From adcb18ea89af71645cfe096fb131e9a0c0bd2882 Mon Sep 17 00:00:00 2001 From: aloctavodia Date: Sun, 3 Dec 2017 10:28:05 -0300 Subject: [PATCH 1/2] add densityplot --- docs/source/api/plots.rst | 2 +- docs/source/notebooks/model_averaging.ipynb | 184 +++++++++++--------- pymc3/plots/__init__.py | 1 + pymc3/plots/densityplot.py | 155 +++++++++++++++++ 4 files changed, 256 insertions(+), 86 deletions(-) create mode 100644 pymc3/plots/densityplot.py diff --git a/docs/source/api/plots.rst b/docs/source/api/plots.rst index f3ee9b7229b..464149b9d41 100644 --- a/docs/source/api/plots.rst +++ b/docs/source/api/plots.rst @@ -6,4 +6,4 @@ Plots .. automodule:: pymc3.plots :members: traceplot, plot_posterior, forestplot, compareplot, autocorrplot, - energyplot, kdeplot + energyplot, kdeplot, densityplot diff --git a/docs/source/notebooks/model_averaging.ipynb b/docs/source/notebooks/model_averaging.ipynb index 4b330286a8d..3d826e34c7a 100644 --- a/docs/source/notebooks/model_averaging.ipynb +++ b/docs/source/notebooks/model_averaging.ipynb @@ -10,7 +10,7 @@ "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", - "plt.style.use(['seaborn-darkgrid', 'seaborn-colorblind'])\n", + "plt.style.use(['seaborn-darkgrid'])\n", "import pymc3 as pm\n", "import numpy as np\n", "import pandas as pd" @@ -171,7 +171,7 @@ "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", - "100%|██████████| 2500/2500 [00:03<00:00, 752.92it/s]\n" + "100%|██████████| 2500/2500 [00:06<00:00, 389.20it/s]\n" ] } ], @@ -179,41 +179,14 @@ "with pm.Model() as model_0:\n", " alpha = pm.Normal('alpha', mu=0, sd=10)\n", " beta = pm.Normal('beta', mu=0, sd=10)\n", - " epsilon = pm.HalfNormal('epsilon', 10)\n", + " sigma = pm.HalfNormal('sigma', 10)\n", " \n", " mu = alpha + beta * d['neocortex']\n", " \n", - " kcal = pm.Normal('kcal', mu=mu, sd=epsilon, observed=d['kcal.per.g'])\n", + " kcal = pm.Normal('kcal', mu=mu, sd=sigma, observed=d['kcal.per.g'])\n", " trace_0 = pm.sample(2000)" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For the first model I am going to check the posterior using the `traceplot` function, you can do the same for the other models." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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tqqrC3/72N1xyySVRP4dtJzqg1g74tSS4TkJOdPajSCUNqS6UK6EUtHWdsMpF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B49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\nRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "pm.traceplot(trace_0);" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -223,7 +196,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -232,7 +205,7 @@ "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", - "100%|██████████| 2500/2500 [00:03<00:00, 709.73it/s]\n" + "100%|██████████| 2500/2500 [00:05<00:00, 467.04it/s]\n" ] } ], @@ -258,7 +231,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -267,7 +240,7 @@ "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", - "100%|██████████| 2500/2500 [00:04<00:00, 503.03it/s]\n" + "100%|██████████| 2500/2500 [00:07<00:00, 347.50it/s]\n" ] } ], @@ -288,13 +261,68 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now that we have sampled the posterior for the 3 models, we are going to use WAIC (Widely applicable information criterion) to compare the 3 models. We can do this using the `compare` function included with PyMC3." + "Now that we have sampled the posterior for the 3 models, we are going to compare them visually. One option is to use the `forestplot` function that supports plotting more than one trace." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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6dSpdu3Zl1qxZDBgwgNTUVP7zn/+YYygvLyc5ORmtVsv//M//kJaWRmJiIiaT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\n/vfkaq+vGdkVP50bDveTypqRXW0QnRB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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "traces = [trace_0, trace_1, trace_2]\n", + "pm.forestplot(traces);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another option is to plot several traces in a same plot is to use `densityplot`. This plot is somehow similar to a forestplot, but we get truncated KDE plots (by default 95% credible intervals) grouped by variable names together with a point estimate (by default the mean)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vD6/jt0vuoT6xs32zQhgPldiNFdmens3BZEayZR5vDLjakPKamqUOKikpxX7b0nyqtagt\npbCt9D8LUMYj2zenywdgSvtCK+dDxdwYcR3n3CGfZsaIf+uydbaK/TsA/i7DggXvc9111/Dgg4/m\nFiyMRMLNFiycOfO1vS5YmO+UU6bywguvUV3dvpq2zCQhfCM7K8T/rP4LFu2YFcJLYMV2YEV3Apo9\na0taQ0prPF38taWOoqBFgtXGoD1DyktfdyyFbVnYxmCHt0B4K7q0L7qsX7PzqUqdUoImyMubXmT5\nrmV8a8J35JypbuJgFiwsFElQosNFUhEeXvkAC3a818ZZIQykoljR7ViJhvQtygbVvBkv5TU1b/X0\npLQ/+e+PIV3bdDNJ3bYsAhbY0R1YsR0t+qlsZVMd6M2G8Hpu+eAmrh57DZMPmVKIYogOdDALFhaK\n/yMURWXl7hX8ftlvaEjubsOsECY96CGyDeXG0rfs0aTkaUPSaxr0IImp/fZ8zzxtSLeMKhxLEUhk\n+qnsUDpRhapRyqIqWEXci/Obpb/k3CHn8/kR/4bdRU1+QoAkKNFBXO3y3PqneWHjcwStwH6a9Awq\nvgsrvBWlk+zZjAfgeun+pWyjlSSmjpN9L3M1K9JD7IM6gb17A8rajFfWH1PahxK7hIAV4OWNL7Jq\n90qumfBteof6FDB60ZPIIAkfKPYyRJ167pr/CzZE1lHpVGG3tiYSpCdpTdRnEpMLWBgr7zyozMCH\nZEcNfGiPIh4kARx0/PmPdBQELI2lFLqkT3o6JTtEQ2o3JU4p3xr/Hcb3PuLgY85T7N8BKP4yyHIb\nolvJDoR4ct1juJ5HdWAvTXr5iclzMXnnLqXvh1RHjsgT7Zb/frsGXM/CUhCM7sSJ1WGCFVSXDyCq\nPX6x6A4uHvEFzh964UHOAiL8QhYs7CTF/qsFirMMdYmdPLTifpbWL6aqpBLLtPZbx6DidbkaU3qx\nv+Y1Jt8kph5eg2pNfvNq0NLYSoETIlnWjwZLcUSfSXxj3LeoCLT/l/GeivE7sKdiL4PUoETRM8Yw\np+Zt/rrqEVI6RXWwNwHbbraaa1Mf0xaUl2pRYzKG9FQ+2geJSexVfl9VQqd/WARNgmDDJvpaFstT\nEW5pXM+3j7yBw3qNKlicovuSBCXabFeinkdW/YmFdR9SZpdTFizfY4vMqLzw5vRM4spqWnyPbGLS\nueHOkpSKQ/5+SmpFEnC0oXdkJ5FYPT+d920uHXs1pw+9QJbvEB1KEpTYL2MM82vn8Oiqh0l4iVb7\nmlQqjNW4CeXGafXkWk/npiKSQ1jxyu67bD9VQEMgWsdjH9/FqnUvcMUxt1FSPqCgMYruQxKU2Kfd\nyd38eeWDfFS3gDK7nOo9JxJ1Y7B7C3aikT0Tk5s5uVbOYep+8hMVnk2ZNry7axHrXv883x4yg4FH\nfBUTqixkiKIbkAQlWmWMYcGO93lo5f0kvHjLWpOXxIpswYrvIj8xdfgcecLXmpYSUZS4Ntstw62b\nnuRra59j2pgr0zNtB8oKGqMoXpKgRAvhVJi/ffII82vmUuqUNV9+QbvpKYmitekJXG0HpRSep7vN\njOKi/bL7ulQrUtriPifBByvu51srnsA56iqSI88DO1jQGMWBSyTi3H33XSxbtgRjYMKEI7j++psI\nhUo69XUlQYlmltUv4Q/L7yWcamy+2q3RqNgO7PA2QKdXrFUK1zO4nia7WLokpZ5NAUEUjgdzHViq\nd3Pj/LuZuPivxKZcQ2rYaftclr47mbnpn/xz0wud+hrnDbmAs4ec16mvAfDoow/jeR6PPvo4xhhu\nu+2H/PWvf+b//b9vdOrrSoISAKR0iqfXPckrm14iaIXypioyqHg9VuMWlHExysYzNinX5FZgzV8z\nTwhIL2tfpSGqDLdUaD4d3s6lb9xKRb8xxI/9Nm5/WW+qKx3selCTJ0/h0EMHYmVmfhkzZixr167p\n9LjlRF0fKHQZtsW2ct/S37ApspHKQCW2sgGDSjZiNW5GuXE0FimjckPEIS8pFftJrlD8ZfBx/B6G\nsAVDkxZX7daMDlg4w04kMfUadOUwoPDfgY7g5zJ05HpQ27Zt5eqrv8KNN/6Ak08+tc0xyIm6ot3m\n18zl4ZX34xqP6uyCgqkodngTJCO4Jt2nkD70GakpiXazUVRqw+ag5if94OJ6h0+teJuq9fNwxn8W\nb/JXARlI0dk6Yj2o5cuXcfPN32PGjC+2KzkdKElQPVTSS/DY6r8wa9sblNnllDsV4CVQjZshvjs9\nBZGxc9UkSUziYCgUvTQkleGJ3kmWxIN8bpfDoA+fonT5S0RP/iaMvKDZ4omiYx3selCvvfYKd999\nF9dddyNnn31uR4a2V5KgeqDaWA2/XXI3m6Ib08uwaxe3fj12fCeeBpd0YpJJAURHCxpFwBiWlLqs\nCXn8264yJkQNvV67G0r/jHvcf1I1/iz58PnMO+/M4te//iW/+tXvGDduQpe9riSoHmZx3ULuW/Yb\nkjpJGeXE6jYRSuxAGUNS2SilpLYkOpVCUelBXBke6RPnmJjDZxur6BVtpPTNH7H53UfwTvgOQ8ce\nJ1Mn+cR99/0aMNx55+2524488iiuv/6mTn1dGSThA11RBmMMz294hqfX/R3PtbEiDVS6O1BGo5XN\nQTXi+biDvs2KvQxFGr/ODKAoM4pLdocYl3Ao1WFs47Gq9ChSU77JpAkTKQnsZY0xHyn2Y5HMZi4K\nIu7Fueeje3mvdj7BWIJ+pg4bg8ZCK/kIiMKxUFRqiFvwUO84k+MOFzWUU64Vo+MLMbO/yTvvnkB4\n4pc5+cjx9KuQPqrOIOtBdZJi/9UCnVeGeMrj1U9W8cjqe9DuBgbrRpxMYurQ8XhF+uu9mWIvQzeI\nXxtN2IaQVny+IcRRCQfLGMp1I55RvO5MY93Qz3HGpDFMHFiJbfmr+a/Yj0VSgxJdYtOuGK+tqOWV\n1fNJlj1KJbuo0hqNhUfPOItfFB8r0zeVUIa/Vcd5L2Ezo6EEo6qwjMc53luk1r3D65um8VjF2Zwy\ncQzTDj+E6tLA/p9cFCWpQflAR5TB1YYPNtbzwuLtrK6pZ6jzD7b1mkfIGEKmg2tMeyr2X+9Q/GXo\nZvGbTN+UBZzXGOKUWAAbhW1cyk0U1yjetE/klcCZjBg+inPH92fCob2wCjiootiPRX6sQUmC8oGD\nKcOuWIo3Vu7ghaXbScZjnKTnoMue493SFGVaYXdFjanYD45Q/GXopvG7GKIW9PcsLtldwlA3PVjC\nMh7lJgLAB+pI/hk4k51lh3PehAFMO7wvfcq6fmLaYj8WSYLqBMX+oYD2l8EYw+odUV5cup156+oI\n6ARn8C7T3Bd4tDrG2oCiQiusrhowXuwHRyj+MnTj+E0mSXkKTowGOC8cotSkP9vKaMpNGAVssgby\nrHUOH9sTmTCkL+eNH8CRgypxuqivqtiPRZKgOkGxfyig7WVIupr3NtTzzKJtbKyPUW7CnKvmclZi\nJpucBPf1UURU+oz9Lj2bqdgPjlD8ZegB8WeHpJea9CCKIxNO0+fcGEpNDAeXhArxun0Ks+wTaQwd\nyjnj+nH66H4M6NW5IwCL/VgkCaoTFPuHAvZfhrpoktdW1PLPpTXEXI9D2M15+k2mJd7CxuXVsiBP\nV7o4htwvyy5V7AdHKP4y9KD4E8oQt+DwhM3nG0s4xGvejO2YFGUmigFW26P4J9NY6BzB4Yf24bwJ\n/TlmSDWO3fFN38V+LJIE1QmK/UMBrZfBGMPKmggvLN3OexvqMQZG2rWcm3qVY5PvotDstMr43yqX\nhSUu5R44hZoDotgPjlD8Zehh8WcHUShgeiTI6ZEggT0//8ZQZiLYaFwcZttTeds+kS3BkZwzvj9n\njOnYWlWxH4skQXWCYv9QQPMyJFzN/HV1PLNoG1t2xwHDZGc9ZydeZlxqGQpDWFWwOQCPVMeot0zX\nN+ntqdgPjlD8Zeih8WcHUVRqxRcaQoxNOq1+F9Kj/yIYFLtUFa9ZJ/OePYX+g0dywRGHMmnQwZ9X\nVezHIklQnaDYPxSQLsPKjfW8trKWl5fVkHQ1JbbmeLOIcxMvMcDbhgHCqhdGwZzSFM/1SqCAcu2D\nkxWL/eAIxV+GHh5/TBlSFoxPOFzUEKKP3ksTnjEESVJi4hgU69Rg/mWfwqrSKZx+5Cg+NfrAz6sq\n9mORJKhOUMwfCm0MS7Y2MvOTnby3ZicGGBCIcbI7j+nxmZSZKC4OMVUKStFoaR6vjLMi6FGmadmk\nUSjFfnCE4i+DxI/B0GiBDZwZDnJatJVmv2YPaBpYoQ18bE3gbeckKkaexLkThzDqkLJ2TVZbzMci\nkATVKYrxQ9EYd5m1eicvLNlGfSyFY1uMVpv5VOINpibfRWGIqxJSKn0uh8GwKOTy98oEceWDJr09\nFfvBEYq/DBJ/TrbZr0orZjSEGLeXZr9mL2905rwqQ8I4vG2fyKrep3Hc0VM5fkRfQs7+B1UU47Eo\nnySoTlAsHwpjDJ/siPDyshrmrK1HG0Ol4zLVLGZ68nUGpTYAhoiqyMwunrbb0vyjMsHSoEuJgVAh\nRuntT7EfHKH4yyDxt5Bt9huVsPlcYwn9vbaN3Mv2V3kGtqt+vBE6nd4TzuW0Iw7jkH1MVlssx6K9\nkQTVCfz+oYgmPeauq+P5xdvY1pDAAKMDOzgl+Q4nJt8hYFJ4yiFKabNF2jwM75ameL5XghT4r9aU\nr9gPjlD8ZZD4W5Ud7QdwSjTAWZFQ20/FMIYQcQI6iWcU7zrHsHnQeRwz5SSOGFjZovnP78ei/ZEE\n1Qn8+KEwxrCuLsarK2p465OduNpQbcc51iziU4k3GOxtAiCiyvGUg1KK/N2wNuDx98o4tbam1E99\nTXtT7AdHKP4ySPz75GGIWOkWiM80BpkaT8/t11bZqZW0NtRafXm7/DwGTzmfE0YPpjyYnnPbj8ei\n9pAE1Qn89KGIJF3mravnxSXb2dIQR2mPyc46Tk7N4ejkAlTmfIzsoIesbILaaWteqkiwsMTF1lBm\nfFxrylfsB0co/jJI/G2SzJzke4hrcXFjiNFJu33fsUytytFJkgR4yzmF+OjPcuKREzlqZF927451\nXvCdTBJUJyh0gjLGsKImzGsrdzBnbR2epxlpbeUU/T4nJucQMnEUukXfUr6oZXi1LMHsshQGqNB0\n3Tx6HaHYD45Q/GWQ+NvMYIgpcDP9U58Nhxjotn/FXtu4lJkInoZF9gQ+7v9ZjjjyBI4b3qcoVgDe\nkySoTlCoBLUjnODt1XW8sryGXbEU/XUNp1gLOTk5m966DoUmqspx1d7PqYgpw9ulSd6oSOFiKNe0\nq9nBN4r94AjFXwaJv92y/VMGOCbucE44RO+9nT+1D9kJazGwUQ3kxeCn6T3uNM4YO5DhfUrbNVS9\nkCRBdYKuTFCRpMsHG3fx2oodrKwJ01fv5DgWcZo3h/7e9szw8BBJQs2a8PYUU4bZpUn+VZEkpaBM\nK5wiPrYU/cERir8MEv8By05CawGnRtPTJpUfwGhZBZToKDYuu0wFzzrnsa7vNM46YggnjuhDRcjf\n68NKguoEnf2mpjzN4q2N/GvVDt7fsIve3k6OMYv4lDeXQXoLAAkVJEHJPpMSQEQZ3ilL8lZ5kqSC\nMi8zAEIOLoVX7GWQ+A9adiCFA5weDnJqLNiuyZfzBzsFTZyQSRIlxEv2mcwKnMz44UM4c8whHDGw\n65YAaQ9JUJ2gM97UlKdZuq2Rt9fUMX9dPZXuTiZ7H3O6mc9gbzMASRUk3oakBLDL0rxdlmJ2WRIP\nKNN7TOzqgy/nQSn2+KH4yyDxdxgXQ9SGoFGcEQ5wUhsT1Z6jcSE9s3qpieFi85p9Kq86pxML9uWM\nMYcwbWRfXzUBSoLqBB31psZTHku3NzJ3bT3z1tVT7dZwlLeIT+n5DM7UlNqTlABqbc2/yhN8UOJi\naCUxZfnoy3lAij1+KP4ySPwdLoUhZkPAwBnhICfvJ1G1lqCysgMqDBZzAyfwDNPZ4fSjT1mQ6aMP\n4cTD+jCoqqSzitImkqA6wcG8qfXRJAu3NDB7TR2LtzYwQG9nkruIT5n5DNA1KEy7k5LBsD6geb08\nyfKgC7RhVJ4Pv5ztUuzxQ/GXQeLvNNlE5Zh0H9Up0QCVrQym2FeCykqfTxUGFB8Hjub5wDms1gNR\nwKGVJZwx5hCOG1bNoZVdn6wkQXWC9ryprjas2RHho80NzF1Xx5ZdMYaZTRyjF3GKfpc+uh6FIaFC\nJPYz0GFPHoZlIZfXypNsdjRJ9SSXAAAgAElEQVSKdGJq0zkWPv5ytkmxxw/FXwaJv9O5mT4qGzgu\nFmBaNEi/vOmT2pKgctsaTYVpBBQrA+N4ueTTLNUjSHjpxw+sLOH00X05bnhvBnZRspIE1Qn29aYa\nY9jWmGDZtkY+2Libj7c0oLwkI93VHM9CjvM+pNREsdDEVQlJgu1KSgBxZfigJMXr5UkaLZNZ1bad\nJ9gWwZdzn4o9fij+Mkj8XcbLWyxxTNLmjEiQkSkbS1ltTlA5xlBhwigMm+yhvFx6PkudI4i5EHfT\nP3T7VQQ5ddQhTB1WxWF92jfDentIguoE+W+qMYbtjQk+2RHhw00NfLx5N+GkS6XezRF6JcebjznC\nXYpCY6OJqdLcjOHtVWtr3ilL8m5pChcIHcxErkX05WxVsccPxV8Gib/L5Z9H1UcrTo+EmBx3KDmQ\n44AxlJkoNh67rN68XHI+C0LHksIh4WpiSY1lQXnQ4aTD+nDssGrG9q8g2IZZ1ttKElQH87Sh0cCC\n1Tv4aPNuFm1tJJbyCOgUh5n1HKVWMjX1If31dgwKgyKqyvY6o8N+Xw/DipDHW2VJ1gQ9MPsY+NAe\nRfjlbKbY44fiL4PEXzAGQ0JBUqWHqB8Tczg+FmSIax3QVGUhEydoEiRUCW+VTGdO6FQarCoAkq4m\nknSxlIVScNSgSk46rA9HDqo84IUWsyRBHaR4ymNtXZRVtRE+2rSblbVhlLLwUglGsIkjWMtkbyEj\n3LWAwsIloUra3Z+0p5225oOSFO+UpYgrg0U6MXXYPHlF/OUEij9+KP4ySPyFpxSe0UQsAyj6ehan\nRANMSjitDqrYH8ekKDNRNBYfBo/hrZLpbLSH5Y5lnjZEkh7aGIyBwVUlnHRYHyYNqmTkIeXtPtdK\nElQ7GGOoCSdZszPCsm1hFm1pYEtDHNtSKC/B4Woz41jHUd5ihqdWA2ChSREgrkow6uCqvjFlWBpK\nMbvMZaPjAXTezOLF/uUs9vih+Msg8RdeXhlytSoLMDAyZXNCzGF8ItDuJsD8ARXb7YG8HjqLhaHJ\nJFXT4AljDPGUJpbysC0L21JMGtSLqUOrmXBoLwb0Cu2370oS1D5Ekx7r6qJ8siPCoi0NrKwJk/Q0\nBqjSuxirNjHWrGG8u5SB3hY0NpZxca0QMUIHnZAgPZx0acjlvVKXlUEXFNj6AAY9tFexfzmLPX4o\n/jJI/IW3lzIYDFEFWmUHVjhMjTmMTbazv8oYSoin15DDYV7oRN4NnchGe3iLFiJXG6JJD08blILK\nEocpQ6qZPLiSMf0r6FPWsu9dElSGqw1bdsdZsyPCsu2NLN0WpiacwLYUxksxQm1lNBuZ4K1glLuK\nchPBoLDQJFSIJMFcQmrP0M79ebMswbO9kgQzfUtdNqN4sX85iz1+KP4ySPyF14Yy6Mxy9NmtRqVs\npsQcxiQdqtrRDJhd9Vdj0WBV8U5oGguCx1Jv922xrTGGlJdOWEqBNtC3PMDkwVUcNaiKw/uV07c8\n2HMTVDzlsWhrA5/URli0pZG1dREg/UZV0cBotYmxZi3jUssZ4m3MJCMPjUVcleDi7LUPqSMT1Mzy\nBDPLE+36oHSIYv9yFnv8UPxlkPgLr51l0JllPzwFKBjgWkyOOYxLOgxyrbb9QDaGIElKTJyUCvDj\nqp8Rtcr38xBDMpOwrEzCqip1mDqiD2P7lnF4v3IGVZZ0+HD2A0lQXTK97rx19dz79lpsBSUBm2GB\nBj4Tf5bR7koq9W48bBxcEipEWJV3SHOdEEL4mYWi3AAm3QxYb2le7pXkVZMkYBQTEjaTEgGOSOxj\nUUWlSBIiqUJU6EYCJIF9JyilFCFHEcoMUc/WsGat2sEbyzWgcGzFmH7lHDW4igkDenF4v30/Z2fp\nkgSlAcdS9C5LD4McmtzEscn5RFQ5DaryoEbYCSFEsVMoSgyUpMdj4WL4qMRlQanLD2vLqdKdd4xU\nShF0FGWOjeumA3B1eiHWRVsbsZTi8SuO6bTX35eCVVVSBNInyUpyEkKIZhwUvbTCLlCrp2MpKkIO\nfcoCuJ4uTBAUMEEJIYQQ+yIJSgghhC9JghJCCOFLkqCEEEL4kiQoIYQQvtQlw8yF6C7Wv1fHx89s\nI16XwgpZBLUhnjSUH1rJxE/3Zvhx1YUOUYhuQxKUEG20/r06Pvy/bQz6+mDKR5cTWRWh9sFNVCUU\nHHYuH/7fawCSpIToIF2WoDxtiKfSJ4ElXQ/LuDg6cdDP25EzpFjaxVOQVAUY91/sp4MVe/yw3zIs\n/mcNg74+mIrxFQDpv18fQuJPG4mtepPe53yPxS/dycDjK7sg2FYU+z4o9vihw8tgAEcncdpyoq7R\nJFIeccs7oNdyDLkTdf2iSxLUgF4hhvUuzSUSzxlArTsEi4N/Myyl0B2UoXoTZ4AX65Dnag9F0+SR\nxajY44e2lSGyNcGI0c2nfCkfXc76Og+oZeiQCWzf3ki5ObBVmg9Gse+DYo8fOqcMh3gKbVcRbcPa\nTnWqjJLSKnpbB/b5CwRsUqmWx+TDDzm4hRAPhm+W2zhQnT0Db1co9jIUe/zQtjJMPelIrBkqV4MC\nCC8Lp2tQqi+hM79D8N0/88G89zs73BaKfR8Ue/xQ/GXw42zmMopPiDb6r+t/SM1DNYSXhTGuIbws\nTO2Dm4jGLczoTxF57XfcfMNNhQ5TiG5DBkkI0UYzZnwRgB/+5L9Yt3UdVsiixCgakh5Dtn/EzT/5\nCTNmfKGwQQrRjUiCEqIdZsz4Yi5RCSE61z77oIQQQohCkT4oIYQQviQJSgghhC9JghJCCOFLvhsk\nobXmxz/+MStWrCAYDHL77bczfPjw3P233347CxYsoLw8fcLk73//e37729+yfPlyAGpra6msrOTJ\nJ59sddtevdo/Fr+jy/DWW29x3333ATBhwgR+9KMfkUgkuOGGG9i5cyfl5eXcdddd9OnTh3/961/c\nd999OI7DjBkz+OIXO7+D/kDiD4fD3HDDDYTDYVKpFN///vc5+uijmTlzJj//+c8ZOHAgAP/5n//J\ncccd57v4AaZNm8aIESMAmDx5Mtdff31B3v8DLcODDz7I22+/DUBDQwM7duxg9uzZPPLIIzz11FP0\n6dMHgP/+7/9m5MiRBYt/2bJl3HHHHbltP/roI+677z4mTpzI9773PeLxOP379+dnP/sZpaWlPPnk\nkzz++OM4jsM3v/lNTj/99E6N/WDKcPjhh3PzzTfjeR7GGG677TZGjhxZNPtg0qRJnHPOOYwZMwaA\nM888kyuuuKJg+wDjM6+88oq56aabjDHGfPjhh+Yb3/hGs/svueQSs3PnzlYfm0wmzec//3mzfPny\n/W7bmfZVhsbGRnP++efn4nrggQfMzp07zcMPP2x++9vfGmOMeeGFF8xPfvITk0wmzZlnnml27dpl\nEomE+dznPmdqamp8Gf9vfvMb88gjjxhjjFm9erW56KKLjDHG3HPPPebll1/u9JgPNv5169aZq6++\nutnzFOr9P9Ay5LvqqqvMrFm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f7mhXtslPmviEED4kCaobS+g9akV5NSiLvDWhlIVKSQ1K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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pm.densityplot(traces);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we have sampled the posterior for the 3 models, we are going to use WAIC (Widely applicable information criterion) to compare the 3 models. We can do this using the `compare` function included with PyMC3." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, "outputs": [ { "data": { @@ -329,52 +357,51 @@ " \n", " \n", " 2\n", - " -15.6028\n", - " 2.58324\n", + " -15.23\n", + " 2.66\n", " 0\n", - " 0.886902\n", - " 4.87873\n", + " 0.88\n", + " 4.73\n", " 0\n", " 1\n", " \n", " \n", " 1\n", - " -9.06902\n", - " 1.94716\n", - " 6.53382\n", - " 0.0463751\n", - " 3.90116\n", - " 2.22293\n", + " -9.04\n", + " 2\n", + " 6.19\n", + " 0.05\n", + " 3.99\n", + " 2.09\n", " 1\n", " \n", " \n", " 0\n", - " -7.21287\n", - " 1.92019\n", - " 8.38997\n", - " 0.0667233\n", - " 3.06726\n", - " 4.23772\n", - " 0\n", + " -7.08\n", + " 1.96\n", + " 8.15\n", + " 0.07\n", + " 2.85\n", + " 4.08\n", + " 1\n", " \n", " \n", "\n", "" ], "text/plain": [ - " WAIC pWAIC dWAIC weight SE dSE warning\n", - "2 -15.6028 2.58324 0 0.886902 4.87873 0 1\n", - "1 -9.06902 1.94716 6.53382 0.0463751 3.90116 2.22293 1\n", - "0 -7.21287 1.92019 8.38997 0.0667233 3.06726 4.23772 0" + " WAIC pWAIC dWAIC weight SE dSE warning\n", + "2 -15.23 2.66 0 0.88 4.73 0 1\n", + "1 -9.04 2 6.19 0.05 3.99 2.09 1\n", + "0 -7.08 1.96 8.15 0.07 2.85 4.08 1" ] }, - "execution_count": 7, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "traces = [trace_0, trace_1, trace_2]\n", "models = [model_0, model_1, model_2]\n", "comp = pm.compare(traces, models, method='BB-pseudo-BMA')\n", "comp" @@ -393,19 +420,13 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|██████████| 1000/1000 [00:01<00:00, 872.82it/s]\n" - ] - } - ], + "outputs": [], "source": [ - "ppc_w = pm.sample_ppc_w(traces, 1000, models, weights=comp.weight.sort_index(ascending=True))" + "ppc_w = pm.sample_ppc_w(traces, 1000, models,\n", + " weights=comp.weight.sort_index(ascending=True),\n", + " progressbar=False)" ] }, { @@ -419,19 +440,12 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|██████████| 1000/1000 [00:00<00:00, 1580.25it/s]\n" - ] - } - ], + "outputs": [], "source": [ - "ppc_2 = pm.sample_ppc(trace_2, 1000, model_2)" + "ppc_2 = pm.sample_ppc(trace_2, 1000, model_2,\n", + " progressbar=False)" ] }, { @@ -443,14 +457,14 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -503,7 +517,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.1" + "version": "3.6.2" } }, "nbformat": 4, diff --git a/pymc3/plots/__init__.py b/pymc3/plots/__init__.py index 991de670d96..73c5cac2f32 100644 --- a/pymc3/plots/__init__.py +++ b/pymc3/plots/__init__.py @@ -5,3 +5,4 @@ from .posteriorplot import plot_posterior, plot_posterior_predictive_glm from .traceplot import traceplot from .energyplot import energyplot +from .densityplot import densityplot diff --git a/pymc3/plots/densityplot.py b/pymc3/plots/densityplot.py new file mode 100644 index 00000000000..ef1a0134791 --- /dev/null +++ b/pymc3/plots/densityplot.py @@ -0,0 +1,155 @@ +import numpy as np +try: + import matplotlib.pyplot as plt +except ImportError: # mpl is optional + pass +from .kdeplot import fast_kde +from .utils import get_default_varnames +from ..stats import hpd + + +def densityplot(trace, models=None, varnames=None, alpha=0.05, + point_estimate='mean', colors='cycle', opacity=0.75, + figsize=None, textsize=12, plot_transformed=False, ax=None): + """ + Generates KDE plots truncated at their 100*(1-alpha) % credible intervals + from a trace or list of traces. KDE plots are grouped per variable and + different colors assigned to models. + + Parameters + ---------- + trace : trace or list of traces + Trace(s) from an MCMC sample. + models : list + List with names for the models in the list of traces. Useful when + plotting more that one trace. + varnames: list + List of variables to plot (defaults to None, which results in all + variables plotted). + alpha : float + Alpha value for (1-alpha)*100% credible intervals (defaults to 0.05). + point_estimate : str or None + Plot a point estimate per variable. Values should be 'mean' (default), + 'median' or None. Defaults to 'mean'. + colors : list or string, optional + list with valid matplotlib colors, one color per model. Alternative a + string can be passed. If the string is `cycle `, it will automatically + chose a color per model from the matyplolib's cycle. If a single color + is passed, eg 'k', 'C2', 'red' this color will be used for all models. + Defauls to 'C0' (blueish in most matplotlib styles) + opacity : float + opacity level for the density plots, opaqueness increase from 0 to 1. + Default value is 0.75. + figsize : tuple + Figure size. If None, size is (6, number of variables * 2) + textsize : int + Text size of the lenged. Default 12 + plot_transformed : bool + Flag for plotting automatically transformed variables in addition to + original variables (defaults to False). + ax : axes + Matplotlib axes. + + Returns + ------- + + ax : Matplotlib axes + + """ + if point_estimate not in ('mean', 'median', None): + raise ValueError("Point Estimate should be 'mean' or 'median'") + + if not isinstance(trace, (list, tuple)): + trace = [trace] + + lenght_trace = len(trace) + + if models is None: + if lenght_trace > 1: + models = ['m_{}'.format(i) for i in range(lenght_trace)] + else: + models = [''] + elif len(models) != lenght_trace: + raise ValueError("The number of names for the models does not " + "match the number of models") + + lenght_models = len(models) + + if colors == 'cycle': + colors = ['C{}'.format(i % 10) for i in range(lenght_models)] + elif isinstance(colors, str): + colors = [colors for i in range(lenght_models)] + + if varnames is None: + varnames = [] + for tr in trace: + varnames_tmp = get_default_varnames(tr.varnames, plot_transformed) + for v in varnames_tmp: + if v not in varnames: + varnames.append(v) + + if figsize is None: + figsize = (6, len(varnames) * 2) + + fig, kplot = plt.subplots(len(varnames), 1, squeeze=False, figsize=figsize) + kplot = kplot.flatten() + + for v_idx, vname in enumerate(varnames): + for t_idx, tr in enumerate(trace): + if vname in tr.varnames: + vec = tr.get_values(vname) + k = np.size(vec[0]) + if k > 1: + vec = np.split(vec.T.ravel(), k) + for i in range(k): + _kde_helper(vec[i], vname, colors[t_idx], alpha, + point_estimate, opacity, kplot[v_idx]) + else: + _kde_helper(vec, vname, colors[t_idx], alpha, + point_estimate, opacity, kplot[v_idx]) + if lenght_trace > 1: + for m_idx, m in enumerate(models): + kplot[0].plot([], label=m, c=colors[m_idx]) + kplot[0].legend(fontsize=textsize) + + fig.tight_layout() + + return kplot + + +def _kde_helper(vec, vname, c, alpha, point_estimate, opacity, ax): + """ + Helper function to plot truncated kde plots with point estimates. + + Parameters + ---------- + + vec : array + 1D array from trace + vname : str + variable name + c : str + matplotlib color + point_estimate : str or None + 'mean' or 'median' + opacity : float + 0 to 1 value controling the opacity of the kdeplot + ax : matplotlib axes + """ + density, l, u = fast_kde(vec) + x = np.linspace(l, u, len(density)) + hpd_ = hpd(vec, alpha) + cut = (x > hpd_[0]) & (x < hpd_[1]) + ax.fill_between(x[cut], density[cut], color=c, alpha=opacity) + + if point_estimate is not None: + if point_estimate == 'mean': + ps = np.mean(vec) + if point_estimate == 'median': + ps = np.median(vec) + ax.plot(ps, 0, 'o', color=c, markeredgecolor='k') + + ax.set_yticks([]) + ax.set_title(vname) + for pos in ['left', 'right', 'top']: + ax.spines[pos].set_visible(False) From 172a9b057beace3062ca09db3c167bac65b9cbce Mon Sep 17 00:00:00 2001 From: aloctavodia Date: Sun, 10 Dec 2017 10:36:29 -0300 Subject: [PATCH 2/2] add new default style and new options, add test and update release notes and example --- RELEASE-NOTES.md | 1 + docs/source/notebooks/model_averaging.ipynb | 72 +++++++++------- pymc3/plots/densityplot.py | 92 ++++++++++++--------- pymc3/tests/test_plots.py | 5 +- 4 files changed, 101 insertions(+), 69 deletions(-) diff --git a/RELEASE-NOTES.md b/RELEASE-NOTES.md index 1d7609a1227..7b6a24d4ef4 100644 --- a/RELEASE-NOTES.md +++ b/RELEASE-NOTES.md @@ -14,6 +14,7 @@ algorithm (#2544) - Michael Osthege added support for population-samplers and implemented differential evolution metropolis (`DEMetropolis`). For models with correlated dimensions that can not use gradient-based samplers, the `DEMetropolis` sampler can give higher effective sampling rates. (also see [PR#2735](https://github.com/pymc-devs/pymc3/pull/2735)) - Forestplot supports multiple traces (#2736) +- Add new plot, densityplot (#2741) ### Fixes diff --git a/docs/source/notebooks/model_averaging.ipynb b/docs/source/notebooks/model_averaging.ipynb index 3d826e34c7a..aeaaaeb60c8 100644 --- a/docs/source/notebooks/model_averaging.ipynb +++ b/docs/source/notebooks/model_averaging.ipynb @@ -171,7 +171,9 @@ "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", - "100%|██████████| 2500/2500 [00:06<00:00, 389.20it/s]\n" + "Multiprocess sampling (2 chains in 2 jobs)\n", + "NUTS: [sigma_log__, beta, alpha]\n", + "100%|██████████| 2500/2500 [00:03<00:00, 678.85it/s] \n" ] } ], @@ -205,7 +207,9 @@ "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", - "100%|██████████| 2500/2500 [00:05<00:00, 467.04it/s]\n" + "Multiprocess sampling (2 chains in 2 jobs)\n", + "NUTS: [sigma_log__, beta, alpha]\n", + "100%|██████████| 2500/2500 [00:03<00:00, 670.85it/s]\n" ] } ], @@ -240,7 +244,11 @@ "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", - "100%|██████████| 2500/2500 [00:07<00:00, 347.50it/s]\n" + "Multiprocess sampling (2 chains in 2 jobs)\n", + "NUTS: [sigma_log__, beta, alpha]\n", + "100%|██████████| 2500/2500 [00:05<00:00, 448.13it/s]\n", + "/home/osvaldo/Documentos/Proyectos/01_PyMC3/pymc3/pymc3/step_methods/hmc/nuts.py:452: UserWarning: The acceptance probability in chain 1 does not match the target. It is 0.88222106478, but should be close to 0.8. Try to increase the number of tuning steps.\n", + " % (self._chain_id, mean_accept, target_accept))\n" ] } ], @@ -271,9 +279,9 @@ "outputs": [ { "data": { - "image/png": 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6dSpdu3Zl1qxZDBgwgNTUVP7zn/+YYygvLyc5ORmtVsv//M//kJaWRmJiIiaT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\n/vfkaq+vGdkVP50bDveTypqRXW0QnRB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Gmpoa0tLS0Gq1/M///A/Z2dmkpqZiMpmsirEt2Ls3DVdXJ5snls46T7k+LezK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\nVpPEIixMmDBJxliEEFaTxCI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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -299,9 +307,9 @@ "outputs": [ { "data": { - "image/png": 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75GGIWOkWiM80BpkaT8/t11bZqZW0NtRafXm7/DwGTzmfE0YPpjyYnnPbj8ei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\nutnzFOr9P9Ay5LvqqqvMrFm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f7mhXtslPmviEED4kCaobS+g9akV5NSiLvDWhlIVKSQ1K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wMJ5kp6Mri63zqdN1ZWT/QEYkBhHt54ZDcrC+8CuWZryJXbLzYMpCRkWMET8E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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -357,32 +365,32 @@ " \n", " \n", " 2\n", - " -15.23\n", - " 2.66\n", + " -15.2\n", + " 2.65\n", " 0\n", - " 0.88\n", - " 4.73\n", + " 0.87\n", + " 4.8\n", " 0\n", " 1\n", " \n", " \n", " 1\n", - " -9.04\n", - " 2\n", - " 6.19\n", - " 0.05\n", - " 3.99\n", - " 2.09\n", + " -9.02\n", + " 2.01\n", + " 6.18\n", + " 0.06\n", + " 4.02\n", + " 2.1\n", " 1\n", " \n", " \n", " 0\n", - " -7.08\n", - " 1.96\n", - " 8.15\n", + " -7.29\n", + " 1.88\n", + " 7.91\n", " 0.07\n", - " 2.85\n", - " 4.08\n", + " 2.93\n", + " 4.09\n", " 1\n", " \n", " \n", @@ -390,10 +398,10 @@ "" ], "text/plain": [ - " WAIC pWAIC dWAIC weight SE dSE warning\n", - "2 -15.23 2.66 0 0.88 4.73 0 1\n", - "1 -9.04 2 6.19 0.05 3.99 2.09 1\n", - "0 -7.08 1.96 8.15 0.07 2.85 4.08 1" + " WAIC pWAIC dWAIC weight SE dSE warning\n", + "2 -15.2 2.65 0 0.87 4.8 0 1\n", + "1 -9.02 2.01 6.18 0.06 4.02 2.1 1\n", + "0 -7.29 1.88 7.91 0.07 2.93 4.09 1" ] }, "execution_count": 8, @@ -421,7 +429,9 @@ { "cell_type": "code", "execution_count": 9, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "ppc_w = pm.sample_ppc_w(traces, 1000, models,\n", @@ -441,7 +451,9 @@ { "cell_type": "code", "execution_count": 10, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "ppc_2 = pm.sample_ppc(trace_2, 1000, model_2,\n", @@ -462,9 +474,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, diff --git a/pymc3/plots/densityplot.py b/pymc3/plots/densityplot.py index ef1a0134791..891fb5fd812 100644 --- a/pymc3/plots/densityplot.py +++ b/pymc3/plots/densityplot.py @@ -8,13 +8,12 @@ from ..stats import hpd -def densityplot(trace, models=None, varnames=None, alpha=0.05, - point_estimate='mean', colors='cycle', opacity=0.75, - figsize=None, textsize=12, plot_transformed=False, ax=None): +def densityplot(trace, models=None, varnames=None, alpha=0.05, point_estimate='mean', + colors='cycle', outline=True, hpd_markers='', shade=0., figsize=None, textsize=12, + plot_transformed=False, ax=None): """ - Generates KDE plots truncated at their 100*(1-alpha) % credible intervals - from a trace or list of traces. KDE plots are grouped per variable and - different colors assigned to models. + Generates KDE plots truncated at their 100*(1-alpha)% credible intervals from a trace or list of + traces. KDE plots are grouped per variable and colors assigned to models. Parameters ---------- @@ -29,24 +28,28 @@ def densityplot(trace, models=None, varnames=None, alpha=0.05, alpha : float Alpha value for (1-alpha)*100% credible intervals (defaults to 0.05). point_estimate : str or None - Plot a point estimate per variable. Values should be 'mean' (default), - 'median' or None. Defaults to 'mean'. + Plot point estimate per variable. Values should be 'mean', 'median' or None. + Defaults to 'mean'. colors : list or string, optional - list with valid matplotlib colors, one color per model. Alternative a - string can be passed. If the string is `cycle `, it will automatically - chose a color per model from the matyplolib's cycle. If a single color - is passed, eg 'k', 'C2', 'red' this color will be used for all models. - Defauls to 'C0' (blueish in most matplotlib styles) - opacity : float - opacity level for the density plots, opaqueness increase from 0 to 1. - Default value is 0.75. + List with valid matplotlib colors, one color per model. Alternative a string can be passed. + If the string is `cycle `, it will automatically choose a color per model from matplolib's + cycle. If a single color is passed, e.g. 'k', 'C2' or 'red' this color will be used for all + models. Defaults to 'C0' (blueish in most matplotlib styles) + outline : boolean + Use a line to draw the truncated KDE and. Defaults to True + hpd_markers : str + A valid `matplotlib.markers` like 'v', used to indicate the limits of the hpd interval. + Defaults to empty string (no marker). + shade : float + Alpha blending value for the shaded area under the curve, between 0 (no shade) and 1 + (opaque). Defaults to 0. figsize : tuple Figure size. If None, size is (6, number of variables * 2) textsize : int - Text size of the lenged. Default 12 + Text size of the legend. Default 12. plot_transformed : bool - Flag for plotting automatically transformed variables in addition to - original variables (defaults to False). + Flag for plotting automatically transformed variables in addition to original variables + Defaults to False. ax : axes Matplotlib axes. @@ -57,7 +60,7 @@ def densityplot(trace, models=None, varnames=None, alpha=0.05, """ if point_estimate not in ('mean', 'median', None): - raise ValueError("Point Estimate should be 'mean' or 'median'") + raise ValueError("Point estimate should be 'mean' or 'median'") if not isinstance(trace, (list, tuple)): trace = [trace] @@ -70,8 +73,7 @@ def densityplot(trace, models=None, varnames=None, alpha=0.05, else: models = [''] elif len(models) != lenght_trace: - raise ValueError("The number of names for the models does not " - "match the number of models") + raise ValueError("The number of names for the models does not match the number of models") lenght_models = len(models) @@ -102,11 +104,12 @@ def densityplot(trace, models=None, varnames=None, alpha=0.05, if k > 1: vec = np.split(vec.T.ravel(), k) for i in range(k): - _kde_helper(vec[i], vname, colors[t_idx], alpha, - point_estimate, opacity, kplot[v_idx]) + _kde_helper(vec[i], vname, colors[t_idx], alpha, point_estimate, + hpd_markers, outline, shade, kplot[v_idx]) else: - _kde_helper(vec, vname, colors[t_idx], alpha, - point_estimate, opacity, kplot[v_idx]) + _kde_helper(vec, vname, colors[t_idx], alpha, point_estimate, + hpd_markers, outline, shade, kplot[v_idx]) + if lenght_trace > 1: for m_idx, m in enumerate(models): kplot[0].plot([], label=m, c=colors[m_idx]) @@ -117,30 +120,45 @@ def densityplot(trace, models=None, varnames=None, alpha=0.05, return kplot -def _kde_helper(vec, vname, c, alpha, point_estimate, opacity, ax): +def _kde_helper(vec, vname, c, alpha, point_estimate, hpd_markers, + outline, shade, ax): """ - Helper function to plot truncated kde plots with point estimates. - - Parameters - ---------- - vec : array 1D array from trace vname : str variable name c : str matplotlib color + alpha : float + Alpha value for (1-alpha)*100% credible intervals (defaults to 0.05). point_estimate : str or None 'mean' or 'median' - opacity : float - 0 to 1 value controling the opacity of the kdeplot + shade : float + Alpha blending value for the shaded area under the curve, between 0 (no shade) and 1 + (opaque). Defaults to 0. ax : matplotlib axes """ density, l, u = fast_kde(vec) x = np.linspace(l, u, len(density)) hpd_ = hpd(vec, alpha) - cut = (x > hpd_[0]) & (x < hpd_[1]) - ax.fill_between(x[cut], density[cut], color=c, alpha=opacity) + cut = (x >= hpd_[0]) & (x <= hpd_[1]) + + xmin = x[cut][0] + xmax = x[cut][-1] + ymin = density[cut][0] + ymax = density[cut][-1] + + if outline: + ax.plot(x[cut], density[cut], color=c) + ax.plot([xmin, xmin], [-0.5, ymin], color=c, ls='-') + ax.plot([xmax, xmax], [-0.5, ymax], color=c, ls='-') + + if hpd_markers: + ax.plot(xmin, 0, 'v', color=c, markeredgecolor='k') + ax.plot(xmax, 0, 'v', color=c, markeredgecolor='k') + + if shade: + ax.fill_between(x, density, where=cut, color=c, alpha=shade) if point_estimate is not None: if point_estimate == 'mean': @@ -152,4 +170,4 @@ def _kde_helper(vec, vname, c, alpha, point_estimate, opacity, ax): ax.set_yticks([]) ax.set_title(vname) for pos in ['left', 'right', 'top']: - ax.spines[pos].set_visible(False) + ax.spines[pos].set_visible(0) diff --git a/pymc3/tests/test_plots.py b/pymc3/tests/test_plots.py index cd1b0d56d27..b55935ccfeb 100644 --- a/pymc3/tests/test_plots.py +++ b/pymc3/tests/test_plots.py @@ -6,7 +6,7 @@ from .checks import close_to from .models import multidimensional_model, simple_categorical -from ..plots import traceplot, forestplot, autocorrplot, plot_posterior, energyplot +from ..plots import traceplot, forestplot, autocorrplot, plot_posterior, energyplot, densityplot from ..plots.utils import make_2d from ..step_methods import Slice, Metropolis from ..sampling import sample @@ -30,7 +30,7 @@ def test_plots(): plot_posterior(trace) autocorrplot(trace) energyplot(trace) - + densityplot(trace) def test_energyplot(): with asmod.build_model(): @@ -64,6 +64,7 @@ def test_plots_multidimensional(): traceplot(trace) plot_posterior(trace) forestplot(trace) + densityplot(trace) @pytest.mark.xfail(condition=(theano.config.floatX == "float32"), reason="Fails on GPU due to njobs=2") def test_multichain_plots():