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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",
"scatter = hv.Scatter(\n",
" data=df,\n",
" kdims=['Droplet Diameter (um)'],\n",
" vdims=['Spindle Length (um)']\n",
")\n",
"\n",
"scatter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Good and coworkers proposed two models for the relationship between spindle length and droplet diameter. In the first model, the spindle length is independent of the droplet diameter and drawn out of a Normal distribution.\n",
"\n",
"\\begin{align}\n",
"l_i \\sim \\text{Norm}(\\phi, \\sigma)\\;\\forall i.\n",
"\\end{align}\n",
"\n",
"In the second model, the spindle length depends on the droplet diameter according to the equation below, and the spindle lengths vary from the theoretical model in a Normal fashion.\n",
"\n",
"\\begin{align}\n",
"&\\mu_i = \\frac{\\gamma d_i}{\\left(1 + (\\gamma d_i/\\phi)^3\\right)^{1/3}}\\\\[1em]\n",
"&l_i \\sim \\text{Norm}(\\mu_i, \\sigma)\\;\\forall i.\n",
"\\end{align}\n",
"\n",
"These are the two models we will graphically assess, starting with the second model, which establishes a relationship between spindle length and droplet diameter."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Assessing the model for spindle length dependent on droplet diameter\n",
"\n",
"As was the case with our studies of the Singer, et al. data on mRNA counts, we do also need functions from previous lessons here to compute the MLE. You can skip this, since it is copied directly from previous lessons. The important result is that we get the MLE for the three parameters, $\\gamma$, $\\phi$, and $\\sigma$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"γ* = 0.860475\n",
"φ* = 38.231250\n",
"σ* = 3.753422\n"
]
}
],
"source": [
"def theor_spindle_length(gamma, phi, d):\n",
" \"\"\"Compute spindle length using mathematical model\"\"\"\n",
" return gamma * d / np.cbrt(1 + (gamma * d / phi)**3)\n",
"\n",
"\n",
"def log_likelihood(params, d, ell):\n",
" \"\"\"Log likelihood of spindle length model.\"\"\"\n",
" gamma, phi, sigma = params\n",
"\n",
" if gamma <= 0 or gamma > 1 or phi <= 0:\n",
" return -np.inf\n",
"\n",
" mu = theor_spindle_length(gamma, phi, d)\n",
" return np.sum(st.norm.logpdf(ell, mu, sigma))\n",
"\n",
"\n",
"def spindle_mle(d, ell):\n",
" \"\"\"Compute MLE for parameters in spindle length model.\"\"\"\n",
" with warnings.catch_warnings():\n",
" warnings.simplefilter(\"ignore\")\n",
"\n",
" res = scipy.optimize.minimize(\n",
" fun=lambda params, d, ell: -log_likelihood(params, d, ell),\n",
" x0=np.array([0.5, 35, 5]),\n",
" args=(d, ell),\n",
" method='Powell'\n",
" )\n",
"\n",
" if res.success:\n",
" return res.x\n",
" else:\n",
" raise RuntimeError('Convergence failed with message', res.message)\n",
" \n",
"\n",
"mle_params = spindle_mle(df['Droplet Diameter (um)'].values, df['Spindle Length (um)'].values)\n",
"\n",
"# Take a look\n",
"print(\"γ* = {0:f}\\nφ* = {1:f}\\nσ* = {2:f}\".format(*mle_params))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sampling out of the generative model\n",
"\n",
"As before, we want to see what kind of data sets are predicted by the generative model when parametrized by the MLEs of the parameters. We therefore need to write a function to obtain the samples. The extra wrinkle here is that we need to also provide values for the droplet diameter for which we want the samples. In this model, we assume that the droplet diameters are measured exactly and that they determine the spindle length (of course neglecting the variation we model in the residuals)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"rg = np.random.default_rng()\n",
"\n",
"def sample_spindle(gamma, phi, sigma, d, size=1):\n",
" \"\"\"Generate samples of spindle length vs droplet diameter.\"\"\"\n",
" samples = np.empty((size, len(d)))\n",
"\n",
" for i in range(size):\n",
" mu = theor_spindle_length(gamma, phi, d)\n",
" samples[i] = np.maximum(0, rg.normal(mu, sigma))\n",
"\n",
" return samples"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that this function returns a array of shape `(size, len(d))`. That is, each row of the outputted array of samples corresponds to one set of measurements for prescribed droplet diameters `d`.\n",
"\n",
"We will generate samples for the droplet diameters going from zero to 250 microns."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"d_theor = np.linspace(0, 250, 200)\n",
"samples = sample_spindle(*mle_params, d_theor, size=5000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Making the predictive regression plot\n",
"\n",
"Now that we have our samples, we compute the percentiles of the spindle length for each value of $d$. We then generate the plot from these percentiles, with the data overlaid. The `bebi103.viz.predictive_regression()` function accomplishes this for us. We need to provide it with the samples of spindle length (with the shape we have already prescribed), as well as the $d$-values for which the samples were generated. We also need to provide the data as an array with two columns, the first being the diameter and the second the spindle length."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
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"source": [
"p = bebi103.viz.predictive_regression(\n",
" samples=samples,\n",
" samples_x=d_theor,\n",
" data=df[['Droplet Diameter (um)', 'Spindle Length (um)']].values,\n",
" x_axis_label='droplet diameter (µm)',\n",
" y_axis_label='spindle length (µm)',\n",
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"source": [
"In this plot, we see that roughly 20% of the data points (there are 670 total points) lie outside the middle 80%, so the model is consistent with the measured data.\n",
"\n",
"In my view, **this** is not regression results should be plotted, not simple with a \"best fit line\", which does not reveal the full generative model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Viewing differences\n",
"\n",
"We may also wish to get a plot of how different the data are from the model. In this case, the median spindle length is subtracted off of all samples such that the median is zero. We also need to subtract it from the data to make a comparison. That means that we have to draw our samples from the generative distribution for values of the droplet diameter that were actually measured."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
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"source": [
"samples = sample_spindle(*mle_params, df['Droplet Diameter (um)'].values, size=5000)\n",
"\n",
"p = bebi103.viz.predictive_regression(\n",
" samples=samples,\n",
" samples_x=df['Droplet Diameter (um)'].values,\n",
" data=df[['Droplet Diameter (um)', 'Spindle Length (um)']].values,\n",
" diff=True,\n",
" x_axis_label='droplet diameter (µm)',\n",
" y_axis_label='diff. spindle length (µm)',\n",
")\n",
"\n",
"bokeh.io.show(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Importantly, there does not seem to be any systematic way in which the measurements deviate from the model. In other words, whether a data point lies outside the 80% envelope and whether it lies above or below looks independent of droplet diameter."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Graphical assessment of the Normal model\n",
"\n",
"In the model where the \n",
"\n",
"As [we have learned](http://bebi103.caltech.edu.s3-website-us-east-1.amazonaws.com/2019a/content/lessons/lesson_08/mle_normal.html), the MLE for the parameters for the Normal model are the same as the plug-in estimates."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"phi = np.mean(df['Spindle Length (um)'])\n",
"sigma = np.std(df['Spindle Length (um)'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can then draw our samples directly out of a Normal distribution with location parameter $\\phi^*$ and scale parameter $\\sigma^*$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"samples = rg.normal(phi, sigma, size=(5000, len(df)))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
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/bImkP0CKoxIaPbo/QJrKEpVhxT9AxiJ/zjq+P0CqdqmP25Y/QHBa0ZF1vD9AcBBgePaYP0Cit3Wgg5o/QPpzltiolj9Aihm8C+CLP0AI2K+sdp0/QDzJbs8yij9AqwGiQ561P0DA8ine0Yw/QKrPDqxtlz9AygNpQleRP0C87LBSydM/QGSWrvgisz9AmG2jtIypP0BKYHH+OMw/QMn83hdllz9AjT97m9mnP0AYu6C455o/QCamszvAiT9AYgHwhC2wP0B2G7BTrLM/QJJni86ktT9A2KIKP42dP0CGtgrBipw/QNz7e0Y4oj9AvlN9tq+KP0DeM5iMDak/QI5RqRsMpz9AOkk5wZ+iP0CmYZuckaE/QJh+EBp3gj9AZcfWgkmnP0De1kSvCLw/QPesoh4wqD9AWkxYyBKUP0DqxcaEzMo/QIzqAj0inz9APlCtnwOzP0CecP58VrE/QETAKuM2nj9AVjUODPCUP0AFqmqGsbc/QBpz2sCglz9AD/04ptepP0A+jQcLlKY/QHwMfjh8qT9ArcPd+D2NP0BS7/bmAr8/QBBJanQitz9AiglqJbC0P0C6nHq7XsU/QJ+IkfnstT9AAvdmwgSuP0BQGbtsq7k/QL77eiBajz9AxrkFk+nRP0DO7Twn8Jg/QPC7Rh1kgT9AgWIOLPyaP0Ai0jJDSrw/QJKcUroNpj9AVkZvKjy9P0DeboKhLJc/QOyckDc0jj9AWnbsY/WuP0BGfqPpMbI/QNTyGS1+kz9AraVz77u4P0Dme6FJrKA/QN+Ox7Q0xz9AOplL9euiP0CezrXS2aw/QBrWoZ8emT9AIKwlli+cP0Cr5+Uzd6k/QAcYumFzqT9AbkY3j5ueP0DtDDSfaa8/QCPgMu5zpj9A2CiiCemnP0BnH7584JQ/QPCXh238tj9AOsiH0ZmOP0A09SK6Aq0/QFIHVPsDmD9A/EwJIAuDP0BJKGS3npI/QO55e3i3nz9A8Lg2lnCXP0Dh1wF+Vac/QBTkoZNlmD9ACfTcShOqP0BSHEpliqg/QIARgxzIiT9AHClwbd6cP0CyOWIavog/QDi1y7BYfD9AW9VvUbajP0BsLcOXjqw/QMq9Faxaij9Avps2wSiJP0D6gkxbVa4/QF4voK8vwT9AOPcHblC5P0B8WJxh+o4/QD6Xl3UvtT9AmFTrqoWsP0BImCDLSrs/QLILHUUssD9ArKphRGB7P0B6inmc/YE/QMDZ3CO5rD9AfBZr+F6QP0AT/WmJtJw/QAJCBEWAvD9ANgCoBDy9P0AE2R7B7Mk/QMqS7kU1oz9AC0EVzZ+hP0CyY7PZAac/QN5KF0w33z9AIQohYqy7P0CsloTHpqw/QO5Gcpj5fD9AvJRifSisP0B8FkuDi3w/QOBdQ/TQoj9A3mrNH1KrP0CqMwsrxa8/QITd7ZrDiz9ACp7B8siXP0CIpJmsF8E/QO7n9PVDrj9AmRPqCQWjP0Aju7Pqn5Q/QAqKpTtNgT9AUjGdQDDBP0BwC8kQKqg/QHqiE+gkkT9A4hLxk+WPP0AwZ/zAtK8/QB5Hx0y1rT9AiqMhkx2WP0Derds6cZk/QLcA/UCXvD9AjNnFzERyP0DI7StuZJ4/QGeqg9oMxj9AsNPrzvmpP0A6FA1fxaY/QCQJt6rVsj9AwL4vwn/HP0DYWwZlt6o/QKy4GlVPrz9Am8zDdAuCP0Dca2qcOLE/QGbuMbGoyT9ALtP90tisP0Dl6UnGsp8/QKLkpe6Ghj9AN0TGa9rSP0A+JxK7zsk/QP3mBosqkT9AFomV8qKrP0DgZlo4sJ4/QCEJogTdqD9AGVljy4nSP0D2fvK0V6I/QKxBXDUVvj9ALmyZKWK5P0A2010XQJc/QHY+PrPRyz9A3kv6TFqqP0AfeE1y15o/QFo9RT8tlT9ArMtfp6veP0Au1yBrasQ/QHpWaMo+gD9AplJzLiStP0B9vQOY8Y0/QFZ5+GBCtj9AB+Dxd6WoP0AeEBSd234/QDT52bPnkT9Ash3Fk+qzP0AWT7FQ27U/QPga0naguz9A/PhAyAupP0BMoVKdOLo/QOZwPjC7jz9Ayc5O9/yCP0DM98vb1s0/QBCy2Lm3sj9AWFMD01a+P0Aj1Y6EWiBBQBLWqR7aDUFAXJ1JUjAZQUCgVFIVbu1AQK4HA3gl/EBAcloBHKEQQUDmRjzAghRBQCNJU2+rA0FApJOS2qgLQUCfwXa23w1BQPWVP7OO/UBA5G1JiAwEQUB3jF+2CAlBQPj2vc4+HEFAbwplcIYIQUA+1sckCApBQIe71qnD/0BAGWtMsjQSQUAzZLoj3hhBQKJ4si6r9kBAqufa48j6QEDhSjt1Ow5BQJ+KR6sNGkFAthp816IGQUDcm34nKRNBQO97K8swDkFAyrJhljkQQUD8FNtzIRxBQOyTEmcjE0FAlirU1N4BQUD7++IWKgZBQHr4V5GsDkFAy6GC6msWQUCM/EntLSBBQOpkDTzx+0BAWuYPE8kGQUCJazmPcwFBQIqYFs7/CkFAgHYXr4cEQUBDkIjgmgZBQFPh/Yy5B0FAgGUxpBUKQUB6FofbDQ1BQGiUz4FnCEFAC+lKv/oBQUDafVrj1wxBQPaoOfXKHEFAsCovgZwMQUCMvgGVRA5BQMoJdGPYEkFA0oenoy37QECs4+6ty/lAQKAT7GflC0FAZi777hkOQUAR9I7ebP1AQHP1IHb5CEFAOnAj3rgCQUBR7+/FriBBQOQQlKy4+EBATDN6Tyb7QEAR3xdGcQpBQDm8Lzi3CkFAmqSfTRoQQUA+5NTL2/1AQC45b6Km+UBA2mLISQwVQUA95IOlXQZBQFUxra7zBUFArOektdzxQEDIZTXYgSdBQK6RVzbg9EBAnz1ddtMRQUBq70Zs7Q5BQO12m2K5E0FAAU1yEUcRQUDlb6lCgglBQFOukNOTCUFA5wvHxpsVQUBcCp9+JhRBQJYPPp0BEUFA26rKYi0RQUCzG2XdWwJBQAy3kUzYDkFA9tR6Mf/8QEBstqEgrvBAQAFLT76eFkFAauXWdhAaQUAMsGamURdBQLwei7N6AkFAYsRJY2kHQUBiob7schFBQP0Ac03OIEFAvBWtq9YTQUCspyZa1wJBQC4xdNe1BUFArmb0KD0cQUBAcfsRmPxAQDq+3AP++kBAVUTPA+IDQUAE4N5pKAxBQLvcZ6JiB0FAJcDPfXAHQUCnjJeEgwdBQHQShIYRAUFA2+a2HdADQUCJGSQIpgtBQImdnb9xCEFA5DiOVMz/QEAl85C9gu1AQNNZltge+0BA1pAZ6igTQUCQkWdUZQpBQI/SU31ODkFAlErGhJD/QEByL38qNwtBQKVORgPqJEFAPM0uqKsBQUA8rfEYFhVBQBxSNToDCEFApIvko6MJQUCAf7XyGAVBQHn6sJZ9+UBA39LH1A0aQUBAt0VwYwNBQJMJqIhyF0FAogmwoLsSQUD4oMrBzwpBQMgCExUEAUFA0rkpQ98UQUBWflnioQlBQIkY2OyJ90BAeF7lmNAMQUAA8sNAjAtBQDfYfye9CEFA+RpkdFIZQUCW/qBrHgRBQMvC90e1/kBAYeH5h2kEQUC6v8l8TB1BQF4Wbrav+0BApDb9Z9QHQUAV1AG0aBxBQM8gOYX6DkFAWFhp1mwWQUDSp2LEshBBQJe8xdyQDEFAudyTgqEKQUCClww6+PVAQDDMUO8wDEFAcvIKPIUNQUCoX+VG9gNBQFJ+PXt2AEFAfN/JGoYJQUBndAKNsQFBQDw+spIK/kBAArEEQc4CQUDTBnkxxRRBQORvkn5jDUFAW0GTUMYQQUDuwwBVI/hAQKq/NOa0DkFADV37htD/QEBc9NnEXg5BQEw1K2JCBUFAHMjmrfv9QEC4ho5Civ1AQG4SHi5qB0FAJFxhKXkKQUDJ0dosBwVBQCXuMTuRCUFA5NrhPNICQUAYXlGG4QdBQI2tqWCrEkFAPEEcouYFQUBqpYRQbApBQHJSBc/1BkFA9y9d2j4DQUDmm074SAdBQIAjzeTNAkFAVopp5v8dQUBakT3cCBBBQCV0Zz19DkFAwjNEiBkOQUASV9KGNwRBQGw5j9lcAEFApEP52TMMQUDHG1HxiQJBQHMAB9hnAEFAnbdg520HQUDMPbfAcP5AQMdarLhG+EBADHIMx2ILQUA1d8bbQPZAQKSTMCk4EUFAAPoG+VIAQUBTnUEWNw9BQJ7TSZG9BkFAq5zI1OAVQUA+o6p4dQtBQE2s1eGhA0FA5nU9uOEHQUBsxxCSyv9AQKyZdUGFCkFAfwP3GBADQUAcYuZ9IAFBQH4b/jjwEEFAU9sJMYUUQUBQlzRz8wdBQDAp+2wrEUFA+I6Pp1URQUCVaCk3+BVBQGJlZAqZ7kBASFOAln78QEBIL8VnLxFBQJZzEu1TGkFAxr/4AGMIQUDKfwkhUQdBQCFngYlhB0FALluR/rQTQUCx6MdzcwhBQL83dQy6B0FAlm1tImMYQUDeT+MglA5BQLqDvdV9EkFAQ5gy8tACQUDFxhvfMhNBQHvTM3rMAUFAlYdRkP8HQUDfpsqLP/5AQLN/97EiAEFAZsmiBfQdQUACZZwlXQJBQOeVu4BFBkFAQ5ibFsAGQUDUdGJDDQRBQDjwuaUWCUFAuhY7WskXQUDL4K3ZoRNBQKRtwJEZAUFAVzjIrAELQUCKVibQxApBQIMfZqoGCUFATtvS1ecjQUA0CHq9vwtBQMK2nq5w/EBATMChgLcLQUCvQ33F9fhAQEyO7yNv/kBAjtEXqsEPQUCOhYNqcvBAQPY2huag/0BAdcgD/aoDQUCMt2D0RwlBQA+FFpn2DUFAE58+NyMTQUDKkWmxDR5BQLMaHahR80BAl914gNcMQUDmLIN+IRdBQIDqZaG1/kBA+qXkbtwVQUBpxkPMpRFBQDcV2CouAEFAeGx5TwgYQUCbS+8vgwdBQEFB+6NXA0FAAP15NrAHQUAQNfo6qwtBQAqfhE0PIEFAbYjihLcVQUC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\",\"dtype\":\"float64\",\"shape\":[1340]}},\"selected\":{\"id\":\"1633\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1632\",\"type\":\"UnionRenderers\"}},\"id\":\"1563\",\"type\":\"ColumnDataSource\"}],\"root_ids\":[\"1521\"]},\"title\":\"Bokeh Application\",\"version\":\"1.4.0\"}};\n",
" var render_items = [{\"docid\":\"3fe4957d-adbe-4fd6-b67d-963204af8228\",\"roots\":{\"1521\":\"58b19b59-440a-4f77-ae4a-e7b2e8246248\"}}];\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": "1521"
}
},
"output_type": "display_data"
}
],
"source": [
"p = bebi103.viz.predictive_regression(\n",
" samples=samples,\n",
" samples_x=df['Droplet Diameter (um)'].values,\n",
" data=df[['Droplet Diameter (um)', 'Spindle Length (um)']].values,\n",
" x_axis_label='droplet diameter (µm)',\n",
" y_axis_label='spindle length (µm)',\n",
")\n",
"\n",
"bokeh.io.show(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, only about 20% of the data points lie outside the 80% envelope. However, the data points tend to fall below the 80% envelope only for small droplet diameters and above only for large droplet diameters."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## General method of graphical predictive model assessment\n",
"\n",
"When using both predictive ECDFs and predictive regression curves, we did the same procedure, which you can imagine generalizing.\n",
"\n",
"1. Compute the MLE of the parameters for the generative model in question.\n",
"2. Use the MLE to parametrize the model and generate many data sets out of the model.\n",
"3. Make a plot showing percentile regions of the generated data sets.\n",
"4. Overlay the measured data set.\n",
"5. Evaluate how many of the measured data points lie outside the percentile regions of the generated data sets.\n",
"\n",
"Predictive ECDFs and regression curves are just two (often used) examples of this prescription, and you can develop your own as is useful for the model and data set you are working with."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Computing environment"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPython 3.7.5\n",
"IPython 7.9.0\n",
"\n",
"numpy 1.17.4\n",
"pandas 0.24.2\n",
"scipy 1.3.1\n",
"bokeh 1.4.0\n",
"bokeh_catplot 0.1.6\n",
"bebi103 0.0.45\n",
"jupyterlab 1.2.3\n"
]
}
],
"source": [
"%load_ext watermark\n",
"%watermark -v -p numpy,pandas,scipy,bokeh,bokeh_catplot,bebi103,jupyterlab"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}