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"text/plain": [
":Scatter [Droplet Diameter (um)] (Spindle Length (um))"
]
},
"execution_count": 2,
"metadata": {
"application/vnd.holoviews_exec.v0+json": {
"id": "1004"
}
},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_csv('../data/good_invitro_droplet_data.csv', comment='#')\n",
"\n",
"hv.Scatter(\n",
" data=df,\n",
" kdims='Droplet Diameter (um)',\n",
" vdims='Spindle Length (um)',\n",
")"
]
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"metadata": {},
"source": [
"## Visualization with ArviZ\n",
"\n",
"[ArviZ](https://arviz-devs.github.io/arviz/index.html) has lots of handy visualization of MCMC results, and it is a very promising package to use to quickly get plots. It currently still has some drawbacks. First, some plots are not rendered properly with Bokeh. This problem will likely be fixed very soon with future releases. Second, some of the aesthetic choices in the plots would not be my first choice. There are other specific drawbacks to the ArviZ visualizations that I will point out as we go along.\n",
"\n",
"For each of the visualizations below, I show how to construct the visualization using ArviZ, but also using the bebi103 package."
]
},
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"metadata": {},
"source": [
"## The model and samples\n",
"\n",
"We will briefly repeat the sampling of the model as we did in [a previous lesson](http://bebi103.caltech.edu.s3-website-us-east-1.amazonaws.com/2020b/content/lessons/lesson_04/regression_with_stan.html). As a reminder, the model is \n",
"\n",
"\\begin{align}\n",
"&\\phi \\sim \\text{LogNorm}(\\ln 20, 0.75),\\\\[1em]\n",
"&\\gamma \\sim \\text{Beta}(1.1, 1.1), \\\\[1em]\n",
"&\\sigma = \\text{HalfNorm}(10,\\\\[1em]\n",
"&\\mu_i = \\frac{\\gamma d_i}{\\left(1+(\\gamma d_i/\\phi)^3\\right)^{\\frac{1}{3}}} \\;\\forall i, \\\\[1em]\n",
"&l_i \\mid d_i, \\gamma, \\phi, \\sigma \\sim \\text{Norm}(\\mu_i, \\sigma) \\;\\forall i.\n",
"\\end{align}\n",
"\n",
"We used the following Stan code to implement this model.\n",
"\n",
"```stan\n",
"functions {\n",
" real ell_theor(real d, real phi, real gamma_) {\n",
" real denom_ratio = (gamma_ * d / phi)^3;\n",
" return gamma_ * d / (1 + denom_ratio)^(1.0 / 3.0);\n",
" }\n",
"}\n",
"\n",
"\n",
"data {\n",
" int N;\n",
" real d[N];\n",
" real ell[N];\n",
"}\n",
"\n",
"\n",
"parameters {\n",
" real phi;\n",
" real gamma_;\n",
" real sigma;\n",
"}\n",
"\n",
"\n",
"model {\n",
" phi ~ lognormal(log(20.0), 0.75);\n",
" gamma_ ~ beta(1.1, 1.1);\n",
" sigma ~ normal(0.0, 10.0);\n",
"\n",
" for (i in 1:N) {\n",
" ell[i] ~ normal(ell_theor(d[i], phi, gamma_), sigma);\n",
" }\n",
"}\n",
"```\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's obtain some samples so we can start to look at visualizations. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
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"name": "stderr",
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"text": [
"INFO:cmdstanpy:stan to c++ (/Users/bois/Dropbox/git/bebi103_course/2020/b/content/lecture_notes/lecture_04/spindle.hpp)\n",
"INFO:cmdstanpy:compiling c++\n",
"INFO:cmdstanpy:compiled model file: /Users/bois/Dropbox/git/bebi103_course/2020/b/content/lecture_notes/lecture_04/spindle\n",
"INFO:cmdstanpy:start chain 1\n",
"INFO:cmdstanpy:start chain 2\n",
"INFO:cmdstanpy:finish chain 2\n",
"INFO:cmdstanpy:start chain 3\n",
"INFO:cmdstanpy:finish chain 1\n",
"INFO:cmdstanpy:start chain 4\n",
"INFO:cmdstanpy:finish chain 3\n",
"INFO:cmdstanpy:finish chain 4\n"
]
}
],
"source": [
"sm = cmdstanpy.CmdStanModel(stan_file='spindle.stan')\n",
"\n",
"data = dict(\n",
" N=len(df),\n",
" d=df[\"Droplet Diameter (um)\"].values,\n",
" ell=df[\"Spindle Length (um)\"].values,\n",
")\n",
"\n",
"samples = sm.sample(\n",
" data=data,\n",
" chains=4,\n",
" sampling_iters=1000,\n",
")\n",
"\n",
"samples = az.from_cmdstanpy(posterior=samples)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Examining traces\n",
"\n",
"The first type of visualization we will explore is useful for diagnosing potential problems with the sampler."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Trace plots\n",
"\n",
"**Trace plots** are a common way of visualizing the trajectory a sampler takes through parameter space. We plot the value of the parameter versus step number. You can make these plots using `bebi103.viz.trace_plot()`. By default, the traces are colored according to chain number. In our sampling we just did, we used Stan's default of four chains."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Trace plots with ArviZ\n",
"\n",
"To make plots with ArviZ, the basic syntax is `az.plot_***(samples, backend='bokeh')`, where `***` is the kind of plot you want. The `backend='bokeh'` kwarg indicates that you want the plot rendered with Bokeh. Let's make a trace plot."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
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wK7qP8aJr3YUZ+o/ObNdoQ+W6z/x1CMNbmvrP1mmXyLeOus/c/IiE/Br6j9zR//LtWjrP3VyhuKOt+s/C0RPyqSG6z/2XnzRHq/qP/oOfuIAeuo/mWN5Vz3g7D+azeMwmD/tPzDw3Hu45Ow/HeT1YFL87D+IK2fvjLbrP40MchdhCuw/V5V9VwR/6z/bb+1EScjrPxHfiVkvBus/JEbPLXQl6z9zLO+qB0zsP56ymq4nOuw/+s+aH39p7D/EBaBRuvTrP0mdgCbChus/rYkFvqJb7D/1LXO6LCbrP4Hrihnh7eo/UP7uHTUm6z+u1R72QgHrP6vq5XeaTOw/9FFGXACa7D9fsvFgi13sP/fJUYAomOw//TBCeLRx6z8BTu/i/bjrPy7IluXrsus/NLvurUhM6z+rd7gdGpbrP84avK/KBew/UFJgAUwZ7D+kqZ7MP3rsP9yDEJAvIew/T+j1J/G56z+Qn41cNyXrP74UHjS77uo/PN154jnb6z9BD7VtGAXrP2NeRxyyAes/7nn+tFGd6j+rWz0nve/rP19AL9y5sOs/Y2NeRxwy7D8CYadYNYjrPzhOCvMeZ+s/BKvq5Xea6z/myTUFMjvrP4rmASzya+s/BB4YQPhQ7D+HTs+7saDrP9yBOuXRDew/zt+EQgSc6z+dvMgE/JrrP528yAT8mus/t0PDYtQ16z+sxhLWxljrPzeq04GsJ+s/r1+wG7Yt6z8W3uUivhPsP9Ju9DEfkOs/v/BKkuf66z+VDtb/OUzsP1Gk+zkFees/lUc3wqKi6z+Q3QVKCqzrP8hhMH+FTOs/75HNVfMc7D/JyFnY0w7sP2b35GGhVus/YRiw5CoW6z+L+49Mh07rPzNt/8pKE+w/qmbWUkDa6z/Thy6ob5nrPy46WWq9X+w/f/s6cM6I6z/ZP08DBknrPzelvFZCd+s/JEil2NG46z/htrbwvFTrPz1IT5FDxOs/ycwFLo+16z8X78ftl8/rP2RYxRuZx+s/5iDoaFVL6z/vxoLCoEzrP9ScvMgEfOw/MSWS6GUU6z9LWYY41sXrP/iJA+j3fes/Ctrk8Emn6z9dUN8yp0vsP8to5POKp+s/kEyHTs+76z+0AG2rWWfrPz2cwHRaN+w/JAot6/4x7D8sKXef4yPsP6t2TUhrDOw/3Zcz2xX66z8Fw7mGGRrsP+PFwhA5few/A2A8g4Z+6j8cCp+tg4PrP7lVEANde+s/XK5+bJIf6z9tOgK4WTzrP03zjlN0pOo/Ek4LXvSV7D8QPSmTGlrrPzJyFva0w+s/5L7VOnG56j/7rgj+t5LrP/uuCP63kus/GqIKf4Y36z9v8fCeA8vrPyWTUzvD1Os/wvuqXKj86z+Af0qVKPvrP8ybw7Xaw+s/9phIaTYP7D8BpaFGIUnsP2YTYFj+fOs/bXTOT3Gc6z9z8bc9QWLrP/TBMjZ0s+s/xHdi1ouh6z9lUdhF0QPsP0bvVMA9T+w/VkW4yaiy6z9HcY46Oq7rPzWZ8bbSa+s/Lq7xmewf7D8Fi8OZX83rPwQb17/rs+o/s3xdhv/06z/mdFlMbL7rPxyVm6ilOes/pWq7Cb5p6z/bMuAsJcvrP6ck63B0les/yyxCsRW06z/DuYYZGk/sP9Y4m44Abus/SmBzDp4J7D8t7GmHv6brP95Wem02Vus/Zr/udOcJ6z8PCd/7GzTrP26GG/D54es/CI7LuKkB7D8Y7lwY6UXsP5UQrKqXX+w/XvOqzmoB6z9XtDnObULsPy5U/rW88uo/+fiE7LwN6z94fHvXoC/rPx5rRga5C+s/ZmZmZmZm6z/g2omSkMjqP+xsyD8zCOs/oRSt3AtM6z8zcEBLV7DqP8ZpiCr8meo/fJ3Ul6Wd6z/a4hqfyX7rP7rA5bFmZOs/NUHUfQBS6z9UVz7L82DsPwJiEi7kEew/+b64VKUt7D8Ww9UBEHfsP8U9lj50weo/SkONQpLZ7D8C1NSytb7sP44j1uJTgOw/ct7/xwkT7D8JGF3eHK7rP36NJEG4guw/PEolPKHX6z9ycOmY84zrP/qcu10vTes/jPLMy2H36z/cKR2s//PrP59Yp8r3DOw/WHVWC+wx7D8BwRw9fm/rPxlwlpLlJOs/Lei9MQQA7D/kvP+PE6brP8amlUIgl+s/xqaVQiCX6z/WU6uvrgrrP0/Pu7GgMOs/kE/IztvY6j9WKqio+pXsP/FKkuf6Pus/zR39L9ci7D8E4nX9gt3rP90ostZQ6us/cM6I0t5g6z/fawiOyzjsP2k2j8Ng/uo/5PkMqDcj6z84hCo1e6DsP90iMNY3MOs/ILjKEwi76z8st7QaEvfrP2QjEK/rF+w/VYmyt5Rz6z9VibK3lHPrP7LWUGovous/OKRRgZPt6j+WeauuQzXrP1k1CHO7F+s/xt0gWita6j9GKLaCpqXqPweVuI5xxeo/7xzKUBXT6j/X+bfLfl3rP4MT0a+tn+s/ejVAaahR6z/bM0sC1NTqP18Lem8MAes/hbacS3FV6j8S+MPPf4/rP8L3/gbtVes/Bp0QOugS7D+/nUSEf5HrP0ykNJvH4eo/TfbP04DB6j99rrZif1nsP1Z+GYwRie0/ZaiKqfQT7T/aIJOMnIXtP+7p6o7Ftu0/FcRA174A7T/h0Fs8vOfrP/J4Wn7gqus/YYkHlE056z8uOIO/X0zrP4HQevgyUe0/Sx3k9WDS7D9olgSoqeXrPy7L12X4z+s/RWKCGr6F6z8oucMmMnPrP5/jo8UZw+o/pTDvcaaJ6z+s4/ih0gjsP6yt2F92T+w/Suza3m5J7D+LGeHtQQjtP6iN6nQg6+w/m1jgK7p16j9FLGLYYUzsP0sd5PVgUuw/XHFxVG4i7D+0PXrDfeTrP7qEQ2/xcOs/LuI7MetF7D8SFaqbi7/rP6QXtftVgOs/EjKQZ5fv6j80aOif4GLrP2WKOQg62us/t+7mqQ456z9btWtCWmPrP8NmgAuy5es/J6H0hZBz6z88UKc8upHrP+W5vg8Hies/6ui4GtmV6z+XytsRTgvrPzl9PV+z3Oo/58WJr3YU6z+q86j4vyPrP+NSlba4Rus/k+LjE7Lz6z8hAg6hSk3rP982UyEeies/3q0s0Vnm6z9ck25L5ALrP65kx0YgXus/iEm4kEdw7D+Tc2IP7WPrPyV1ApoIm+s/bVSnA1lP7D9VvfxOk5nqP+LmVDIA1Oo/n8iTpGum6z/Y17rUCP3qPwA2IEJcOes/5s3hWu1h6z8uGjIepRLrP5595UF6Cus/Qnxgx38B6z+srG2Kx8XrPy/E6o8wDOs/QPomTYMi6z9dxHdi1ovrPzdUjPM3oes/xVT6CWe36z/g8lgzMsjrP+KuXkVGB+s/tdyZCYZz6z8kl/+QfvvrP8r5Yu/FF+s/09nJ4Cj56z/9+iE2WDjrP53aGaa2VOs/zc03onvW6j/a4hqfyX7rP+qymNh83Os/7byNzY7U6j+GqwMg7mrsP1rz4y8t6uw//3bZrztd7T+ISiNm9nntP+YffZOmwes/UFYMVwdA7D8A4q5eRcbrP2GnWDUIc+w/c4V3uYjv6z+9GMqJdpXrP4WX4NQHEuw/K08g7BQr6z9Hc2Tll0HsP273cp8cBew/k8SScve56z92cLA3MSTrP9fZkH9mkOs/sP7PYb486z/5nSYz3lbrP62kFd9QeOw/odrgRPTr6z9St7OvPEjrP53zUxwH3us/HccPlUZM6z/cuTDSi9rqP/ESnPpA8uo/URN9PsoI6z8peXWOAdnqP0dVE0TdB+s/8RExJZJo6z/akH9mEB/rP6WisfZ3Nus/001iEFg56z/Hnj2XqUnrPyqr6Xqia+s/hxiveVVn6z+Krgs/OB/rP4kMq3gj8+s/iQyreCPz6z/+74gK1U3rPw034PPDCOs/Z9E7FXDP6j99rrZif1nrP/RTHAderes/PBbbpKKx6z9zSkBMwgXsP+qURzfCous/ie5Z12g56z8oLPGAsqnrP8mwijcyD+w/S+ZY3lUP6z9BKVq5F5jrP9SYEHNJVeo/ZYuk3ejj6j8sLSP1nkrrP/AZidAItus/vCTOiqgJ6z8ZOKClK1jrP7CNeLKbmes/n8w/+iZN6z/BWN/A5EbrPw7Xag97oes/ZtzUQPO56j/M8QpET8rqP7dELjiDv+o/SN45lKGq6j+XqrTFNT7qP3L8UGnEzOs/4Qoo1NNH7D9KXwg57//rP7sJvmn67Os/QWMmUS/46j/fiO5Z1+jrPyGSIcfWs+s/jBNf7ShO6z/APGTKh6DqP2K9UStMX+o/pg2HpYEf6z96bqErESjrP916TQ8Kyus/MQxYchUL7D8RGOsbmFzqP5/jo8UZw+s/XRjpRe1+6z+wjA3d7A/sP9jYJaq3Bus/tDnObcI97D+MMbCO4wfrP3QJh97i4es/TvBN02eH6z9xICQLmMDrP4xqEVFMXuw/TfOOU3Qk7D9q+YGrPIHrPxtIF5tWCus/WKzhIvd06z8kDAOWXMXrP++SOCuipus/ZOlDF9Q37D/htUsbDkvrPxH92vrpP+o/iulCrP4I6j/vVSsTfinrPz9SRIZVPOs/wmnBi74C6z89YB4y5UPrP48X0uEhDOs/RwGiYMYU6z/9h/Tb14HrPz3zcth9x+s/ke9S6pJx6z+46jpUU5LrP9+mP/uRous/H5268lke6z9wJxHhX4TqP+Nve4LEdus/Qu23dqKk6z8LJ2n+mFbrP3ZQiesYV+s/8UV7vJAO6z8ew2M/iyXrP5YgI6DCEes/GeQuwhRl6z9ZEwt8RbfrP/g2/dmPlOs/qkavBigN7D/wMy4cCEnrP/H1tS41wus//DiaIys/6z/AkxYuqzDrPx11dFyN7Os/voi2Y+qu6j9/aydKQiLrP7rA5bFm5Oo/K01KQbeX6z+Hw9LAj2rrPyGvB5PiY+s/M6SK4lXW6z+hSzj0Fo/rP8tneR7cnes/ycnErYKY6z93TUhrDDrrP3Zu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\",\"dtype\":\"float64\",\"shape\":[1000]},\"sigma\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]},\"phi\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]},\"sigma\":{\"__ndarray__\":\"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sHLwQkA+6Nms+gxDQNbFbTSAF0NAcF8HzhkZQ0BRa5p3nCpDQDPEsS5uK0NApb3BFybTQkDpt68D58RCQEku/yH9/kJA07zjFB0RQ0ASg8DKoT1DQHh6pSxDFENAYhBYObQYQ0B9rrZif/FCQDLmriXkO0NAih9j7lo6Q0Bd3EYDeONCQAmKH2PuIkNACYofY+4aQ0Djx5i7liBDQOQUHcnlR0NAaW/whclkQ0Dwp8ZLNzlDQJkqGJXUOUNAmbuWkA8iQ0CcM6K0NwBDQDSAt0CCAkNAs3vysFD7QkBHcvkP6f9CQIV80LNZrUJARIts5/vhQkA17zhFR1pDQIPAyqFF5kJAofgx5q7dQkDvOEVHcslCQLmNBvAWeENAowG8BRI8Q0Cfq63YX0ZDQBSuR+F6TENAV+wvuydHQ0D99nXgnFlDQOXQItv5TkNAxf6ye/LQQkD4U+Olm+RCQGfV52or7kJAuECC4scIQ0C5/If0299CQAisHFpka0NA4JwRpb1xQ0B9PzVeujFDQKCJsOHpRUNAZvfkYaFWQ0C1pnnHKVJDQHE9CtejEENA4XoUrkcBQ0CY3ZOHhbpCQMbctYR8CENABhIUP8bsQkAnoImw4QFDQEaU9gZfCENASOF6FK63QkDZX3ZPHuZCQEa28/3UCENAuK8D54xQQ0B4eqUsQ+RCQGb35GGhBkNAJuSDns0qQ0AAb4EExfdCQMWPMXctUUNAc9cS8kEnQ0B6Nqs+VxNDQHEbDeAtQENAO99PjZc+Q0Ap7Q2+MOlCQDY8vVKWcUNAMnctIR9cQ0ALRiV1AsJCQH6MuWsJ6UJA+THmriXkQkB/arx0k+BCQF3cRgN4u0JACmgibHjaQkBHA3gLJPhCQFOWIY51GUNAn6ut2F9OQ0BI4XoUrkdDQNzXgXNGHENAzczMzMxsQ0BrK/aX3RtDQOPHmLuWKENA3SQGgZU7Q0CqYFRSJ6hCQOhqK/aXhUJAb/CFyVSBQkB/+zpwzshCQJ5eKcsQz0JAQmDl0CKzQkDtnjws1MJCQNCzWfW5AkNA+FPjpZsUQ0DSb18HzhlDQGiz6nO1/UJA/7J78rAoQ0BmiGNd3BZDQKd5xyk6SkNA3gIJih9bQ0BPr5RliAtDQJOpglFJ9UJAWYY41sVNQ0DEsS5uo3FDQCDSb18HJkNAWDm0yHZGQ0CSy39Ivx1DQA8LtaZ5/0JAB84ZUdrjQkCGWtO84+RCQJayDHGs60JAVTAqqRNIQ0CwA+eMKH1DQMGopE5AK0NAxf6ye/L4QkBHcvkP6e9CQF1txf6yA0NAJuSDns0CQ0Djx5i7lhhDQCfChqdXGkNAIR/0bFYFQ0AZ4lgXtxFDQC2yne+nLkNAeHqlLEP8QkCAt0CC4i9DQKpgVFInMENABoGVQ4tMQ0DV52or9m9DQMl2vp8aX0NALUMc6+IOQ0BZF7fRAAZDQDMzMzMzA0NAW7G/7J70QkAg0m9fB9ZCQIqw4emV8kJAx0s3iUHwQkASFD/G3F1DQOwvuycPU0NATmIQWDk0Q0CDwMqhRSZDQB6n6EguB0NASL99HTgfQ0DiWBe30RhDQJwzorQ3KENA1CtlGeIQQ0Atsp3vp05DQOxRuB6FA0NAKe0NvjD5QkBU46WbxOhCQNxGA3gL5EJAQ61p3nHaQkD7XG3F/ipDQNqs+lxtHUNAfT81XrrxQkCGyVTBqNxCQAKaCBue3kJABFYOLbJ1Q0DF/rJ78mBDQEHxY8xdS0NAUiegibABQ0D4U+OlmxxDQLTIdr6fKkNAb4EExY/pQkA9m1Wfqx1DQFFrmnec6kJAP1dbsb8MQ0AXt9EA3jJDQD55WKg1NUNAIEHxY8wVQ0AgQfFjzBVDQNV46SYxGENASnuDL0z2QkALtaZ5x1lDQAaBlUOLVENAHcnlP6SHQ0CKsOHplTpDQAg9m1Wfk0NAj1N0JJcnQ0DzjlN0JCdDQL6fGi/dJENA4C2QoPgZQ0A3iUFg5bBCQIzbaABv8UJAqDXNO04JQ0Dc14FzRsxCQFwgQfFj1EJAqRPQRNj4QkDHuriNBgBDQHqlLEMca0NAQKTfvg6kQkBos+pztRVDQL3jFB3JLUNAzTtO0ZEUQ0AwKqkT0AxDQIofY+5aIkNASgwCK4cuQ0ANcayL2zhDQE8eFmpNa0NA2qz6XG1NQ0DTvOMUHflCQH/ZPXlYUENAObTIdr7fQkAdyeU/pNdCQMGopE5AY0NAfh04Z0TpQkCwcmiR7QRDQBE2PL1SDkNAat5xio4sQ0Byio7k8g9DQAAAAAAAOENAtMh2vp8aQ0CBJsKGpx9DQBKlvcEXHkNAhA1Pr5RFQ0Dwp8ZLNwlDQNSa5h2nEENA6Gor9pcFQ0BO0ZFc/hNDQCsYldQJ+EJAwTkjSnsjQ0DqlbIMcVRDQDarPldb6UJAB/AWSFAkQ0DXo3A9Ci9DQHWTGARW3kJAYOXQItsZQ0DM7snDQi1DQOm3rwPnTENAZapgVFLfQkDT3uALk+FCQEATYcPTy0JAbcX+sntSQ0DKw0KtaTZDQNobfGEyRUNADwu1pnk/Q0AkufyH9CtDQBgmUwWjMkNAKVyPwvU4Q0DKw0KtaU5DQPCnxks3YUNA8rBQa5pvQ0BXW7G/7O5CQPcGX5hM7UJAL90kBoHtQkBfKcsQx0JDQInS3uALQ0NAYcPTK2UhQ0Atsp3vpz5DQKUsQxzrKkNA4JwRpb2RQ0A8TtGRXIZDQNcS8kHPhkNAt2J/2T0JQ0Dgvg6cM1pDQJhuEoPA4kJAqaROQBMRQ0DkFB3J5UdDQJ/Nqs/VFkNAJzEIrBwSQ0DZzvdT4xVDQAmKH2PuAkNAJ8KGp1ciQ0Bv8IXJVCFDQFuxv+yeZENA1xLyQc9GQ0D6fmq8dOtCQAHeAgmK30JAJ8KGp1fSQkCWsgxxrNtCQKH4MeauRUNA5x2n6EgWQ0CF61G4Hh1DQMRCrWneIUNA0ZFc/kMyQ0DqlbIMcTxDQIJzRpT2RkNA1QloImw4Q0Cn6Egu/zlDQNejcD0KJ0NAtRX7y+4pQ0AT8kHPZnVDQDMzMzMzY0NADJOpglGRQ0ApyxDHuuBCQKMjufyHFENAxY8xdy3hQkDb+X5qvCRDQHbgnBGlPUNA+Q/pt69TQ0DkFB3J5S9DQFmGONbFHUNA4zYawFsIQ0AVHcnlP3RDQNlfdk8ebkNABcWPMXf1QkDM7snDQvVCQP8h/fZ16EJAVHQkl/8QQ0CpE9BE2PBCQDqSy39I30JAt2J/2T3hQkAHzhlR2iNDQPCnxks3IUNAvw6cM6JUQ0DEQq1p3klDQGTMXUvIN0NANs07TtExQ0DOGVHaGxxDQMcpOpLLD0NARrbz/dQgQ0B0RpT2Bi9DQJjdk4eF+kJAR3L5D+nnQkAOvjCZKnBDQKfoSC7/QUNAFvvL7skLQ0CIY13cRhtDQGIQWDm0GENAescpOpIbQ0DLoUW28y1DQAfOGVHaC0NAF7fRAN4iQ0B4eqUsQwRDQN21hHzQ+0JAQxzr4jY6Q0A9m1WfqyVDQG3n+6nxIkNAeHqlLEMcQ0BcIEHxYwxDQLKd76fGI0NAJ8KGp1eqQkA/xty1hERDQDLmriXkO0NA/Yf029dpQ0DsUbgehaNDQOELk6mCuUNAyJi7lpCvQ0BqvHSTGPxCQPhT46Wb/EJAzF1LyAcNQ0DdtYR80ANDQFMFo5I6yUJAVHQkl//4QkBrmnecohtDQDY8vVKWUUNA8BZIUPwoQ0AdWmQ73/9CQNv5fmq8DENANe84RUf6QkDOqs/VVgxDQJjdk4eF4kJAB1+YTBUcQ0BN845TdPRCQEvIBz2bLUNAVp+rrdjfQkDsUbgehQNDQFR0JJf/AENAmbuWkA9KQ0DarPpcbR1DQN0kBoGVS0NAsp3vp8ZDQ0CHp1fKMvRCQOOlm8QgAENAmN2Th4XiQkCY3ZOHheJCQL3jFB3JDUNApb3BFybrQkAyVTAqqRtDQD9XW7G/FENAHqfoSC4XQ0ADCYofY2ZDQI4G8BZIaENAjnVxGw1AQ0BI4XoUrk9DQATnjCjtVUNAmG4Sg8BSQ0AgY+5aQkZDQPmgZ7PqY0NAPE7RkVxmQ0B88rBQa1JDQPmgZ7PqW0NAhXzQs1kdQ0Bd/kP67RNDQFFrmnecSkNAgQTFjzHfQkBtVn2utupCQP2H9NvXSUNA6pWyDHFsQ0AsZRniWDdDQNejcD0KN0NAFNBE2PDsQkA+eVioNS1DQC6QoPgxNkNAKqkT0EQ4Q0D+ZffkYUlDQFafq63YJ0NAyeU/pN8uQ0BFR3L5D9FCQFioNc07zkJAWYY41sUlQ0ArGJXUCSBDQGWqYFRSx0JAKjqSy384Q0CWIY51cXNDQA8LtaZ5N0NAZF3cRgMAQ0Bbsb/snhRDQOjZrPpcJUNAmG4Sg8ASQ0AkufyH9BNDQOXQItv5NkNAsHJoke30QkBWDi2ynS9DQFD8GHPXMkNAlWWIY108Q0B9PzVeuilDQBTQRNjwVENAkQ96NqsWQ0D7OnDOiEpDQNQrZRniMENACtejcD0SQ0DHuriNBuBCQFOWIY516UJAOpLLf0jfQkDpt68D5xRDQNxoAG+BZENAeekmMQhUQ0D1SlmGOPZCQMbctYR8SENAgLdAguIvQ0DKw0KtaS5DQC0hH/RsbkNAAd4CCYo3Q0AGEhQ/xjxDQMx/SL99NUNAVp+rrdgvQ0Bt5/up8UJDQFRSJ6CJEENAA3gLJCg+Q0DpJjEIrDxDQHEbDeAtKENAgZVDi2wHQ0Ar9pfdkx9DQP8h/fZ1uEJA7uvAOSO6QkCoxks3iclCQNSa5h2n+EJAumsJ+aAfQ0BSuB6F60lDQJMYBFYOLUNAAiuHFtkuQ0BnRGlv8DVDQF1txf6yG0NAKVyPwvVQQ0AXSFD8GFtDQMcpOpLLR0NAHcnlP6Q3Q0AdyeU/pDdDQHrHKTqSK0NA4umVsgzpQkDek4eFWgtDQC/dJAaB7UJAfT81Xrr5QkAep+hILh9DQBB6Nqs+50JAY3/ZPXkQQ0BUUiegiVhDQBsv3SQGSUNA8kHPZtVnQ0C1FfvL7hFDQLFQa5p3/EJAyxDHurhNQ0ClTkATYVtDQHE9CtejQENA/Yf029cJQ0C0WfW52jJDQFtCPujZVENAyJi7lpAnQ0Dn+6nx0iVDQGFUUiegwUJAvsEXJlM9Q0CoNc07TjFDQOeMKO0NTkNA4umVsgxJQ0CIhVrTvFNDQKMBvAUSbENA+1xtxf5SQ0C6SQwCK+dCQAWjkjoB/UJAhxbZzvf7QkCwA+eMKO1CQHDOiNLeIENAFD/G3LX0QkAhH/RsVuVCQBKDwMqhVUNAK4cW2c4HQ0AWak3zjiNDQJXUCWgiHENAoWez6nMVQ0AZBFYOLeJCQAK8BRIU30JAy6FFtvN1Q0Dpt68D51RDQG3F/rJ7KkNATKYKRiX1QkDn+6nx0iVDQO58PzVeWkNAOpLLf0g/Q0DcaABvgTxDQDxO0ZFcHkNAUI2XbhJTQ0CSy39Iv01DQA6+MJkqOENAxm00gLcwQ0CDwMqhRRZDQCfChqdXMkNAMZkqGJVUQ0Cz6nO1FUNDQM3MzMzMJENAI9v5fmocQ0D8GHPXEvJCQI2XbhKDSENA/kP67es4Q0CjAbwFEsxCQDojSnuDz0JA5q4l5IP2QkC+wRcmUyVDQNDVVuwv80JAa5p3nKITQ0AE54wo7fVCQOAtkKD42UJA+u3rwDnjQkAzMzMzM9NCQKYKRiV1akNAIGPuWkJGQ0DzjlN0JCdDQEOtad5xKkNAysNCrWkWQ0D67evAOSNDQPT91Hjp/kJAJzEIrBw6Q0DufD81XuJCQBWMSuoE9EJAZvfkYaEuQ0BApN++DgRDQOtztRX7G0NA9ihcj8JFQ0CBlUOLbA9DQLIubqMBPENAseHplbIsQ0Dkg57Nqg9DQFR0JJf/8EJAcM6I0t7wQkDTvOMUHelCQGq8dJMYFENAjSjtDb7gQkCWIY51ccNCQBzr4jYaQENACmgibHgaQ0AawFsgQSlDQLG/7J48HENADJOpglEhQ0ASg8DKoTVDQMiYu5aQ90JAS8gHPZtFQ0Byio7k8h9DQAisHFpkK0NA2qz6XG09Q0BZF7fRAA5DQAkbnl4pe0NAVcGopE5wQ0ANcayL20hDQGB2Tx4WKkNATRWMSupUQ0Bz1xLyQU9DQN5xio7kYkNA7Z48LNRCQ0CYTBWMSkpDQG3n+6nxKkNAL90kBoE1Q0Ar9pfdk/dCQEOtad5x+kJAI9v5fmr8QkAnoImw4RFDQAyTqYJREUNACKwcWmRrQ0CeXinLEFdDQIV80LNZVUNAwOyePCzcQkDJ5T+k3/5CQNV46SYxIENATx4Wak07Q0CvlGWIYzVDQBTQRNjwRENArWnecYoOQ0BMN4lBYA1DQDSitDf4CkNAn6ut2F/eQkDXo3A9Cv9CQHDOiNLeCENAvJaQD3oOQ0BUUiegifhCQKs+V1ux50JA/fZ14JxZQ0DOGVHaG0RDQAu1pnnHMUNArfpcbcUOQ0CutmJ/2Q1DQLWmeccpKkNAldQJaCI8Q0BJLv8h/U5DQKg1zTtOGUNAFNBE2PAcQ0Am5IOezTJDQDC7Jw8LPUNAc9cS8kH/QkDkFB3J5Q9DQAu1pnnHKUNAfh04Z0QhQ0BfmEwVjAJDQB04Z0RpH0NAduCcEaUlQ0Ctad5xit5CQCQofoy5C0NAHOviNhpAQ0A0orQ3+EJDQPjCZKpghENAMzMzMzMbQ0AwTKYKRh1DQAFNhA1PJ0NAqDXNO04hQ0BUUiegiShDQDsBTYQN/0JAvJaQD3oGQ0CgGi/dJPZCQOqVsgxx1EJAFmpN844DQ0DHuriNBhhDQAmKH2PuCkNAIbByaJElQ0DuWkI+6PFCQO2ePCzU8kJAp+hILv/xQkA/xty1hOxCQH6MuWsJ6UJAVn2utmJ/Q0A=\",\"dtype\":\"float64\",\"shape\":[1000]},\"sigma\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]},\"phi\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]},\"sigma\":{\"__ndarray__\":\"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" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" clearInterval(timer);\n",
" embed_document(root);\n",
" } else {\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" clearInterval(timer);\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" }\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "1651"
}
},
"output_type": "display_data"
}
],
"source": [
"az.plot_trace(samples, backend='bokeh');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"ArviZ generates two plots for each variable. The plots to the right show the **trace** of the sampler. In this plot, the x-axis is the iteration number of the steps of the walker and the y-axis is the values of the parameter for that step.\n",
"\n",
"ArviZ also plots a picture of the marginalized posterior distribution for each trace to the left. The issue I have these plots because they use [kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation) for the posterior plot. KDE involves selecting a bandwidth, which leaves an adjustable parameter. I prefer simply to plot the ECDFs of the samples to visualize the marginal distributions, as I [show below](#Plots-of-marginalized-distributions)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Trace plots with bebi103\n",
"\n",
"To make trace plots with the bebi103 module, you can do the following."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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]
},
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},
{
"data": {
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\",\"dtype\":\"float64\",\"shape\":[1000]}},\"selected\":{\"id\":\"2398\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"2397\",\"type\":\"UnionRenderers\"}},\"id\":\"2275\",\"type\":\"ColumnDataSource\"}],\"root_ids\":[\"2435\"]},\"title\":\"Bokeh Application\",\"version\":\"1.4.0\"}};\n",
" var render_items = [{\"docid\":\"8372ecdc-43c7-44c3-8b3a-95e090a1657a\",\"roots\":{\"2435\":\"09848f70-46eb-4198-ac6b-bcab3690b483\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" clearInterval(timer);\n",
" embed_document(root);\n",
" } else {\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" clearInterval(timer);\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" }\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "2435"
}
},
"output_type": "display_data"
}
],
"source": [
"bokeh.io.show(\n",
" bebi103.viz.trace_plot(samples)\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Interpetation of trace plots\n",
"\n",
"These trace plots look pretty good; the sampler is bounding around a central value. Trace plots are very commonly used, which is why I present them here, but are not particularly useful. This is not just my opinion. [Here](https://youtu.be/E8vdXoJId8M?t=669) is what Dan Simpson has to say about trace plots."
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"### Parallel coordinate plots\n",
"\n",
"As Dan Simpson pointed out in his talk I linked to above, plots that visualize diagnostics effectively are better. We will talk more about diagnostics of MCMC in later lessons, but for now, I will display one of the diagnostic plots Dan showed in his talk. Here, we put the parameter names on the x-axis, and we plot the values of the parameters on the y-axis. Each line in the plot represents a single sample of the set of parameters."
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"source": [
"#### Parallel coordinate plots with ArviZ"
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\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"3008\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"2838\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"3005\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"xs_units\":\"screen\",\"ys_units\":\"screen\"},\"id\":\"3010\",\"type\":\"PolyAnnotation\"},{\"attributes\":{\"formatter\":{\"id\":\"3005\",\"type\":\"BasicTickFormatter\"},\"major_label_orientation\":1.5707963267948966,\"major_label_overrides\":{\"0\":\"phi\",\"1\":\"gamma_\",\"2\":\"sigma\"},\"ticker\":{\"id\":\"2876\",\"type\":\"FixedTicker\"}},\"id\":\"2840\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"2841\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"2852\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"3012\",\"type\":\"Selection\"},{\"attributes\":{\"callback\":null,\"overlay\":{\"id\":\"3009\",\"type\":\"BoxAnnotation\"}},\"id\":\"2853\",\"type\":\"BoxSelectTool\"},{\"attributes\":{},\"id\":\"3007\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"callback\":null,\"overlay\":{\"id\":\"3010\",\"type\":\"PolyAnnotation\"}},\"id\":\"2854\",\"type\":\"LassoSelectTool\"},{\"attributes\":{},\"id\":\"2850\",\"type\":\"PanTool\"},{\"attributes\":{},\"id\":\"2858\",\"type\":\"SaveTool\"},{\"attributes\":{},\"id\":\"2836\",\"type\":\"LinearScale\"},{\"attributes\":{\"text\":\"\",\"text_color\":{\"value\":\"black\"},\"text_font_size\":{\"value\":\"12pt\"}},\"id\":\"3004\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"2856\",\"type\":\"RedoTool\"},{\"attributes\":{\"line_alpha\":{\"value\":0.05},\"xs\":{\"field\":\"xs\"},\"ys\":{\"field\":\"ys\"}},\"id\":\"2872\",\"type\":\"MultiLine\"},{\"attributes\":{},\"id\":\"2855\",\"type\":\"UndoTool\"}],\"root_ids\":[\"2831\"]},\"title\":\"Bokeh Application\",\"version\":\"1.4.0\"}};\n",
" var render_items = [{\"docid\":\"8f063493-a393-40d9-b89c-8e74bc8ade49\",\"roots\":{\"2831\":\"2705fd95-a799-4fd5-9baa-b7ec3416455e\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" clearInterval(timer);\n",
" embed_document(root);\n",
" } else {\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" clearInterval(timer);\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" }\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "2831"
}
},
"output_type": "display_data"
}
],
"source": [
"az.plot_parallel(samples, backend='bokeh');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To make sure we compare things of the same magnitude so we can better see the details of how the parameters vary with respect to each other, we scale the samples by the minimum and maximum values."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
" \n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/javascript": [
"(function(root) {\n",
" function embed_document(root) {\n",
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ttributes\":{},\"id\":\"3100\",\"type\":\"SaveTool\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"xs_units\":\"screen\",\"ys_units\":\"screen\"},\"id\":\"3262\",\"type\":\"PolyAnnotation\"},{\"attributes\":{\"source\":{\"id\":\"3113\",\"type\":\"ColumnDataSource\"}},\"id\":\"3117\",\"type\":\"CDSView\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"3092\",\"type\":\"PanTool\"},{\"id\":\"3093\",\"type\":\"BoxZoomTool\"},{\"id\":\"3094\",\"type\":\"WheelZoomTool\"},{\"id\":\"3095\",\"type\":\"BoxSelectTool\"},{\"id\":\"3096\",\"type\":\"LassoSelectTool\"},{\"id\":\"3097\",\"type\":\"UndoTool\"},{\"id\":\"3098\",\"type\":\"RedoTool\"},{\"id\":\"3099\",\"type\":\"ResetTool\"},{\"id\":\"3100\",\"type\":\"SaveTool\"},{\"id\":\"3101\",\"type\":\"HoverTool\"}]},\"id\":\"3102\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"3099\",\"type\":\"ResetTool\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"3261\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"line_alpha\":{\"value\":0.05},\"xs\":{\"field\":\"xs\"},\"ys\":{\"field\":\"ys\"}},\"id\":\"3114\",\"type\":\"MultiLine\"},{\"attributes\":{\"callback\":null},\"id\":\"3076\",\"type\":\"DataRange1d\"},{\"attributes\":{\"formatter\":{\"id\":\"3259\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"3088\",\"type\":\"BasicTicker\"}},\"id\":\"3087\",\"type\":\"LinearAxis\"}],\"root_ids\":[\"3073\"]},\"title\":\"Bokeh Application\",\"version\":\"1.4.0\"}};\n",
" var render_items = [{\"docid\":\"c3de2939-f648-4686-a554-c0b7f6541d1d\",\"roots\":{\"3073\":\"63a3d1c3-0a47-41f8-b3f7-c770243667ac\"}}];\n",
" root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
"\n",
" }\n",
" if (root.Bokeh !== undefined) {\n",
" embed_document(root);\n",
" } else {\n",
" var attempts = 0;\n",
" var timer = setInterval(function(root) {\n",
" if (root.Bokeh !== undefined) {\n",
" clearInterval(timer);\n",
" embed_document(root);\n",
" } else {\n",
" attempts++;\n",
" if (attempts > 100) {\n",
" clearInterval(timer);\n",
" console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
" }\n",
" }\n",
" }, 10, root)\n",
" }\n",
"})(window);"
],
"application/vnd.bokehjs_exec.v0+json": ""
},
"metadata": {
"application/vnd.bokehjs_exec.v0+json": {
"id": "3073"
}
},
"output_type": "display_data"
}
],
"source": [
"az.plot_parallel(samples, backend='bokeh', norm_method='minmax');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Parallel coordinate plots with bebi103"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
" \n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/javascript": [
"(function(root) {\n",
" function embed_document(root) {\n",
" \n",
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"source": [
"bokeh.io.show(\n",
" bebi103.viz.parcoord_plot(\n",
" samples,\n",
" transformation=\"minmax\",\n",
" pars=[\"phi\", \"gamma_\", \"sigma\"],\n",
" )\n",
")"
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{
"cell_type": "markdown",
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"source": [
"#### Intepretation of parallel coordinate plots\n",
"\n",
"Normally, samples with problems are plotted in another color to help diagnose the problems. In this particular set of samples, there were no problems, so everything looks fine.\n",
"\n",
"Interestingly, the \"neck\" between `phi` and `gamma_` is indicative of anticorrelation. When φ is high, γ is low, and vice-versa."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plots of marginalized distributions\n",
"\n",
"While we cannot in general plot a multidimensional distribution, we can plot marginalized distributions, either of one parameter or of two."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting marginalized distributions of one parameter\n",
"\n",
"There are three main options for plotting marginalized distributions of a single parameter.\n",
"\n",
"1. A kernel density estimate of the marginalized posterior.\n",
"2. A histogram of the marginalized posterior.\n",
"3. An ECDF of the samples out of the posterior for a particular parameter. This approximates the CDF of the marginalized distribution.\n",
"\n",
"I prefer (3), though (2) is a good option as well. For continuous parameter, ArviZ offers only a KDE plot."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting marginalized distributions with ArviZ\n",
"\n",
"We already saw that ArviZ can give these plots along with trace plots. We can also directly plot them using the `az.plot_density()`. When using this function, the distributions are truncated at the bound of the **highest probability density region**, or **HPD**. If we're considering a 95% credible interval, the HPD interval is the shortest interval that contains 95% of the probability of the posterior. By default, `az.plot_density()` truncates the plot of the KDE of the PDF for a 94% HPD."
]
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{
"cell_type": "code",
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},
"metadata": {
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"output_type": "display_data"
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],
"source": [
"az.plot_density(samples, backend='bokeh', figsize=(11, 4));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Plotting marginalized distributions with bokeh_catplot\n",
"\n",
"To get samples out of the marginalized posterior for a single parameter, we simply ignore the values of the parameters that are not the one of interest. We can then use `bokeh_catplot` to make plots of histograms or ECDFs.\n",
"\n",
"To do so, we need to convert the posterior samples to a tidy data frame."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
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