├── .gitignore ├── Chapter 1 ├── 01_Thinking_Probabilistically_a_Bayesian_Inference_Primer (3).ipynb ├── hpd.py ├── mauna_loa_CO2.csv └── plot_post.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 └── fish.csv ├── Chapter 8 └── 08_Gaussian_processes.ipynb ├── LICENSE ├── MCMC-sampling-for-dummies.ipynb └── README.md /.gitignore: -------------------------------------------------------------------------------- 1 | .ipynb_checkpoints/ 2 | .DS_Store 3 | *.png 4 | __pycache__/ 5 | -------------------------------------------------------------------------------- /Chapter 1/hpd.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 | 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1.983250000000000000e+03,3.447699999999999818e+02 293 | 1.983333000000000084e+03,3.455799999999999841e+02 294 | 1.983416999999999916e+03,3.451399999999999864e+02 295 | 1.983500000000000000e+03,3.438100000000000023e+02 296 | 1.983583000000000084e+03,3.422099999999999795e+02 297 | 1.983666999999999916e+03,3.396899999999999977e+02 298 | 1.983750000000000000e+03,3.398199999999999932e+02 299 | 1.983833000000000084e+03,3.409800000000000182e+02 300 | 1.983916999999999916e+03,3.428199999999999932e+02 301 | 1.984000000000000000e+03,3.435199999999999818e+02 302 | 1.984083000000000084e+03,3.443299999999999841e+02 303 | 1.984166999999999916e+03,3.451100000000000136e+02 304 | 1.984250000000000000e+03,3.468799999999999955e+02 305 | 1.984333000000000084e+03,3.472500000000000000e+02 306 | 1.984416999999999916e+03,3.466200000000000045e+02 307 | 1.984500000000000000e+03,3.452200000000000273e+02 308 | 1.984583000000000084e+03,3.431100000000000136e+02 309 | 1.984666999999999916e+03,3.408999999999999773e+02 310 | 1.984750000000000000e+03,3.411800000000000068e+02 311 | 1.984833000000000084e+03,3.428000000000000114e+02 312 | 1.984916999999999916e+03,3.440400000000000205e+02 313 | 1.985000000000000000e+03,3.447900000000000205e+02 314 | 1.985083000000000084e+03,3.458199999999999932e+02 315 | 1.985166999999999916e+03,3.472500000000000000e+02 316 | 1.985250000000000000e+03,3.481700000000000159e+02 317 | 1.985333000000000084e+03,3.487400000000000091e+02 318 | 1.985416999999999916e+03,3.480699999999999932e+02 319 | 1.985500000000000000e+03,3.463799999999999955e+02 320 | 1.985583000000000084e+03,3.445099999999999909e+02 321 | 1.985666999999999916e+03,3.429200000000000159e+02 322 | 1.985750000000000000e+03,3.426200000000000045e+02 323 | 1.985833000000000084e+03,3.440600000000000023e+02 324 | 1.985916999999999916e+03,3.453799999999999955e+02 325 | 1.986000000000000000e+03,3.461100000000000136e+02 326 | 1.986083000000000084e+03,3.467799999999999727e+02 327 | 1.986166999999999916e+03,3.476800000000000068e+02 328 | 1.986250000000000000e+03,3.493700000000000045e+02 329 | 1.986333000000000084e+03,3.500299999999999727e+02 330 | 1.986416999999999916e+03,3.493700000000000045e+02 331 | 1.986500000000000000e+03,3.477599999999999909e+02 332 | 1.986583000000000084e+03,3.457300000000000182e+02 333 | 1.986666999999999916e+03,3.446800000000000068e+02 334 | 1.986750000000000000e+03,3.439900000000000091e+02 335 | 1.986833000000000084e+03,3.454800000000000182e+02 336 | 1.986916999999999916e+03,3.467200000000000273e+02 337 | 1.987000000000000000e+03,3.478399999999999750e+02 338 | 1.987083000000000084e+03,3.482900000000000205e+02 339 | 1.987166999999999916e+03,3.492300000000000182e+02 340 | 1.987250000000000000e+03,3.508000000000000114e+02 341 | 1.987333000000000084e+03,3.516600000000000250e+02 342 | 1.987416999999999916e+03,3.510699999999999932e+02 343 | 1.987500000000000000e+03,3.493299999999999841e+02 344 | 1.987583000000000084e+03,3.479200000000000159e+02 345 | 1.987666999999999916e+03,3.462699999999999818e+02 346 | 1.987750000000000000e+03,3.461800000000000068e+02 347 | 1.987833000000000084e+03,3.476399999999999864e+02 348 | 1.987916999999999916e+03,3.487799999999999727e+02 349 | 1.988000000000000000e+03,3.502500000000000000e+02 350 | 1.988083000000000084e+03,3.515400000000000205e+02 351 | 1.988166999999999916e+03,3.520500000000000114e+02 352 | 1.988250000000000000e+03,3.534100000000000250e+02 353 | 1.988333000000000084e+03,3.540400000000000205e+02 354 | 1.988416999999999916e+03,3.536200000000000045e+02 355 | 1.988500000000000000e+03,3.522200000000000273e+02 356 | 1.988583000000000084e+03,3.502699999999999818e+02 357 | 1.988666999999999916e+03,3.485500000000000114e+02 358 | 1.988750000000000000e+03,3.487200000000000273e+02 359 | 1.988833000000000084e+03,3.499100000000000250e+02 360 | 1.988916999999999916e+03,3.511800000000000068e+02 361 | 1.989000000000000000e+03,3.526000000000000227e+02 362 | 1.989083000000000084e+03,3.529200000000000159e+02 363 | 1.989166999999999916e+03,3.535299999999999727e+02 364 | 1.989250000000000000e+03,3.552599999999999909e+02 365 | 1.989333000000000084e+03,3.555199999999999818e+02 366 | 1.989416999999999916e+03,3.549700000000000273e+02 367 | 1.989500000000000000e+03,3.537500000000000000e+02 368 | 1.989583000000000084e+03,3.515199999999999818e+02 369 | 1.989666999999999916e+03,3.496399999999999864e+02 370 | 1.989750000000000000e+03,3.498299999999999841e+02 371 | 1.989833000000000084e+03,3.511399999999999864e+02 372 | 1.989916999999999916e+03,3.523700000000000045e+02 373 | 1.990000000000000000e+03,3.535000000000000000e+02 374 | 1.990083000000000084e+03,3.545500000000000114e+02 375 | 1.990166999999999916e+03,3.552300000000000182e+02 376 | 1.990250000000000000e+03,3.560400000000000205e+02 377 | 1.990333000000000084e+03,3.570000000000000000e+02 378 | 1.990416999999999916e+03,3.560699999999999932e+02 379 | 1.990500000000000000e+03,3.546700000000000159e+02 380 | 1.990583000000000084e+03,3.527599999999999909e+02 381 | 1.990666999999999916e+03,3.508199999999999932e+02 382 | 1.990750000000000000e+03,3.510400000000000205e+02 383 | 1.990833000000000084e+03,3.526899999999999977e+02 384 | 1.990916999999999916e+03,3.540699999999999932e+02 385 | 1.991000000000000000e+03,3.545899999999999750e+02 386 | 1.991083000000000084e+03,3.556299999999999955e+02 387 | 1.991166999999999916e+03,3.570299999999999727e+02 388 | 1.991250000000000000e+03,3.584800000000000182e+02 389 | 1.991333000000000084e+03,3.592200000000000273e+02 390 | 1.991416999999999916e+03,3.581200000000000045e+02 391 | 1.991500000000000000e+03,3.560600000000000023e+02 392 | 1.991583000000000084e+03,3.539200000000000159e+02 393 | 1.991666999999999916e+03,3.520500000000000114e+02 394 | 1.991750000000000000e+03,3.521100000000000136e+02 395 | 1.991833000000000084e+03,3.536399999999999864e+02 396 | 1.991916999999999916e+03,3.548899999999999864e+02 397 | 1.992000000000000000e+03,3.558799999999999955e+02 398 | 1.992083000000000084e+03,3.566299999999999955e+02 399 | 1.992166999999999916e+03,3.577200000000000273e+02 400 | 1.992250000000000000e+03,3.590699999999999932e+02 401 | 1.992333000000000084e+03,3.595799999999999841e+02 402 | 1.992416999999999916e+03,3.591700000000000159e+02 403 | 1.992500000000000000e+03,3.569399999999999977e+02 404 | 1.992583000000000084e+03,3.549200000000000159e+02 405 | 1.992666999999999916e+03,3.529399999999999977e+02 406 | 1.992750000000000000e+03,3.532300000000000182e+02 407 | 1.992833000000000084e+03,3.540899999999999750e+02 408 | 1.992916999999999916e+03,3.553299999999999841e+02 409 | 1.993000000000000000e+03,3.566299999999999955e+02 410 | 1.993083000000000084e+03,3.571000000000000227e+02 411 | 1.993166999999999916e+03,3.583199999999999932e+02 412 | 1.993250000000000000e+03,3.594100000000000250e+02 413 | 1.993333000000000084e+03,3.602300000000000182e+02 414 | 1.993416999999999916e+03,3.595500000000000114e+02 415 | 1.993500000000000000e+03,3.575299999999999727e+02 416 | 1.993583000000000084e+03,3.554800000000000182e+02 417 | 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.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 | -------------------------------------------------------------------------------- /Chapter 7/fish.csv: -------------------------------------------------------------------------------- 1 | count;livebait;camper;persons;child;hours 2 | 0;0;0;1;0;21.124 3 | 0;1;1;1;0;5.732 4 | 0;1;0;1;0;1.323 5 | 0;1;1;2;1;0.548 6 | 1;1;0;1;0;1.695 7 | 0;1;1;4;2;0.493 8 | 0;1;0;3;1;0.033 9 | 0;1;0;4;3;0.004 10 | 0;0;1;3;2;0.217 11 | 1;1;1;1;0;4.031 12 | 0;1;0;4;1;0.145 13 | 0;1;1;3;2;0.084 14 | 1;0;0;3;0;4.91 15 | 2;1;0;3;0;2.292 16 | 0;1;1;1;0;16.787 17 | 1;1;1;1;0;8.657 18 | 0;1;0;4;1;0.046 19 | 0;1;1;3;2;0.142 20 | 1;1;1;2;1;0.83 21 | 0;1;0;3;1;0.888 22 | 1;1;0;4;1;1.002 23 | 5;1;1;4;0;6.638 24 | 0;1;1;2;1;0.745 25 | 3;1;1;2;0;6.902 26 | 30;1;1;3;0;4.269 27 | 0;1;1;2;0;16.734 28 | 13;1;1;4;0;5.241 29 | 0;1;0;2;1;0.345 30 | 0;1;0;1;0;1.084 31 | 0;1;0;4;3;0.008 32 | 0;1;0;1;0;2.514 33 | 0;1;1;3;1;0.515 34 | 11;1;1;4;0;33.394 35 | 5;1;1;4;1;1.193 36 | 0;1;1;1;0;2.164 37 | 1;0;0;2;0;5.242 38 | 1;1;1;2;1;0.526 39 | 7;1;1;4;1;3.471 40 | 0;1;1;3;1;0.103 41 | 14;1;1;4;1;0.229 42 | 0;1;1;1;0;20.501 43 | 32;1;1;4;0;10.545 44 | 0;0;0;3;2;0.046 45 | 1;0;1;4;0;14.528 46 | 0;1;0;4;2;0.07 47 | 0;1;1;1;0;8.441 48 | 0;1;1;2;1;1.355 49 | 1;1;0;1;0;4.726 50 | 5;1;1;2;1;1.872 51 | 0;1;0;2;1;0.128 52 | 1;1;1;2;1;1.329 53 | 0;1;1;2;1;0.493 54 | 22;1;1;4;0;4.552 55 | 0;0;0;2;0;8.001 56 | 15;1;1;3;0;13.864 57 | 0;0;1;1;0;65.34 58 | 0;1;1;1;0;8.353 59 | 0;1;1;1;0;3.863 60 | 5;1;1;4;1;3.53 61 | 4;1;1;1;0;5.099 62 | 2;1;0;2;0;2.955 63 | 0;1;1;2;1;8.127 64 | 2;1;0;2;1;0.929 65 | 32;1;1;4;0;12.781 66 | 0;1;0;4;3;0.015 67 | 0;1;1;1;0;4.957 68 | 1;1;0;1;0;3.04 69 | 0;1;0;3;2;0.063 70 | 0;1;1;1;0;7.475 71 | 0;1;1;2;1;0.277 72 | 7;1;1;3;0;9.667 73 | 0;1;0;4;3;0.007 74 | 0;0;0;4;2;0.067 75 | 0;1;1;3;2;0.04 76 | 0;0;1;1;0;2.493 77 | 0;1;0;2;0;0.65 78 | 0;1;0;3;2;0.043 79 | 0;1;1;1;0;26.244 80 | 0;1;0;2;1;0.788 81 | 2;1;0;4;0;4.031 82 | 3;1;1;4;1;0.664 83 | 1;1;0;2;1;0.726 84 | 5;1;1;3;0;14.212 85 | 0;1;0;1;0;1.279 86 | 2;1;1;1;0;5.578 87 | 1;0;0;3;1;0.578 88 | 0;0;0;4;1;0.078 89 | 1;1;1;1;0;9.611 90 | 149;1;1;4;0;35.592 91 | 0;1;1;3;2;0.063 92 | 1;1;1;3;1;0.677 93 | 0;1;0;2;0;1.093 94 | 0;1;1;3;0;2.643 95 | 1;1;0;2;1;1.024 96 | 0;1;0;4;2;0.177 97 | 0;1;1;3;1;0.223 98 | 0;1;0;4;2;0.013 99 | 2;0;0;4;0;0.486 100 | 2;1;1;2;0;19.356 101 | 29;1;0;4;0;2.364 102 | 3;1;1;1;0;7.851 103 | 0;0;1;2;0;9.643 104 | 0;1;0;4;2;0.126 105 | 5;0;0;3;0;0.895 106 | 0;1;1;2;0;0.712 107 | 0;1;0;4;1;0.069 108 | 0;1;1;1;0;2.044 109 | 0;1;0;3;1;0.146 110 | 0;1;1;4;1;0.145 111 | 1;1;1;4;1;3.901 112 | 7;1;1;1;0;24.001 113 | 1;1;1;2;0;8.369 114 | 0;1;0;1;0;0.159 115 | 2;0;0;4;1;2.081 116 | 0;1;0;3;2;0.113 117 | 2;1;0;2;0;3.647 118 | 0;1;0;2;1;0.777 119 | 0;1;0;4;1;0.464 120 | 0;0;1;3;1;0.428 121 | 1;1;1;3;2;0.389 122 | 0;1;0;2;1;0.198 123 | 0;1;0;1;0;12.361 124 | 0;0;1;4;3;0.06 125 | 0;1;0;1;0;1.792 126 | 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0;1;1;4;3;0.019 172 | 2;1;1;3;0;13.549 173 | 4;1;1;2;1;4.652 174 | 5;1;0;4;0;6.215 175 | 9;1;0;2;0;11.008 176 | 0;1;0;4;2;0.055 177 | 0;1;0;2;0;24.031 178 | 0;1;1;2;0;5.817 179 | 0;1;0;1;0;3.245 180 | 21;1;1;2;0;11.812 181 | 0;1;0;1;0;1.415 182 | 6;1;1;3;0;10.054 183 | 0;1;0;2;1;0.434 184 | 0;0;1;2;0;18.943 185 | 0;1;1;2;1;0.668 186 | 0;1;0;3;1;0.208 187 | 16;1;1;4;1;2.586 188 | 0;0;0;3;2;0.031 189 | 0;1;1;3;2;0.179 190 | 4;1;1;4;0;32.206 191 | 2;1;1;2;1;1.82 192 | 10;1;1;3;0;13.179 193 | 0;0;1;1;0;5.104 194 | 0;1;1;1;0;6.946 195 | 0;0;0;1;0;1.157 196 | 2;0;1;2;0;19.554 197 | 1;1;1;2;0;3.624 198 | 3;1;0;1;0;2.723 199 | 0;1;1;3;1;0.362 200 | 0;1;1;4;2;0.092 201 | 21;1;1;2;0;3.658 202 | 0;1;0;2;1;0.125 203 | 0;1;0;2;0;9.964 204 | 2;0;1;1;0;9.075 205 | 0;0;1;2;1;4.811 206 | 3;1;1;4;1;0.42 207 | 0;1;1;3;1;0.315 208 | 38;1;1;4;0;3.285 209 | 0;1;1;4;3;0.01 210 | 0;1;1;1;0;11.767 211 | 0;1;0;1;0;1.293 212 | 1;1;1;1;0;18.708 213 | 3;1;0;1;0;35.388 214 | 0;1;1;1;0;4.083 215 | 1;1;0;2;0;9.216 216 | 0;1;0;4;2;0.009 217 | 0;0;0;2;1;0.324 218 | 0;1;0;4;2;0.041 219 | 0;1;0;3;1;0.067 220 | 5;1;1;4;2;1.775 221 | 0;1;0;4;2;0.113 222 | 0;0;0;4;1;0.275 223 | 2;1;0;3;0;1.005 224 | 0;1;1;2;1;4.349 225 | 0;1;1;1;0;2.606 226 | 0;1;0;2;1;0.515 227 | 1;1;1;2;0;17.493 228 | 4;1;1;3;1;20.896 229 | 0;1;0;1;0;1.843 230 | 0;1;1;3;2;0.095 231 | 2;1;1;2;1;3.955 232 | 3;1;1;1;0;8.508 233 | 0;1;0;4;2;0.064 234 | 0;1;0;3;1;0.168 235 | 0;1;0;2;0;2.724 236 | 0;0;0;2;0;0.643 237 | 1;1;1;1;0;25.568 238 | 2;1;1;2;0;2.583 239 | 0;1;1;1;0;2.14 240 | 6;1;1;3;0;8.663 241 | 4;1;1;2;0;2.529 242 | 1;1;1;2;0;35.574 243 | 1;1;1;4;2;0.268 244 | 0;0;0;2;0;2.88 245 | 1;1;1;3;1;0.48 246 | 0;1;0;3;0;3.727 247 | 0;1;1;2;0;10.219 248 | 0;1;1;4;3;0.004 249 | 0;1;1;2;1;1.969 250 | 0;1;1;3;2;0.075 251 | 0;1;1;2;1;0.233 252 | -------------------------------------------------------------------------------- /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 | # 用Python做贝叶斯分析 2 | 3 | 本书代码部分使用的是Python3.5以上的版本，因此建议你使用Python3的最新版，尽管本书的大部分代码都能在更早的版本上运行（包括Python2.7，不过可能需要稍微修改下）。 4 | 5 | 安装Python和Python库最简单的方法是使用Anaconda（一个用于科学计算的软件），你可以从这里了解和下载Anaconda [https://www.continuum.io/downloads](https://www.continuum.io/downloads)。在安装好Anaconda之后，可以使用`conda install 库的名称`来安装相关的Python库。 6 | 7 | 本书会用到以下Python库： 8 | 9 | - Ipython 5.0 10 | - NumPy 1.11.1 11 | - SciPy 0.18.1 12 | - Pandas 0.18.1 13 | - Matplotlib 1.5.3 14 | - Seaborn 0.7.1 15 | - PyMC3 3.1rc3 16 | 17 | 注意： 18 | 19 | 1. 如果你已经安装了Python2.7版本的Anaconda，可以通过执行`conda create -n py3 python=3 anaconda`增加一个py3的环境，然后运行`source activate py3`切换过去，运行完代码之后，执行`source deactivate`切回去。 20 | 21 | 2. 通过`pip install pymc3`安装的PyMC3版本会比较旧，建议直接运行`pip install git+https://github.com/pymc-devs/pymc3`安装。 22 | 23 | ## 相关书籍 24 | 25 | - [贝叶斯方法：概率编程与贝叶斯推断](http://www.epubit.com.cn/book/details/4274) 26 | - [概率编程实战](http://www.epubit.com.cn/book/details/4366) 27 | - [Statistical Rethinking](https://book.douban.com/subject/26607925/) 28 | - [Doing Bayesian Data Analysis, Second Edition](https://book.douban.com/subject/26206378/) 29 | - [Bayesian Data Analysis, Third Edition](https://book.douban.com/subject/17380364/) 30 | 31 | ## 建议和反馈 32 | 33 | 请直接提[issue](https://github.com/findmyway/Bayesian-Analysis-with-Python/issues)。 34 | --------------------------------------------------------------------------------