": "3.8.12" 116 | } 117 | }, 118 | "nbformat": 4, 119 | "nbformat_minor": 5 120 | } 121 | -------------------------------------------------------------------------------- /Ch5/Central_Limit_Theorem.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "e9a36957", 6 | "metadata": {}, 7 | "source": [ 8 | "# Central Limit Theorem\n", 9 | "\n", 10 | "In this code, we generate multiple samples of random variables and calculate the mean of each sample. The means are then stored in the “sample_means” list. We plot a histogram of these sample means, which represents the empirical distribution of the means.\n", 11 | "\n", 12 | "The code also calculates the theoretical mean and standard deviation of the distribution of sample means based on the number of variables being summed. It then plots the corresponding normal distribution curve using these theoretical parameters.\n", 13 | "\n", 14 | "By running this code, you can observe how the empirical distribution of sample means converges towards a normal distribution, as predicted by the Central Limit Theorem. The histogram should resemble the shape of the normal distribution curve." 15 | ] 16 | }, 17 | { 18 | "cell_type": "code", 19 | "execution_count": 2, 20 | "id": "d0ae6803", 21 | "metadata": {}, 22 | "outputs": [], 23 | "source": [ 24 | "import numpy as np\n", 25 | "import matplotlib.pyplot as plt" 26 | ] 27 | }, 28 | { 29 | "cell_type": "code", 30 | "execution_count": 3, 31 | "id": "8aab2190", 32 | "metadata": {}, 33 | "outputs": [ 34 | { 35 | "data": { 36 | "image/png": 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\n", 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" 39 | ] 40 | }, 41 | "metadata": { 42 | "needs_background": "light" 43 | }, 44 | "output_type": "display_data" 45 | } 46 | ], 47 | "source": [ 48 | "# Define the number of samples to draw\n", 49 | "num_samples = 1000\n", 50 | "\n", 51 | "# Define the number of random variables to sum\n", 52 | "num_variables = 10\n", 53 | "\n", 54 | "# Store the means of each sample\n", 55 | "sample_means = []\n", 56 | "\n", 57 | "# Generate samples and calculate means\n", 58 | "for _ in range(num_samples):\n", 59 | " # Generate a sample of random variables\n", 60 | " sample = np.random.rand(num_variables)\n", 61 | " \n", 62 | " # Calculate the mean of the sample\n", 63 | " sample_mean = np.mean(sample)\n", 64 | " \n", 65 | " # Store the sample mean\n", 66 | " sample_means.append(sample_mean)\n", 67 | "\n", 68 | "# Plot the histogram of sample means\n", 69 | "plt.hist(sample_means, bins=30, density=True, alpha=0.5, color='blue')\n", 70 | "\n", 71 | "# Calculate the theoretical mean and standard deviation\n", 72 | "theoretical_mean = 0.5\n", 73 | "theoretical_std = 1 / np.sqrt(12 * num_variables)\n", 74 | "\n", 75 | "# Generate a range of x values\n", 76 | "x = np.linspace(theoretical_mean - 3 * theoretical_std, theoretical_mean + 3 * theoretical_std, 100)\n", 77 | "\n", 78 | "# Calculate the corresponding y values using the normal distribution formula\n", 79 | "y = 1 / (np.sqrt(2 * np.pi * theoretical_std**2)) * np.exp(-(x - theoretical_mean)**2 / (2 * theoretical_std**2))\n", 80 | "\n", 81 | "# Plot the theoretical normal distribution curve\n", 82 | "plt.plot(x, y, color='red', linewidth=2)\n", 83 | "\n", 84 | "# Set plot labels and title\n", 85 | "plt.xlabel('Sample Mean')\n", 86 | "plt.ylabel('Probability Density')\n", 87 | "plt.title('Convergence towards Normal Distribution')\n", 88 | "\n", 89 | "# Display the plot\n", 90 | "plt.show()" 91 | ] 92 | } 93 | ], 94 | "metadata": { 95 | "kernelspec": { 96 | "display_name": "Python 3 (ipykernel)", 97 | "language": "python", 98 | "name": "python3" 99 | }, 100 | "language_info": { 101 | "codemirror_mode": { 102 | "name": "ipython", 103 | "version": 3 104 | }, 105 | "file_extension": ".py", 106 | "mimetype": "text/x-python", 107 | "name": "python", 108 | "nbconvert_exporter": "python", 109 | "pygments_lexer": "ipython3", 110 | "version": "3.8.12" 111 | } 112 | }, 113 | "nbformat": 4, 114 | "nbformat_minor": 5 115 | } 116 | -------------------------------------------------------------------------------- /Ch6/Marginal_vs_conditional_distribution_functions..ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "7a243bc4", 6 | "metadata": {}, 7 | "source": [ 8 | "# Marginal and conditional distribution functions.\n", 9 | "\n", 10 | "To demonstrate the comparison between marginal and conditional probability distribution functions, we'll create a simple example using Python and matplotlib. We'll consider two random variables, X and Y, and visualize their marginal and conditional probability distributions.\n", 11 | "\n", 12 | "The `marginal_prob_distribution` function calculates the marginal probability distribution of a random variable. It uses NumPy's histogram function to calculate the relative frequencies of different values in the data.\n", 13 | "\n", 14 | "The `conditional_prob_distribution` function calculates the conditional probability distribution of X given a specific value of Y. It filters the data to consider only those instances where Y equals the specified value and then calculates the relative frequencies using the `histogram` function.\n", 15 | "\n", 16 | "The comparison between the marginal and conditional probability distributions allows us to observe how the probabilities of individual outcomes change when we condition on specific values of another random variable. It helps in understanding the relationship between the two variables and their joint behavior." 17 | ] 18 | }, 19 | { 20 | "cell_type": "code", 21 | "execution_count": 5, 22 | "id": "2190e2ec", 23 | "metadata": {}, 24 | "outputs": [], 25 | "source": [ 26 | "import numpy as np\n", 27 | "import matplotlib.pyplot as plt" 28 | ] 29 | }, 30 | { 31 | "cell_type": "code", 32 | "execution_count": 6, 33 | "id": "879f870a", 34 | "metadata": {}, 35 | "outputs": [ 36 | { 37 | "data": { 38 | "image/png": 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\n", 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" 41 | ] 42 | }, 43 | "metadata": { 44 | "needs_background": "light" 45 | }, 46 | "output_type": "display_data" 47 | } 48 | ], 49 | "source": [ 50 | "def generate_data(num_samples):\n", 51 | " # Generate random data for variables X and Y\n", 52 | " X = np.random.randint(1, 7, num_samples) # Random integers from 1 to 6 (inclusive)\n", 53 | " Y = np.random.randint(1, 7, num_samples)\n", 54 | " return X, Y\n", 55 | "\n", 56 | "def marginal_prob_distribution(data):\n", 57 | " # Calculate the marginal probability distribution of a random variable\n", 58 | " return np.histogram(data, bins=np.arange(1, 8), density=True)[0]\n", 59 | "\n", 60 | "def conditional_prob_distribution(data_x, data_y, value_y):\n", 61 | " # Calculate the conditional probability distribution of X given a specific value of Y\n", 62 | " mask = data_y == value_y\n", 63 | " conditional_data = data_x[mask]\n", 64 | " return np.histogram(conditional_data, bins=np.arange(1, 8), density=True)[0]\n", 65 | "\n", 66 | "def main():\n", 67 | " # Define the number of samples\n", 68 | " num_samples = 10000\n", 69 | "\n", 70 | " # Generate random data for X and Y\n", 71 | " X, Y = generate_data(num_samples)\n", 72 | "\n", 73 | " # Calculate the marginal probability distributions of X and Y\n", 74 | " marginal_X = marginal_prob_distribution(X)\n", 75 | " marginal_Y = marginal_prob_distribution(Y)\n", 76 | "\n", 77 | " # Choose a specific value for Y to calculate the conditional probability distribution of X\n", 78 | " value_Y = 3\n", 79 | " conditional_X_given_Y = conditional_prob_distribution(X, Y, value_Y)\n", 80 | "\n", 81 | " # Plot the results\n", 82 | " plt.figure(figsize=(10, 4))\n", 83 | "\n", 84 | " plt.subplot(1, 2, 1)\n", 85 | " plt.bar(np.arange(1, 7), marginal_X, width=0.4, label=\"X\")\n", 86 | " plt.bar(np.arange(1, 7) + 0.4, marginal_Y, width=0.4, label=\"Y\")\n", 87 | " plt.xlabel(\"Values\")\n", 88 | " plt.ylabel(\"Probability\")\n", 89 | " plt.title(\"Marginal Probability Distribution\")\n", 90 | " plt.legend()\n", 91 | "\n", 92 | " plt.subplot(1, 2, 2)\n", 93 | " plt.bar(np.arange(1, 7), conditional_X_given_Y, width=0.4)\n", 94 | " plt.xlabel(\"Values of X (Conditional on Y=3)\")\n", 95 | " plt.ylabel(\"Probability\")\n", 96 | " plt.title(\"Conditional Probability Distribution of X given Y=3\")\n", 97 | "\n", 98 | " plt.tight_layout()\n", 99 | " plt.show()\n", 100 | "\n", 101 | "if __name__ == \"__main__\":\n", 102 | " main()" 103 | ] 104 | } 105 | ], 106 | "metadata": { 107 | "kernelspec": { 108 | "display_name": "Python 3 (ipykernel)", 109 | "language": "python", 110 | "name": "python3" 111 | }, 112 | "language_info": { 113 | "codemirror_mode": { 114 | "name": "ipython", 115 | "version": 3 116 | }, 117 | "file_extension": ".py", 118 | "mimetype": "text/x-python", 119 | "name": "python", 120 | "nbconvert_exporter": "python", 121 | "pygments_lexer": "ipython3", 122 | "version": "3.8.12" 123 | } 124 | }, 125 | "nbformat": 4, 126 | "nbformat_minor": 5 127 | } 128 | -------------------------------------------------------------------------------- /Ch8/Least_squares_solution.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "03be8cf1", 6 | "metadata": {}, 7 | "source": [ 8 | "# Least squares solution of linear regression and correlation coefficients\n", 9 | "\n", 10 | "In this notebook we will underline the relationship between least squares solution of linear regression and correlation coefficients.\n", 11 | "\n", 12 | "### Linear Regression and Correlation Coefficients\n", 13 | "\n", 14 | "In linear regression analysis with two random variables $X$ and $Y$, we aim to compute coefficients that best represent their linear relationship:\n", 15 | "\n", 16 | "$ Y = b + \\beta X + \\epsilon $\n", 17 | "\n", 18 | "The objective is to minimize the variance of the error $ \\text{Var}(\\epsilon) $, and this approach is known as the least squares method. The error variance can be represented as:\n", 19 | "\n", 20 | "$ \\text{Var}(\\epsilon) = \\text{Var}(Y) + \\beta^2 \\text{Var}(X) - 2\\beta \\text{Cov}(X,Y) $\n", 21 | "\n", 22 | "Going deeper with this equation we can derive:\n", 23 | "\n", 24 | "$ \\frac{\\text{Var}(\\epsilon)}{\\text{Var}(Y)} = (1 - \\text{Corr}(X, Y)^2) $\n", 25 | "\n", 26 | "### Coefficient of Determination ($R^2$)\n", 27 | "\n", 28 | "What reported above reveals that the square of correlation coefficient $R^2$ is a measure of the goodness of the linear model:\n", 29 | "\n", 30 | "$ R^2 = \\text{Corr}(X,Y)^2 $\n", 31 | "\n", 32 | "A high $R^2$ value, near 1, indicates that the linear model aptly describes the dependency between the variables. Conversely, when $R^2$ approaches 0, the linear model poorly describes the relationship between the variables." 33 | ] 34 | }, 35 | { 36 | "cell_type": "code", 37 | "execution_count": 2, 38 | "id": "7b4e4b62", 39 | "metadata": {}, 40 | "outputs": [], 41 | "source": [ 42 | "import numpy as np\n", 43 | "import matplotlib.pyplot as plt" 44 | ] 45 | }, 46 | { 47 | "cell_type": "code", 48 | "execution_count": 3, 49 | "id": "3b16b0d2", 50 | "metadata": {}, 51 | "outputs": [ 52 | { 53 | "data": { 54 | "image/png": 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\n", 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" 57 | ] 58 | }, 59 | "metadata": { 60 | "needs_background": "light" 61 | }, 62 | "output_type": "display_data" 63 | }, 64 | { 65 | "name": "stdout", 66 | "output_type": "stream", 67 | "text": [ 68 | "Correlation Coefficient (Corr(X,Y)): 0.8770824028342054\n", 69 | "Coefficient of Determination (R^2): 0.7692735413614232\n", 70 | "Variance of Residuals: 0.8065845639670531\n", 71 | "Expected Variance of Residuals based on R^2: 0.8065845639670501\n" 72 | ] 73 | } 74 | ], 75 | "source": [ 76 | "# Set a random seed for reproducibility\n", 77 | "np.random.seed(42)\n", 78 | "\n", 79 | "# Let's start generating a synthetic dataset\n", 80 | "# --------------------------------\n", 81 | "\n", 82 | "# Generate random values for X\n", 83 | "X = 2 * np.random.rand(100, 1)\n", 84 | "# Generate Y values with a linear relationship to X\n", 85 | "# For this example, we'll assume a true relationship of Y = 4 + 3X + Gaussian noise\n", 86 | "Y = 4 + 3 * X + np.random.randn(100, 1)\n", 87 | "\n", 88 | "# Let's implement the Linear Regression Algorithm\n", 89 | "# --------------------------------------------\n", 90 | "\n", 91 | "# Calculate the covariance between X and Y\n", 92 | "cov_XY = np.mean(X * Y) - np.mean(X) * np.mean(Y)\n", 93 | "\n", 94 | "# Calculate the variance of X\n", 95 | "var_X = np.var(X)\n", 96 | "\n", 97 | "# Determine the coefficient β using the relationship\n", 98 | "# β = Cov(X,Y) / Var(X)\n", 99 | "beta = cov_XY / var_X\n", 100 | "\n", 101 | "# Determine the intercept b\n", 102 | "# b = E(Y) - β * E(X)\n", 103 | "b = np.mean(Y) - beta * np.mean(X)\n", 104 | "\n", 105 | "# Predict values of Y using the obtained b and β\n", 106 | "Y_pred = b + beta * X\n", 107 | "\n", 108 | "# Let's calculate the correlation coefficient, R^2, and relate it to the variance of the errors\n", 109 | "# ------------------------------------------------------------------------------------------\n", 110 | "\n", 111 | "# Calculate the correlation coefficient Corr(X,Y)\n", 112 | "correlation_coefficient = np.corrcoef(X.squeeze(), Y.squeeze())[0, 1]\n", 113 | "\n", 114 | "# Calculate R^2\n", 115 | "R_squared = correlation_coefficient**2\n", 116 | "\n", 117 | "# Calculate the residuals (errors)\n", 118 | "residuals = Y - Y_pred\n", 119 | "\n", 120 | "# Calculate the variance of the residuals\n", 121 | "var_residuals = np.var(residuals)\n", 122 | "\n", 123 | "# Calculate the expected variance of the residuals based on R^2\n", 124 | "expected_var_residuals = np.var(Y) * (1 - R_squared)\n", 125 | "\n", 126 | "# Let's finally plot the results and print the calculated values\n", 127 | "# ---------------------------------------------------\n", 128 | "\n", 129 | "# Plot the original data and the linear regression line\n", 130 | "plt.scatter(X, Y, label=\"Original Data\")\n", 131 | "plt.plot(X, Y_pred, color=\"red\", label=\"Linear Regression Line\")\n", 132 | "plt.xlabel(\"X\")\n", 133 | "plt.ylabel(\"Y\")\n", 134 | "plt.title(\"Linear Regression Fit\")\n", 135 | "plt.legend()\n", 136 | "plt.grid(True)\n", 137 | "plt.show()\n", 138 | "\n", 139 | "# Print the results\n", 140 | "print(f\"Correlation Coefficient (Corr(X,Y)): {correlation_coefficient}\")\n", 141 | "print(f\"Coefficient of Determination (R^2): {R_squared}\")\n", 142 | "print(f\"Variance of Residuals: {var_residuals}\")\n", 143 | "print(f\"Expected Variance of Residuals based on R^2: {expected_var_residuals}\")" 144 | ] 145 | } 146 | ], 147 | "metadata": { 148 | "kernelspec": { 149 | "display_name": "Python 3 (ipykernel)", 150 | "language": "python", 151 | "name": "python3" 152 | }, 153 | "language_info": { 154 | "codemirror_mode": { 155 | "name": "ipython", 156 | "version": 3 157 | }, 158 | "file_extension": ".py", 159 | "mimetype": "text/x-python", 160 | "name": "python", 161 | "nbconvert_exporter": "python", 162 | "pygments_lexer": "ipython3", 163 | "version": "3.8.12" 164 | } 165 | }, 166 | "nbformat": 4, 167 | "nbformat_minor": 5 168 | } 169 | -------------------------------------------------------------------------------- /Ch5/Quantiles_Chebyshev_inequality.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "b7c17cbf", 6 | "metadata": {}, 7 | "source": [ 8 | "# Quantiles and Chebyshev's inequality\n", 9 | "\n", 10 | "The provided code consists of two functions: `chebyshev_bound`, which calculates lower and upper bounds using Chebyshev's inequality for a given dataset and confidence level, and `plot_quantile_comparison`, which generates a plot to compare quantiles of different random variables. The `chebyshev_bound` function calculates the sample mean and standard deviation of the data, and then determines the bounds based on the confidence level using Chebyshev's inequality. The `plot_quantile_comparison` function sorts the data, computes quantiles using the standard normal distribution's cumulative distribution function, and plots the quantiles against the sorted data for each random variable. The code generates three random variables (normal, uniform, and exponential) and calculates quantiles for each. The resulting plot allows visual comparison of quantile behavior across the random variables. The x-axis represents sorted data, while the y-axis displays quantiles. Each curve in the plot corresponds to a different random variable, with the legend providing the corresponding label. The grid facilitates accurate quantile comparisons." 11 | ] 12 | }, 13 | { 14 | "cell_type": "code", 15 | "execution_count": 4, 16 | "id": "d0f84ce6", 17 | "metadata": {}, 18 | "outputs": [], 19 | "source": [ 20 | "import numpy as np\n", 21 | "import matplotlib.pyplot as plt\n", 22 | "from scipy.stats import norm" 23 | ] 24 | }, 25 | { 26 | "cell_type": "code", 27 | "execution_count": 5, 28 | "id": "ffb80a74", 29 | "metadata": {}, 30 | "outputs": [ 31 | { 32 | "data": { 33 | "image/png": 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\n", 34 | "text/plain": [ 35 | "
" 36 | ] 37 | }, 38 | "metadata": { 39 | "needs_background": "light" 40 | }, 41 | "output_type": "display_data" 42 | } 43 | ], 44 | "source": [ 45 | "def chebyshev_bound(data, confidence):\n", 46 | " mean = np.mean(data)\n", 47 | " std = np.std(data)\n", 48 | " k = 1 / np.sqrt(confidence)\n", 49 | " lower_bound = mean - k * std\n", 50 | " upper_bound = mean + k * std\n", 51 | " return lower_bound, upper_bound\n", 52 | "\n", 53 | "def plot_quantile_comparison(data_list, labels):\n", 54 | " plt.figure(figsize=(8, 6))\n", 55 | " for data, label in zip(data_list, labels):\n", 56 | " sorted_data = np.sort(data)\n", 57 | " n = len(sorted_data)\n", 58 | " probabilities = np.arange(1, n + 1) / n\n", 59 | " quantiles = norm.ppf(probabilities, loc=np.mean(data), scale=np.std(data))\n", 60 | " plt.plot(sorted_data, quantiles, label=label)\n", 61 | " plt.xlabel('Data')\n", 62 | " plt.ylabel('Quantiles')\n", 63 | " plt.title('Comparison of Quantiles for Various Random Variables')\n", 64 | " plt.legend()\n", 65 | " plt.grid(True)\n", 66 | " plt.show()\n", 67 | "\n", 68 | "# Generate various random variables for comparison\n", 69 | "np.random.seed(42) # For reproducibility\n", 70 | "size = 1000 # Number of samples for each random variable\n", 71 | "\n", 72 | "normal_data = np.random.normal(loc=0, scale=1, size=size)\n", 73 | "uniform_data = np.random.uniform(low=-1, high=1, size=size)\n", 74 | "exponential_data = np.random.exponential(scale=1, size=size)\n", 75 | "\n", 76 | "# Calculate the quantiles for each random variable\n", 77 | "data_list = [normal_data, uniform_data, exponential_data]\n", 78 | "labels = ['Normal', 'Uniform', 'Exponential']\n", 79 | "\n", 80 | "# Plot the comparison of quantiles using Chebyshev's inequality\n", 81 | "plot_quantile_comparison(data_list, labels)" 82 | ] 83 | }, 84 | { 85 | "cell_type": "code", 86 | "execution_count": null, 87 | "id": "83d38be3", 88 | "metadata": {}, 89 | "outputs": [], 90 | "source": [] 91 | } 92 | ], 93 | "metadata": { 94 | "kernelspec": { 95 | "display_name": "Python 3 (ipykernel)", 96 | "language": "python", 97 | "name": "python3" 98 | }, 99 | "language_info": { 100 | "codemirror_mode": { 101 | "name": "ipython", 102 | "version": 3 103 | }, 104 | "file_extension": ".py", 105 | "mimetype": "text/x-python", 106 | "name": "python", 107 | "nbconvert_exporter": "python", 108 | "pygments_lexer": "ipython3", 109 | "version": "3.8.12" 110 | } 111 | }, 112 | "nbformat": 4, 113 | "nbformat_minor": 5 114 | } 115 | -------------------------------------------------------------------------------- /Ch5/Lévy_alpha-stable_distribution.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "7a901ab7", 6 | "metadata": {}, 7 | "source": [ 8 | "# Lévy alpha-stable distribution\n", 9 | "\n", 10 | "In this code, we perform multiple experiments with Lévy alpha-stable distributed random variables and calculate the histogram of outcomes for each experiment. Additionally, we plot the corresponding theoretical normal distribution curve based on the mean and standard deviation of the outcomes.\n", 11 | "\n", 12 | "The Lévy alpha-stable distribution is a family of probability distributions that includes the Gaussian (normal) distribution as a special case. However, unlike the normal distribution, which satisfies the Central Limit Theorem and converges to a normal distribution for sums of random variables, the Levy-stable distribution does not always follow this pattern. The Central Limit Theorem states that the sum of a large number of independent and identically distributed random variables tends to be approximately normally distributed, regardless of the original distribution.\n", 13 | "\n", 14 | "- For alpha = 2 (Gaussian distribution), beta = 0:\n", 15 | " - The histogram should resemble a bell-shaped curve, similar to the shape of the theoretical normal distribution curve (in red).\n", 16 | " - The mean and standard deviation of the outcomes should match closely with the theoretical values, and the histogram should be well-centered around the mean.\n", 17 | "- For alpha ≠ 2 and beta = 0:\n", 18 | " - The histogram may not closely resemble a normal distribution, even though the theoretical curve is still shown.\n", 19 | " - The shape of the histogram will be influenced by the stability parameter alpha, and it might exhibit heavier tails or skewness.\n", 20 | "- For beta ≠ 0:\n", 21 | " - The histogram might show asymmetry (skewness) and thicker tails compared to the theoretical normal distribution curve.\n", 22 | " - The presence of a non-zero skewness parameter (beta) in the Levy-stable distribution can lead to a significant departure from a normal distribution.\n", 23 | "- For alpha ≠ 2 and beta ≠ 0:\n", 24 | " - The histogram might display more pronounced deviations from a normal distribution, especially when both alpha and beta differ from their standard values.\n", 25 | " - Depending on the values of alpha and beta, the Levy-stable distribution can exhibit various features such as fat tails, heavy skewness, and long tails." 26 | ] 27 | }, 28 | { 29 | "cell_type": "code", 30 | "execution_count": 1, 31 | "id": "a530b273", 32 | "metadata": {}, 33 | "outputs": [], 34 | "source": [ 35 | "import numpy as np\n", 36 | "import matplotlib.pyplot as plt\n", 37 | "from scipy.stats import levy_stable, norm" 38 | ] 39 | }, 40 | { 41 | "cell_type": "code", 42 | "execution_count": 2, 43 | "id": "dba963ec", 44 | "metadata": {}, 45 | "outputs": [ 46 | { 47 | "data": { 48 | "image/png": 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\n", 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" 51 | ] 52 | }, 53 | "metadata": { 54 | "needs_background": "light" 55 | }, 56 | "output_type": "display_data" 57 | } 58 | ], 59 | "source": [ 60 | "def generate_histogram(num_experiments, alpha, beta, subplot_position):\n", 61 | " # Perform the experiments\n", 62 | " outcomes = levy_stable.rvs(alpha, beta, scale=1, size=num_experiments)\n", 63 | "\n", 64 | " # Create a subplot\n", 65 | " plt.subplot(subplot_position)\n", 66 | "\n", 67 | " # Plot the histogram of outcomes\n", 68 | " plt.hist(outcomes, bins=50, density=True, alpha=0.5, color='blue')\n", 69 | "\n", 70 | " # Get mean and standard deviation of outcomes\n", 71 | " mu, std = np.mean(outcomes), np.std(outcomes)\n", 72 | "\n", 73 | " # Generate a range of x values\n", 74 | " x = np.linspace(mu - 3*std, mu + 3*std, 100)\n", 75 | "\n", 76 | " # Calculate the corresponding y values using the normal distribution\n", 77 | " y = norm.pdf(x, mu, std)\n", 78 | "\n", 79 | " # Plot the theoretical normal distribution curve\n", 80 | " plt.plot(x, y, color='red', linewidth=2)\n", 81 | "\n", 82 | " # Set plot title\n", 83 | " plt.title(f'Alpha: {alpha}, Beta: {beta}')\n", 84 | "\n", 85 | "# Set the number of experiments\n", 86 | "num_experiments = 1000\n", 87 | "\n", 88 | "# Create a 2x2 grid of subplots\n", 89 | "fig, axs = plt.subplots(2, 2, figsize=(10, 8))\n", 90 | "\n", 91 | "# Generate histograms for different alphas and betas\n", 92 | "generate_histogram(num_experiments, 1.5, 0, 221)\n", 93 | "generate_histogram(num_experiments, 1.5, 0.5, 222)\n", 94 | "generate_histogram(num_experiments, 2, -0.5, 223)\n", 95 | "generate_histogram(num_experiments, 2, 0, 224)\n", 96 | "\n", 97 | "# Set common labels\n", 98 | "fig.text(0.5, 0, 'Outcome', ha='center', va='center')\n", 99 | "fig.text(0, 0.5, 'Probability Density', ha='center', va='center', rotation='vertical')\n", 100 | "\n", 101 | "# Adjust spacing\n", 102 | "plt.tight_layout()\n", 103 | "\n", 104 | "# Display the plots\n", 105 | "plt.show()\n" 106 | ] 107 | }, 108 | { 109 | "cell_type": "code", 110 | "execution_count": null, 111 | "id": "3e2e64b0", 112 | "metadata": {}, 113 | "outputs": [], 114 | "source": [] 115 | } 116 | ], 117 | "metadata": { 118 | "kernelspec": { 119 | "display_name": "Python 3 (ipykernel)", 120 | "language": "python", 121 | "name": "python3" 122 | }, 123 | "language_info": { 124 | "codemirror_mode": { 125 | "name": "ipython", 126 | "version": 3 127 | }, 128 | "file_extension": ".py", 129 | "mimetype": "text/x-python", 130 | "name": "python", 131 | "nbconvert_exporter": "python", 132 | "pygments_lexer": "ipython3", 133 | "version": "3.8.12" 134 | } 135 | }, 136 | "nbformat": 4, 137 | "nbformat_minor": 5 138 | } 139 | -------------------------------------------------------------------------------- /Ch6/Stress_Testing.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "id": "123a65b5", 6 | "metadata": {}, 7 | "source": [ 8 | "## Visualizing Systemic Risk in a Complex System with Stress using Python and Matplotlib\n", 9 | "\n", 10 | "To understand the systemic risk in a complex system and the effects of stress on this system, we'll employ Python and matplotlib for a visual demonstration. Our system is represented using two interrelated variables, making use of a bivariate normal distribution to demonstrate their relationship.\n", 11 | "\n", 12 | "1. **System Representation**:\n", 13 | " - The complex system is represented by a bivariate normal distribution with specified means and covariance. Here, the mean vector `mean` denotes the average values of the two random variables, and the covariance matrix `cov` signifies how these variables interact with each other.\n", 14 | "\n", 15 | "2. **Modeling Stress**:\n", 16 | " - Stress on the system is modeled using the `apply_stress` function. This function shifts the mean values, simulating a disturbance. By adjusting the `stress_factor` parameter, we can control the intensity of the stress.\n", 17 | "\n", 18 | "3. **Visualization**:\n", 19 | " - Using matplotlib, the original distribution (before stress) is plotted using blue contours, demonstrating the system's behavior in its natural state.\n", 20 | " - Post the application of stress, the disturbed distribution is visualized with red contours, allowing for a comparison between the system's behavior before and after the stress.\n", 21 | " \n", 22 | "Through this visualization, one can observe how the introduction of stress affects the systemic risk in the system. The shift between the blue and red contours visually captures the change in the conditional probabilities of the system's variables, demonstrating the resilience or vulnerability of the system to disturbances." 23 | ] 24 | }, 25 | { 26 | "cell_type": "code", 27 | "execution_count": null, 28 | "id": "4aa9dd65", 29 | "metadata": {}, 30 | "outputs": [], 31 | "source": [ 32 | "import numpy as np\n", 33 | "import matplotlib.pyplot as plt\n", 34 | "from scipy.stats import multivariate_normal" 35 | ] 36 | }, 37 | { 38 | "cell_type": "code", 39 | "execution_count": 6, 40 | "id": "dab82ed7", 41 | "metadata": {}, 42 | "outputs": [ 43 | { 44 | "data": { 45 | "image/png": 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" 48 | ] 49 | }, 50 | "metadata": { 51 | "needs_background": "light" 52 | }, 53 | "output_type": "display_data" 54 | } 55 | ], 56 | "source": [ 57 | "# Set random seed for reproducibility\n", 58 | "np.random.seed(42)\n", 59 | "\n", 60 | "# 1. Define the multivariate normal distribution for the system variables\n", 61 | "# We will assume two variables for simplicity\n", 62 | "mean = [0, 0] # Mean of the two variables\n", 63 | "cov = [[1, 0.5], [0.5, 1]] # Covariance matrix showing some correlation between the variables\n", 64 | "\n", 65 | "# Create a grid of (x, y) coordinates\n", 66 | "x, y = np.mgrid[-3:3:.01, -3:3:.01]\n", 67 | "pos = np.dstack((x, y))\n", 68 | "\n", 69 | "# 2. Define a function to \"stress\" the system. Here, stress is modeled as a change in mean\n", 70 | "def apply_stress(original_mean, stress_factor):\n", 71 | " return [m + stress_factor for m in original_mean]\n", 72 | "\n", 73 | "# 3. Plot the distributions before and after stress\n", 74 | "fig, ax = plt.subplots()\n", 75 | "\n", 76 | "# Before stress\n", 77 | "rv = multivariate_normal(mean, cov)\n", 78 | "ax.contourf(x, y, rv.pdf(pos), levels=25, alpha=0.6, cmap=\"Blues\")\n", 79 | "\n", 80 | "# After stress\n", 81 | "stressed_mean = apply_stress(mean, 1) # Apply a stress factor of 1 to change the mean\n", 82 | "rv_stressed = multivariate_normal(stressed_mean, cov)\n", 83 | "ax.contourf(x, y, rv_stressed.pdf(pos), levels=25, alpha=0.6, cmap=\"Reds\")\n", 84 | "\n", 85 | "ax.set_xlabel('Variable 1')\n", 86 | "ax.set_ylabel('Variable 2')\n", 87 | "ax.set_title('Effect of Stress on System')\n", 88 | "ax.legend(['Before Stress', 'After Stress'])\n", 89 | "\n", 90 | "plt.show()" 91 | ] 92 | } 93 | ], 94 | "metadata": { 95 | "kernelspec": { 96 | "display_name": "Python 3 (ipykernel)", 97 | "language": "python", 98 | "name": "python3" 99 | }, 100 | "language_info": { 101 | "codemirror_mode": { 102 | "name": "ipython", 103 | "version": 3 104 | }, 105 | "file_extension": ".py", 106 | "mimetype": "text/x-python", 107 | "name": "python", 108 | "nbconvert_exporter": "python", 109 | "pygments_lexer": "ipython3", 110 | "version": "3.8.12" 111 | } 112 | }, 113 | "nbformat": 4, 114 | "nbformat_minor": 5 115 | } 116 | --------------------------------------------------------------------------------