├── Chapter 1 ├── 01_Thinking_Probabilistically_a_Bayesian_Inference_Primer (3).ipynb ├── hpd (1).py ├── mauna_loa_CO2 (1).csv └── plot_post (1).py ├── Chapter 2 └── 02_Programming_probabilistically_a_PyMC3_primer (1).ipynb ├── Chapter 3 └── 03_Juggling with multiparametric and Hierarchical models.ipynb ├── Chapter 4 └── 04_Understanding_and_predicting_data_with_linear_regression_models (2).ipynb ├── Chapter 5 └── 05_Classifying_outcomes_with_logistic_regression (2).ipynb ├── Chapter 6 └── 06_Model_comparison.ipynb ├── Chapter 7 └── 07_Mixture_Models (1).ipynb ├── Chapter 8 └── 08_Gaussian_processes.ipynb ├── LICENSE └── README.md /Chapter 1/hpd (1).py: -------------------------------------------------------------------------------- 1 | from __future__ import division 2 | import numpy as np 3 | import scipy.stats.kde as kde 4 | 5 | def hpd_grid(sample, alpha=0.05, roundto=2): 6 | """Calculate highest posterior density (HPD) of array for given alpha. 7 | The HPD is the minimum width Bayesian credible interval (BCI). 8 | The function works for multimodal distributions, returning more than one mode 9 | 10 | Parameters 11 | ---------- 12 | 13 | sample : Numpy array or python list 14 | An array containing MCMC samples 15 | alpha : float 16 | Desired probability of type I error (defaults to 0.05) 17 | roundto: integer 18 | Number of digits after the decimal point for the results 19 | 20 | Returns 21 | ---------- 22 | hpd: array with the lower 23 | 24 | """ 25 | sample = np.asarray(sample) 26 | sample = sample[~np.isnan(sample)] 27 | # get upper and lower bounds 28 | l = np.min(sample) 29 | u = np.max(sample) 30 | density = kde.gaussian_kde(sample) 31 | x = np.linspace(l, u, 2000) 32 | y = density.evaluate(x) 33 | #y = density.evaluate(x, l, u) waitting for PR to be accepted 34 | xy_zipped = zip(x, y/np.sum(y)) 35 | xy = sorted(xy_zipped, key=lambda x: x[1], reverse=True) 36 | xy_cum_sum = 0 37 | hdv = [] 38 | for val in xy: 39 | xy_cum_sum += val[1] 40 | hdv.append(val[0]) 41 | if xy_cum_sum >= (1-alpha): 42 | break 43 | hdv.sort() 44 | diff = (u-l)/20 # differences of 5% 45 | hpd = [] 46 | hpd.append(round(min(hdv), roundto)) 47 | for i in range(1, len(hdv)): 48 | if hdv[i]-hdv[i-1] >= diff: 49 | hpd.append(round(hdv[i-1], roundto)) 50 | hpd.append(round(hdv[i], roundto)) 51 | hpd.append(round(max(hdv), roundto)) 52 | ite = iter(hpd) 53 | hpd = list(zip(ite, ite)) 54 | modes = [] 55 | for value in hpd: 56 | x_hpd = x[(x > value[0]) & (x < value[1])] 57 | y_hpd = y[(x > value[0]) & (x < value[1])] 58 | modes.append(round(x_hpd[np.argmax(y_hpd)], roundto)) 59 | return hpd, x, y, modes 60 | -------------------------------------------------------------------------------- /Chapter 1/mauna_loa_CO2 (1).csv: -------------------------------------------------------------------------------- 1 | 1.959000000000000000e+03,3.154200000000000159e+02 2 | 1.959083000000000084e+03,3.163100000000000023e+02 3 | 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1.993666999999999916e+03,3.536700000000000159e+02 418 | 1.993750000000000000e+03,3.539499999999999886e+02 419 | 1.993833000000000084e+03,3.553000000000000114e+02 420 | 1.993916999999999916e+03,3.567799999999999727e+02 421 | 1.994000000000000000e+03,3.583399999999999750e+02 422 | 1.994083000000000084e+03,3.588899999999999864e+02 423 | 1.994166999999999916e+03,3.599499999999999886e+02 424 | 1.994250000000000000e+03,3.612500000000000000e+02 425 | 1.994333000000000084e+03,3.616700000000000159e+02 426 | 1.994416999999999916e+03,3.609399999999999977e+02 427 | 1.994500000000000000e+03,3.595500000000000114e+02 428 | 1.994583000000000084e+03,3.574900000000000091e+02 429 | 1.994666999999999916e+03,3.558399999999999750e+02 430 | 1.994750000000000000e+03,3.560000000000000000e+02 431 | 1.994833000000000084e+03,3.575899999999999750e+02 432 | 1.994916999999999916e+03,3.590500000000000114e+02 433 | 1.995000000000000000e+03,3.599800000000000182e+02 434 | 1.995083000000000084e+03,3.610299999999999727e+02 435 | 1.995166999999999916e+03,3.616600000000000250e+02 436 | 1.995250000000000000e+03,3.634800000000000182e+02 437 | 1.995333000000000084e+03,3.638199999999999932e+02 438 | 1.995416999999999916e+03,3.633000000000000114e+02 439 | 1.995500000000000000e+03,3.619399999999999977e+02 440 | 1.995583000000000084e+03,3.595000000000000000e+02 441 | 1.995666999999999916e+03,3.581100000000000136e+02 442 | 1.995750000000000000e+03,3.578000000000000114e+02 443 | 1.995833000000000084e+03,3.596100000000000136e+02 444 | 1.995916999999999916e+03,3.607400000000000091e+02 445 | 1.996000000000000000e+03,3.620899999999999750e+02 446 | 1.996083000000000084e+03,3.632900000000000205e+02 447 | 1.996166999999999916e+03,3.640600000000000023e+02 448 | 1.996250000000000000e+03,3.647599999999999909e+02 449 | 1.996333000000000084e+03,3.654499999999999886e+02 450 | 1.996416999999999916e+03,3.650099999999999909e+02 451 | 1.996500000000000000e+03,3.636999999999999886e+02 452 | 1.996583000000000084e+03,3.615400000000000205e+02 453 | 1.996666999999999916e+03,3.595099999999999909e+02 454 | 1.996750000000000000e+03,3.596499999999999773e+02 455 | 1.996833000000000084e+03,3.608000000000000114e+02 456 | 1.996916999999999916e+03,3.623799999999999955e+02 457 | 1.997000000000000000e+03,3.632300000000000182e+02 458 | 1.997083000000000084e+03,3.640600000000000023e+02 459 | 1.997166999999999916e+03,3.646100000000000136e+02 460 | 1.997250000000000000e+03,3.663999999999999773e+02 461 | 1.997333000000000084e+03,3.668399999999999750e+02 462 | 1.997416999999999916e+03,3.656800000000000068e+02 463 | 1.997500000000000000e+03,3.645199999999999818e+02 464 | 1.997583000000000084e+03,3.625699999999999932e+02 465 | 1.997666999999999916e+03,3.602400000000000091e+02 466 | 1.997750000000000000e+03,3.608299999999999841e+02 467 | 1.997833000000000084e+03,3.624900000000000091e+02 468 | 1.997916999999999916e+03,3.643399999999999750e+02 469 | -------------------------------------------------------------------------------- /Chapter 1/plot_post (1).py: -------------------------------------------------------------------------------- 1 | from __future__ import division 2 | import numpy as np 3 | from scipy import stats 4 | import matplotlib.pyplot as plt 5 | from hpd import hpd_grid 6 | 7 | 8 | def plot_post(sample, alpha=0.05, show_mode=True, kde_plot=True, bins=50, 9 | ROPE=None, comp_val=None, roundto=2): 10 | """Plot posterior and HPD 11 | 12 | Parameters 13 | ---------- 14 | 15 | sample : Numpy array or python list 16 | An array containing MCMC samples 17 | alpha : float 18 | Desired probability of type I error (defaults to 0.05) 19 | show_mode: Bool 20 | If True the legend will show the mode(s) value(s), if false the mean(s) 21 | will be displayed 22 | kde_plot: Bool 23 | If True the posterior will be displayed using a Kernel Density Estimation 24 | otherwise an histogram will be used 25 | bins: integer 26 | Number of bins used for the histogram, only works when kde_plot is False 27 | ROPE: list or numpy array 28 | Lower and upper values of the Region Of Practical Equivalence 29 | comp_val: float 30 | Comparison value 31 | 32 | 33 | Returns 34 | ------- 35 | 36 | post_summary : dictionary 37 | Containing values with several summary statistics 38 | 39 | """ 40 | 41 | post_summary = {'mean':0,'median':0,'mode':0, 'alpha':0,'hpd_low':0, 42 | 'hpd_high':0, 'comp_val':0, 'pc_gt_comp_val':0, 'ROPE_low':0, 43 | 'ROPE_high':0, 'pc_in_ROPE':0} 44 | 45 | post_summary['mean'] = round(np.mean(sample), roundto) 46 | post_summary['median'] = round(np.median(sample), roundto) 47 | post_summary['alpha'] = alpha 48 | 49 | # Compute the hpd, KDE and mode for the posterior 50 | hpd, x, y, modes = hpd_grid(sample, alpha, roundto) 51 | post_summary['hpd'] = hpd 52 | post_summary['mode'] = modes 53 | 54 | ## Plot KDE. 55 | if kde_plot: 56 | plt.plot(x, y, color='k', lw=2) 57 | ## Plot histogram. 58 | else: 59 | plt.hist(sample, normed=True, bins=bins, facecolor='b', 60 | edgecolor='w') 61 | 62 | ## Display mode or mean: 63 | if show_mode: 64 | string = '{:g} ' * len(post_summary['mode']) 65 | plt.plot(0, label='mode =' + string.format(*post_summary['mode']), alpha=0) 66 | else: 67 | plt.plot(0, label='mean = {:g}'.format(post_summary['mean']), alpha=0) 68 | 69 | ## Display the hpd. 70 | hpd_label = '' 71 | for value in hpd: 72 | plt.plot(value, [0, 0], linewidth=10, color='b') 73 | hpd_label = hpd_label + '{:g} {:g}\n'.format(round(value[0], roundto), round(value[1], roundto)) 74 | plt.plot(0, 0, linewidth=4, color='b', label='hpd {:g}%\n{}'.format((1-alpha)*100, hpd_label)) 75 | ## Display the ROPE. 76 | if ROPE is not None: 77 | pc_in_ROPE = round(np.sum((sample > ROPE[0]) & (sample < ROPE[1]))/len(sample)*100, roundto) 78 | plt.plot(ROPE, [0, 0], linewidth=20, color='r', alpha=0.75) 79 | plt.plot(0, 0, linewidth=4, color='r', label='{:g}% in ROPE'.format(pc_in_ROPE)) 80 | post_summary['ROPE_low'] = ROPE[0] 81 | post_summary['ROPE_high'] = ROPE[1] 82 | post_summary['pc_in_ROPE'] = pc_in_ROPE 83 | ## Display the comparison value. 84 | if comp_val is not None: 85 | pc_gt_comp_val = round(100 * np.sum(sample > comp_val)/len(sample), roundto) 86 | pc_lt_comp_val = round(100 - pc_gt_comp_val, roundto) 87 | plt.axvline(comp_val, ymax=.75, color='g', linewidth=4, alpha=0.75, 88 | label='{:g}% < {:g} < {:g}%'.format(pc_lt_comp_val, 89 | comp_val, pc_gt_comp_val)) 90 | post_summary['comp_val'] = comp_val 91 | post_summary['pc_gt_comp_val'] = pc_gt_comp_val 92 | 93 | plt.legend(loc=0, framealpha=1) 94 | frame = plt.gca() 95 | frame.axes.get_yaxis().set_ticks([]) 96 | return post_summary 97 | 98 | 99 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2016 Packt 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | # Bayesian Analysis with Python 5 | 6 | This is the code repository for [Bayesian Analysis with Python](https://www.packtpub.com/big-data-and-business-intelligence/bayesian-analysis-python?utm_source=github&utm_medium=repository&utm_campaign=9781785883804), published by Packt. It contains all the supporting project files necessary to work through the book from start to finish. 7 | 8 | **Please follow this [link](https://github.com/aloctavodia/BAP) for an updated version of the code that have been tested to run with the last version of PyMC3.** 9 | 10 | 11 | ## Instructions and Navigations 12 | 13 | All of the code is organized into folders. Each folder starts with a number followed by the chapter name. 14 | 15 | This book is written for Python version >= 3.5, and it is recommended that you use 16 | the most recent version of Python 3 that is currently available, although most of the 17 | code examples may also run for older versions of Python, including Python 2.7 with 18 | minor adjustments. 19 | 20 | Maybe the easiest way to install Python and Python libraries is using Anaconda, 21 | a scientific computing distribution. You can read more about Anaconda and 22 | download it [here](https://www.continuum.io/downloads). Once Anaconda is in 23 | our system, we can install new Python packages with this command: 24 | 25 | ```conda install NamePackage``` 26 | 27 | We will use the following python packages: 28 | 29 | 30 | * Ipython 5.0 31 | * NumPy 1.11.1 32 | * SciPy 0.18.1 33 | * Pandas 0.18.1 34 | * Matplotlib 1.5.3 35 | * Seaborn 0.7.1 36 | * PyMC3 3.0 37 | 38 | ## Errata 39 | 40 | If you find an error in the book please fill an issue or send a PR [here](https://github.com/aloctavodia/BAP) 41 | ### Download a free PDF 42 | 43 | If you have already purchased a print or Kindle version of this book, you can get a DRM-free PDF version at no cost.
Simply click on the link to claim your free PDF. 44 |

https://packt.link/free-ebook/9781785883804

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