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Commit aa54c8e

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Merge pull request #533 from toppare/fix-all-hist-with-normed
all `normed` keywords changed to `density`
2 parents 629d1ba + 18b0e76 commit aa54c8e

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14 files changed

+46
-46
lines changed

14 files changed

+46
-46
lines changed

‎Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -803,7 +803,7 @@
803803
"ax.set_autoscaley_on(False)\n",
804804
"\n",
805805
"plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
806-
" label=\"posterior of $\\lambda_1$\", color=\"#A60628\", normed=True)\n",
806+
" label=\"posterior of $\\lambda_1$\", color=\"#A60628\", density=True)\n",
807807
"plt.legend(loc=\"upper left\")\n",
808808
"plt.title(r\"\"\"Posterior distributions of the variables\n",
809809
" $\\lambda_1,\\;\\lambda_2,\\;\\tau$\"\"\")\n",
@@ -813,7 +813,7 @@
813813
"ax = plt.subplot(312)\n",
814814
"ax.set_autoscaley_on(False)\n",
815815
"plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
816-
" label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", normed=True)\n",
816+
" label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", density=True)\n",
817817
"plt.legend(loc=\"upper left\")\n",
818818
"plt.xlim([15, 30])\n",
819819
"plt.xlabel(\"$\\lambda_2$ value\")\n",

‎Chapter2_MorePyMC/Ch2_MorePyMC_PyMC2.ipynb

Lines changed: 10 additions & 10 deletions
Original file line numberDiff line numberDiff line change
@@ -360,7 +360,7 @@
360360
"\n",
361361
"\n",
362362
"samples = [lambda_1.random() for i in range(20000)]\n",
363-
"plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n",
363+
"plt.hist(samples, bins=70, density=True, histtype=\"stepfilled\")\n",
364364
"plt.title(\"Prior distribution for $\\lambda_1$\")\n",
365365
"plt.xlim(0, 8);"
366366
]
@@ -826,7 +826,7 @@
826826
"figsize(12.5, 4)\n",
827827
"plt.title(\"Posterior distribution of $p_A,ドル the true effectiveness of site A\")\n",
828828
"plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
829-
"plt.hist(mcmc.trace(\"p\")[:], bins=25, histtype=\"stepfilled\", normed=True)\n",
829+
"plt.hist(mcmc.trace(\"p\")[:], bins=25, histtype=\"stepfilled\", density=True)\n",
830830
"plt.legend();"
831831
]
832832
},
@@ -979,7 +979,7 @@
979979
"\n",
980980
"plt.xlim(0, .1)\n",
981981
"plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n",
982-
" label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n",
982+
" label=\"posterior of $p_A$\", color=\"#A60628\", density=True)\n",
983983
"plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
984984
"plt.legend(loc=\"upper right\")\n",
985985
"plt.title(\"Posterior distributions of $p_A,ドル $p_B,ドル and delta unknowns\")\n",
@@ -988,13 +988,13 @@
988988
"\n",
989989
"plt.xlim(0, .1)\n",
990990
"plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n",
991-
" label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n",
991+
" label=\"posterior of $p_B$\", color=\"#467821\", density=True)\n",
992992
"plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n",
993993
"plt.legend(loc=\"upper right\")\n",
994994
"\n",
995995
"ax = plt.subplot(313)\n",
996996
"plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
997-
" label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n",
997+
" label=\"posterior of delta\", color=\"#7A68A6\", density=True)\n",
998998
"plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n",
999999
" label=\"true delta (unknown)\")\n",
10001000
"plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n",
@@ -1353,7 +1353,7 @@
13531353
"source": [
13541354
"figsize(12.5, 3)\n",
13551355
"p_trace = mcmc.trace(\"freq_cheating\")[:]\n",
1356-
"plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n",
1356+
"plt.hist(p_trace, histtype=\"stepfilled\", density=True, alpha=0.85, bins=30,\n",
13571357
" label=\"posterior distribution\", color=\"#348ABD\")\n",
13581358
"plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n",
13591359
"plt.xlim(0, 1)\n",
@@ -1479,7 +1479,7 @@
14791479
"source": [
14801480
"figsize(12.5, 3)\n",
14811481
"p_trace = mcmc.trace(\"freq_cheating\")[:]\n",
1482-
"plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n",
1482+
"plt.hist(p_trace, histtype=\"stepfilled\", density=True, alpha=0.85, bins=30,\n",
14831483
" label=\"posterior distribution\", color=\"#348ABD\")\n",
14841484
"plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n",
14851485
"plt.xlim(0, 1)\n",
@@ -1910,12 +1910,12 @@
19101910
"plt.subplot(211)\n",
19111911
"plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n",
19121912
"plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
1913-
" label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n",
1913+
" label=r\"posterior of $\\beta$\", color=\"#7A68A6\", density=True)\n",
19141914
"plt.legend()\n",
19151915
"\n",
19161916
"plt.subplot(212)\n",
19171917
"plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
1918-
" label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n",
1918+
" label=r\"posterior of $\\alpha$\", color=\"#A60628\", density=True)\n",
19191919
"plt.legend();"
19201920
]
19211921
},
@@ -2074,7 +2074,7 @@
20742074
"prob_31 = logistic(31, beta_samples, alpha_samples)\n",
20752075
"\n",
20762076
"plt.xlim(0.995, 1)\n",
2077-
"plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n",
2077+
"plt.hist(prob_31, bins=1000, density=True, histtype='stepfilled')\n",
20782078
"plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n",
20792079
"plt.xlabel(\"probability of defect occurring in O-ring\");"
20802080
]

‎Chapter2_MorePyMC/Ch2_MorePyMC_PyMC3.ipynb

Lines changed: 10 additions & 10 deletions
Original file line numberDiff line numberDiff line change
@@ -442,7 +442,7 @@
442442
"\n",
443443
"\n",
444444
"samples = lambda_1.random(size=20000)\n",
445-
"plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n",
445+
"plt.hist(samples, bins=70, density=True, histtype=\"stepfilled\")\n",
446446
"plt.title(\"Prior distribution for $\\lambda_1$\")\n",
447447
"plt.xlim(0, 8);"
448448
]
@@ -894,7 +894,7 @@
894894
"figsize(12.5, 4)\n",
895895
"plt.title(\"Posterior distribution of $p_A,ドル the true effectiveness of site A\")\n",
896896
"plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
897-
"plt.hist(burned_trace[\"p\"], bins=25, histtype=\"stepfilled\", normed=True)\n",
897+
"plt.hist(burned_trace[\"p\"], bins=25, histtype=\"stepfilled\", density=True)\n",
898898
"plt.legend();"
899899
]
900900
},
@@ -1049,7 +1049,7 @@
10491049
"\n",
10501050
"plt.xlim(0, .1)\n",
10511051
"plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n",
1052-
" label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n",
1052+
" label=\"posterior of $p_A$\", color=\"#A60628\", density=True)\n",
10531053
"plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
10541054
"plt.legend(loc=\"upper right\")\n",
10551055
"plt.title(\"Posterior distributions of $p_A,ドル $p_B,ドル and delta unknowns\")\n",
@@ -1058,13 +1058,13 @@
10581058
"\n",
10591059
"plt.xlim(0, .1)\n",
10601060
"plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n",
1061-
" label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n",
1061+
" label=\"posterior of $p_B$\", color=\"#467821\", density=True)\n",
10621062
"plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n",
10631063
"plt.legend(loc=\"upper right\")\n",
10641064
"\n",
10651065
"ax = plt.subplot(313)\n",
10661066
"plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
1067-
" label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n",
1067+
" label=\"posterior of delta\", color=\"#7A68A6\", density=True)\n",
10681068
"plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n",
10691069
" label=\"true delta (unknown)\")\n",
10701070
"plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n",
@@ -1428,7 +1428,7 @@
14281428
"source": [
14291429
"figsize(12.5, 3)\n",
14301430
"p_trace = burned_trace[\"freq_cheating\"][15000:]\n",
1431-
"plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n",
1431+
"plt.hist(p_trace, histtype=\"stepfilled\", density=True, alpha=0.85, bins=30, \n",
14321432
" label=\"posterior distribution\", color=\"#348ABD\")\n",
14331433
"plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n",
14341434
"plt.xlim(0, 1)\n",
@@ -1559,7 +1559,7 @@
15591559
"source": [
15601560
"figsize(12.5, 3)\n",
15611561
"p_trace = burned_trace[\"freq_cheating\"]\n",
1562-
"plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n",
1562+
"plt.hist(p_trace, histtype=\"stepfilled\", density=True, alpha=0.85, bins=30, \n",
15631563
" label=\"posterior distribution\", color=\"#348ABD\")\n",
15641564
"plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n",
15651565
"plt.xlim(0, 1)\n",
@@ -1968,12 +1968,12 @@
19681968
"plt.subplot(211)\n",
19691969
"plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n",
19701970
"plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
1971-
" label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n",
1971+
" label=r\"posterior of $\\beta$\", color=\"#7A68A6\", density=True)\n",
19721972
"plt.legend()\n",
19731973
"\n",
19741974
"plt.subplot(212)\n",
19751975
"plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
1976-
" label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n",
1976+
" label=r\"posterior of $\\alpha$\", color=\"#A60628\", density=True)\n",
19771977
"plt.legend();"
19781978
]
19791979
},
@@ -2132,7 +2132,7 @@
21322132
"prob_31 = logistic(31, beta_samples, alpha_samples)\n",
21332133
"\n",
21342134
"plt.xlim(0.995, 1)\n",
2135-
"plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n",
2135+
"plt.hist(prob_31, bins=1000, density=True, histtype='stepfilled')\n",
21362136
"plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n",
21372137
"plt.xlabel(\"probability of defect occurring in O-ring\");"
21382138
]

‎Chapter2_MorePyMC/Ch2_MorePyMC_TFP.ipynb

Lines changed: 6 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -679,7 +679,7 @@
679679
"\n",
680680
"# Visualize our stepwise prior distribution\n",
681681
"plt.figure(figsize(12.5, 5))\n",
682-
"plt.hist(lambda_1_, bins=70, normed=True, histtype=\"stepfilled\")\n",
682+
"plt.hist(lambda_1_, bins=70, density=True, histtype=\"stepfilled\")\n",
683683
"plt.title(r\"Prior distribution for $\\lambda_1$\")\n",
684684
"plt.xlim(0, 8);"
685685
],
@@ -1503,7 +1503,7 @@
15031503
"plt.figure(figsize(12.5, 4))\n",
15041504
"plt.title(\"Posterior distribution of $p_A,ドル the true effectiveness of site A\")\n",
15051505
"plt.vlines(prob_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
1506-
"plt.hist(burned_prob_A_trace_, bins=25, histtype=\"stepfilled\", normed=True)\n",
1506+
"plt.hist(burned_prob_A_trace_, bins=25, histtype=\"stepfilled\", density=True)\n",
15071507
"plt.legend();"
15081508
],
15091509
"execution_count": 20,
@@ -1829,7 +1829,7 @@
18291829
"\n",
18301830
"plt.xlim(0, .1)\n",
18311831
"plt.hist(burned_prob_A_trace_, histtype='stepfilled', bins=25, alpha=0.85,\n",
1832-
" label=\"posterior of $p_A$\", color=TFColor[0], normed=True)\n",
1832+
" label=\"posterior of $p_A$\", color=TFColor[0], density=True)\n",
18331833
"plt.vlines(true_prob_A_, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
18341834
"plt.legend(loc=\"upper right\")\n",
18351835
"plt.title(\"Posterior distributions of $p_A,ドル $p_B,ドル and delta unknowns\")\n",
@@ -1838,13 +1838,13 @@
18381838
"\n",
18391839
"plt.xlim(0, .1)\n",
18401840
"plt.hist(burned_prob_B_trace_, histtype='stepfilled', bins=25, alpha=0.85,\n",
1841-
" label=\"posterior of $p_B$\", color=TFColor[2], normed=True)\n",
1841+
" label=\"posterior of $p_B$\", color=TFColor[2], density=True)\n",
18421842
"plt.vlines(true_prob_B_, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n",
18431843
"plt.legend(loc=\"upper right\")\n",
18441844
"\n",
18451845
"ax = plt.subplot(313)\n",
18461846
"plt.hist(burned_delta_trace_, histtype='stepfilled', bins=30, alpha=0.85,\n",
1847-
" label=\"posterior of delta\", color=TFColor[6], normed=True)\n",
1847+
" label=\"posterior of delta\", color=TFColor[6], density=True)\n",
18481848
"plt.vlines(true_prob_A_ - true_prob_B_, 0, 60, linestyle=\"--\",\n",
18491849
" label=\"true delta (unknown)\")\n",
18501850
"plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n",
@@ -2796,7 +2796,7 @@
27962796
"source": [
27972797
"plt.figure(figsize(12.5, 6))\n",
27982798
"p_trace_ = freq_cheating_samples_\n",
2799-
"plt.hist(p_trace_, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n",
2799+
"plt.hist(p_trace_, histtype=\"stepfilled\", density=True, alpha=0.85, bins=30, \n",
28002800
" label=\"posterior distribution\", color=TFColor[3])\n",
28012801
"plt.vlines([.1, .40], [0, 0], [5, 5], alpha=0.2)\n",
28022802
"plt.xlim(0, 1)\n",

‎Chapter3_MCMC/Ch3_IntroMCMC_PyMC2.ipynb

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -801,7 +801,7 @@
801801
"posterior_std_means = std_trace.mean(axis=0)\n",
802802
"posterior_p_mean = mcmc.trace(\"p\")[:].mean()\n",
803803
"\n",
804-
"plt.hist(data, bins=20, histtype=\"step\", normed=True, color=\"k\",\n",
804+
"plt.hist(data, bins=20, histtype=\"step\", density=True, color=\"k\",\n",
805805
" lw=2, label=\"histogram of data\")\n",
806806
"y = posterior_p_mean * norm.pdf(x, loc=posterior_center_means[0],\n",
807807
" scale=posterior_std_means[0])\n",

‎Chapter3_MCMC/Ch3_IntroMCMC_PyMC3.ipynb

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -785,7 +785,7 @@
785785
"posterior_std_means = std_trace.mean(axis=0)\n",
786786
"posterior_p_mean = trace[\"p\"].mean()\n",
787787
"\n",
788-
"plt.hist(data, bins=20, histtype=\"step\", normed=True, color=\"k\",\n",
788+
"plt.hist(data, bins=20, histtype=\"step\", density=True, color=\"k\",\n",
789789
" lw=2, label=\"histogram of data\")\n",
790790
"y = posterior_p_mean * norm.pdf(x, loc=posterior_center_means[0],\n",
791791
" scale=posterior_std_means[0])\n",

‎Chapter4_TheGreatestTheoremNeverTold/Ch4_LawOfLargeNumbers_PyMC2.ipynb

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -601,10 +601,10 @@
601601
"for i in range(len(submissions)):\n",
602602
" j = submissions[i]\n",
603603
" posteriors.append(posterior_upvote_ratio(votes[j, 0], votes[j, 1]))\n",
604-
" plt.hist(posteriors[i], bins=18, normed=True, alpha=.9,\n",
604+
" plt.hist(posteriors[i], bins=18, density=True, alpha=.9,\n",
605605
" histtype=\"step\", color=colours[i % 5], lw=3,\n",
606606
" label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n",
607-
" plt.hist(posteriors[i], bins=18, normed=True, alpha=.2,\n",
607+
" plt.hist(posteriors[i], bins=18, density=True, alpha=.2,\n",
608608
" histtype=\"stepfilled\", color=colours[i], lw=3, )\n",
609609
"\n",
610610
"plt.legend(loc=\"upper left\")\n",
@@ -654,10 +654,10 @@
654654
"\n",
655655
"for i in range(len(submissions)):\n",
656656
" j = submissions[i]\n",
657-
" plt.hist(posteriors[i], bins=20, normed=True, alpha=.9,\n",
657+
" plt.hist(posteriors[i], bins=20, density=True, alpha=.9,\n",
658658
" histtype=\"step\", color=colours[i], lw=3,\n",
659659
" label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n",
660-
" plt.hist(posteriors[i], bins=20, normed=True, alpha=.2,\n",
660+
" plt.hist(posteriors[i], bins=20, density=True, alpha=.2,\n",
661661
" histtype=\"stepfilled\", color=colours[i], lw=3, )\n",
662662
" v = np.sort(posteriors[i])[int(0.05 * N)]\n",
663663
" # plt.vlines( v, 0, 15 , color = \"k\", alpha = 1, linewidths=3 )\n",

‎Chapter5_LossFunctions/Ch5_LossFunctions_PyMC2.ipynb

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -297,7 +297,7 @@
297297
"plt.plot(x, stats.norm.pdf(x, 35000, 7500), c=\"k\", lw=2,\n",
298298
" label=\"prior dist. of suite price\")\n",
299299
"\n",
300-
"_hist = plt.hist(price_trace, bins=35, normed=True, histtype=\"stepfilled\")\n",
300+
"_hist = plt.hist(price_trace, bins=35, density=True, histtype=\"stepfilled\")\n",
301301
"plt.title(\"Posterior of the true price estimate\")\n",
302302
"plt.vlines(mu_prior, 0, 1.1 * np.max(_hist[0]), label=\"prior's mean\",\n",
303303
" linestyles=\"--\")\n",

‎Chapter5_LossFunctions/Ch5_LossFunctions_TFP.ipynb

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -722,7 +722,7 @@
722722
"plt.plot(prices_, prior_, c=\"k\", lw=2,\n",
723723
" label=\"prior dist. of suite price\")\n",
724724
"\n",
725-
"hist = plt.hist(posterior_price_predictive_samples_, bins=35, normed=True, histtype=\"stepfilled\")\n",
725+
"hist = plt.hist(posterior_price_predictive_samples_, bins=35, density=True, histtype=\"stepfilled\")\n",
726726
"plt.title(\"Posterior of the true price estimate\")\n",
727727
"plt.vlines(mu_prior, 0, 1.1 * np.max(hist[0]), label=\"prior's mean\",\n",
728728
" linestyles=\"--\")\n",

‎Chapter6_Priorities/Ch6_Priors_PyMC2.ipynb

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -1184,7 +1184,7 @@
11841184
" returns[:, i] = _returns\n",
11851185
" plt.subplot(2, 2, i+1)\n",
11861186
" plt.hist(_returns, bins=20,\n",
1187-
" normed=True, histtype=\"stepfilled\",\n",
1187+
" density=True, histtype=\"stepfilled\",\n",
11881188
" color=colors[i], alpha=0.7)\n",
11891189
" plt.title(_stock + \" returns\")\n",
11901190
" plt.xlim(-0.15, 0.15)\n",
@@ -1258,7 +1258,7 @@
12581258
"\n",
12591259
"for i in range(4):\n",
12601260
" plt.hist(mu_samples[:, i], alpha=0.8 - 0.05 * i, bins=30,\n",
1261-
" histtype=\"stepfilled\", normed=True,\n",
1261+
" histtype=\"stepfilled\", density=True,\n",
12621262
" label=\"%s\" % list(stock_returns.keys())[i])\n",
12631263
"\n",
12641264
"plt.vlines(mu_samples.mean(axis=0), 0, 500, linestyle=\"--\", linewidth=.5)\n",
@@ -1302,7 +1302,7 @@
13021302
"for i in range(4):\n",
13031303
" plt.subplot(2, 2, i + 1)\n",
13041304
" plt.hist(mu_samples[:, i], alpha=0.8 - 0.05 * i, bins=30,\n",
1305-
" histtype=\"stepfilled\", normed=True, color=colors[i],\n",
1305+
" histtype=\"stepfilled\", density=True, color=colors[i],\n",
13061306
" label=\"%s\" % list(stock_returns.keys())[i])\n",
13071307
" plt.title(\"%s\" % list(stock_returns.keys())[i])\n",
13081308
" plt.xlim(-0.15, 0.15)\n",

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