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"context": "none", "resolved_location": "matplotlib.pyplot.figure" }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()" + ], + "code_str": "fig", + "lineno": 2, + "end_lineno": 2, + "context": "none", + "resolved_location": "matplotlib.figure.Figure" + }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()", + "add_subplot" + ], + "code_str": "fig.add_subplot", + "lineno": 3, + "end_lineno": 3, + "context": "none", + "resolved_location": "matplotlib.figure.Figure.add_subplot" + }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()", + "add_subplot" + ], + "code_str": "fig.add_subplot", + "lineno": 4, + "end_lineno": 4, + "context": "none", + "resolved_location": "matplotlib.figure.Figure.add_subplot" + }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()", + "add_subplot" + ], + "code_str": "fig.add_subplot", + "lineno": 4, + "end_lineno": 4, + "context": "none", + "resolved_location": "matplotlib.figure.Figure.add_subplot" + }, { "import_components": [ "arviz", @@ -2329,6 +2384,33 @@ "context": "none", "resolved_location": "matplotlib.pyplot.figure" }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()" + ], + "code_str": "fig", + "lineno": 14, + "end_lineno": 14, + "context": "none", + "resolved_location": "matplotlib.figure.Figure" + }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()", + "add_axes" + ], + "code_str": "fig.add_axes", + "lineno": 15, + "end_lineno": 15, + "context": "none", + "resolved_location": "matplotlib.figure.Figure.add_axes" + }, { "import_components": [ "numpy", @@ -3637,17 +3719,6 @@ "context": "none", "resolved_location": "numpy.arange" }, - { - "import_components": [ - "pymc", - "Model" - ], - "code_str": "pm.Model", - "lineno": 6, - "end_lineno": 6, - "context": "none", - "resolved_location": "pymc.Model" - }, { "import_components": [ "pymc", @@ -3714,28 +3785,6 @@ "context": "none", "resolved_location": "pymc.Normal" }, - { - "import_components": [ - "pymc", - "Deterministic" - ], - "code_str": "pm.Deterministic", - "lineno": 17, - "end_lineno": 17, - "context": "none", - "resolved_location": "pymc.Deterministic" - }, - { - "import_components": [ - "pymc", - "Deterministic" - ], - "code_str": "pm.Deterministic", - "lineno": 18, - "end_lineno": 18, - "context": "none", - "resolved_location": "pymc.Deterministic" - }, { "import_components": [ "pymc", @@ -3856,17 +3905,6 @@ { "source": "with pm.Model(coords=coords) as radon_model:\n floor_idx = pm.ConstantData(\"floor_idx\", srrs_mn.floor, dims=\"obs_id\")\n county_idx = pm.ConstantData(\"county_idx\", srrs_mn.county_code, dims=\"obs_id\")", "names": [ - { - "import_components": [ - "pymc", - "Model" - ], - "code_str": "pm.Model", - "lineno": 1, - "end_lineno": 1, - "context": "none", - "resolved_location": "pymc.Model" - }, { "import_components": [ "pymc", @@ -3973,17 +4011,6 @@ { "source": "with radon_model:\n ab_county = pm.Deterministic(\"ab_county\", at.dot(chol, z).T, dims=(\"county\", \"param\"))\n theta = a + ab_county[county_idx, 0] + (b + ab_county[county_idx, 1]) * floor_idx\n\n sigma = pm.Exponential(\"sigma\", 1.0)\n pm.Normal(\"y\", theta, sigma=sigma, observed=srrs_mn.log_radon, dims=\"obs_id\")", "names": [ - { - "import_components": [ - "pymc", - "Deterministic" - ], - "code_str": "pm.Deterministic", - "lineno": 2, - "end_lineno": 2, - "context": "none", - "resolved_location": "pymc.Deterministic" - }, { "import_components": [ "pymc", @@ -4093,17 +4120,6 @@ { "source": "with pm.Model() as linreg_model:\n # use x_ to avoid overwriting x previously defined as np.ndarray\n x_ = pm.MutableData(\"x\", x, dims=\"year\", coords={\"year\": year})\n \n a = pm.Normal(\"a\", 0, 3)\n b = pm.Normal(\"b\", 0, 2)\n sigma = pm.HalfNormal(\"sigma\", 2)\n \n pm.Normal(\"y\", a + b * x_, sigma, observed=y, dims=\"year\")", "names": [ - { - "import_components": [ - "pymc", - "Model" - ], - "code_str": "pm.Model", - "lineno": 1, - "end_lineno": 1, - "context": "none", - "resolved_location": "pymc.Model" - }, { "import_components": [ "pymc", @@ -4357,17 +4373,6 @@ { "source": "with linreg_model:\n pm.set_data({\"x\": x[-1] + x[1:3]}, coords={\"year\": [2022, 2023]})\n pm.sample_posterior_predictive(linreg_idata, predictions=True, extend_inferencedata=True)", "names": [ - { - "import_components": [ - "pymc", - "set_data" - ], - "code_str": "pm.set_data", - "lineno": 2, - "end_lineno": 2, - "context": "none", - "resolved_location": "pymc.set_data" - }, { "import_components": [ "pymc", @@ -5369,6 +5374,32 @@ "context": "none", "resolved_location": "matplotlib.pyplot.figure" }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()" + ], + "code_str": "fig", + "lineno": 34, + "end_lineno": 34, + "context": "none", + "resolved_location": "matplotlib.figure.Figure" + }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()" + ], + "code_str": "fig", + "lineno": 40, + "end_lineno": 40, + "context": "none", + "resolved_location": "matplotlib.figure.Figure" + }, { "import_components": [ "matplotlib", @@ -5407,6 +5438,20 @@ "context": "none", "resolved_location": "matplotlib.gridspec.GridSpec" }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()", + "add_subplot" + ], + "code_str": "fig.add_subplot", + "lineno": 45, + "end_lineno": 45, + "context": "none", + "resolved_location": "matplotlib.figure.Figure.add_subplot" + }, { "import_components": [ "matplotlib", @@ -5420,6 +5465,20 @@ "context": "none", "resolved_location": "matplotlib.gridspec.GridSpec" }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()", + "add_subplot" + ], + "code_str": "fig.add_subplot", + "lineno": 47, + "end_lineno": 47, + "context": "none", + "resolved_location": "matplotlib.figure.Figure.add_subplot" + }, { "import_components": [ "matplotlib", @@ -5433,6 +5492,20 @@ "context": "none", "resolved_location": "matplotlib.gridspec.GridSpec" }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()", + "add_subplot" + ], + "code_str": "fig.add_subplot", + "lineno": 50, + "end_lineno": 50, + "context": "none", + "resolved_location": "matplotlib.figure.Figure.add_subplot" + }, { "import_components": [ "arviz", @@ -5457,6 +5530,20 @@ "context": "none", "resolved_location": "matplotlib.gridspec.GridSpec" }, + { + "import_components": [ + "matplotlib", + "pyplot", + "figure", + "()", + "add_subplot" + ], + "code_str": "fig.add_subplot", + "lineno": 64, + "end_lineno": 64, + "context": "none", + "resolved_location": "matplotlib.figure.Figure.add_subplot" + }, { "import_components": [ "numpy", @@ -5482,17 +5569,6 @@ { "source": "with pm.Model():\n a_shot = from_posterior(\"a_shot\", post[\"a\"].sel(var=\"shot\").values.flatten())\n a_distance = from_posterior(\"a_distance\", post[\"a\"].sel(var=\"distance\").values.flatten())\n \n a_prior = pm.sample_prior_predictive(2000)", "names": [ - { - "import_components": [ - "pymc", - "Model" - ], - "code_str": "pm.Model", - "lineno": 1, - "end_lineno": 1, - "context": "none", - "resolved_location": "pymc.Model" - }, { "import_components": [ "pymc", @@ -5531,17 +5607,6 @@ { "source": "with pm.Model():\n b_shot = from_posterior(\"b_shot\", post[\"b\"].sel(var=\"shot\").values.flatten())\n b_distance = from_posterior(\"b_distance\", post[\"b\"].sel(var=\"distance\").values.flatten())\n \n b_prior = pm.sample_prior_predictive(2000)", "names": [ - { - "import_components": [ - "pymc", - "Model" - ], - "code_str": "pm.Model", - "lineno": 1, - "end_lineno": 1, - "context": "none", - "resolved_location": "pymc.Model" - }, { "import_components": [ "pymc", @@ -5580,17 +5645,6 @@ { "source": "with pm.Model():\n c_shot = from_posterior(\"c_shot\", post[\"c\"].sel(var=\"shot\").values.flatten())\n c_distance = from_posterior(\"c_distance\", post[\"c\"].sel(var=\"distance\").values.flatten())\n 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  • - @@ -328,7 +317,7 @@ document.write(` - - + + - - - - + + + + - - + + - - - - + + + + - - - - - - - - - - + + + + + + + + + + @@ -108,7 +110,7 @@ - @@ -174,7 +172,7 @@ - @@ -237,7 +231,7 @@
    -

    PyMC3 with labeled coords and dims#

    +

    PyMC3 with labeled coords and dims#

    Go crazy with your virtual label-maker!

    @@ -266,13 +260,13 @@

    PyMC3 with labeled coords and dims -

    For the of labeled arrays#

    +

    For the of labeled arrays#

    For all of us who love labeled arrays, PyMC 3.9.0 came with some amazing news: support for using coordinate and dimension names to specify the shapes of variables in a pm.Model. While this is good news by its own merit, its seamless integration with ArviZ even more impactful and relevant.

    This post will focus on using PyMC3 coords and dims and the conversion of traces and models to InferenceData using arviz.from_pymc3. To see InferenceData in action, refer to this example in PyMC docs.

    We will use an example based approach and use models from the example gallery to illustrate how to use coords and dims within PyMC3 models.

    -

    1st example: rugby analytics#

    +

    1st example: rugby analytics#

    We will use an alternative parametrization of the same model used in the rugby analytics example taking advantage of dims and coords. Here, we will use as observations a 2d matrix, whose rows are the matches and whose columns are the field: home and away.

    The first step after preprocessing is to define the dimensions used by the model and their coordinates. In our case, we have 3 dimensions:

      @@ -393,7 +387,7 @@

      1st example: rugby analytics -

      2nd example: radon multilevel model#

      +

      2nd example: radon multilevel model#

      We will now use one of the many models in the A Primer on Bayesian Methods for Multilevel Modeling notebook to dive deeper into coords and dims functionality. We won’t cover the model itself, it’s already explained in the example notebook, we will explain in detail how are labeled coords and dims being used.

      The code used to load and clean the data is hidden, click the button below to see it.

      @@ -528,7 +522,7 @@

      2nd example: radon multilevel model -

      There is life outside the posterior#

      +

      There is life outside the posterior#

      The posterior is the center of Bayesian analysis but other quantities such as the prior or the posterior predictive are also crucial to an analysis workflow. We’ll use a linear regression to quickly showcase some of the key steps in a Bayesian workflow: prior predictive checks, posterior sampling, posterior predictive checks (using LOO-PIT) and out of sample predictions.

      We will start generating some simulated data (code hidden, click to expand) and defining the model. As it’s a simple linear regression we’ll only have scalar parameters, a, b and sigma.

      @@ -575,7 +569,7 @@

      There is life outside the posteriory. We have used everything we have seen so far, the pm.Data container and the labeled dims and coords. We will now simulate a workflow starting from prior predictive checks and finishing with predicting the values of our quantity of interest in 2021 and 2022.

      -

      Priors#

      +

      Priors#

      We start by sampling both prior and prior predictive with pm.sample_prior_predictive. This will generate a dictionary whose keys are variable names and whose values are numpy arrays. We can then pass this dictionary to az.from_pymc3 as the prior argument. ArviZ will then use the information in the pm.Model instance to 1) split the variables between prior and prior_predictive groups, 2) fill the observed_data and constant_data groups and 3) get the dims and coords if present.

      @@ -605,7 +599,7 @@

      Priors

      -

      Posterior#

      +

      Posterior#

      The next step will be computing the posterior. As we have seen, we can use return_inferencedata to get an InferenceData as a result of pm.sample. In this case however, we will store it as an auxiliary variable to then use InferenceData.extend and add the new groups to the linreg_idata.

      @@ -673,7 +667,7 @@

      Posterior -

      Posterior predictive#

      +

      Posterior predictive#

      Our third step will be to evaluate the posterior predictive at the observations so we can perform model checking with functions such as plot_ppc or plot_loo_pit. Here again we are using the extend trick to keep all our data as part of the same InferenceData. This has two main advantages. plot_loo_pit requires both the posterior_predictive group, generated here and the log_likelihood group which was created in pm.sample. In addition, keeping all our data in a single InferenceData means we can store it as a netCDF and share a single file to allow reproducing the whole exploratory analysis of our model.

      @@ -734,7 +728,7 @@

      Posterior predictive

      -

      Predictions#

      +

      Predictions#

      Finally, our last step will be to get some predictions, which in this case is evaluating the posterior predictive at positions different than the observations. In the example below, we are evaluating our predictions at 2021 and 2020. To do so, we are using pm.set_data to modify the values of x to the ones that correspond to these two future years.

      Here we will use from_pymc3_predictions instead of from_pymc3+extend. from_pymc3_predictions combines functionality from both of these functions and let’s the user choose how to handle predictions depending on the goal at hand: if idata_orig is not present, the returned object will be an InferenceData containing only the predictions groups; if idata_orig is present and inplace=False the returned InferenceData will be a copy of idata_orig with the predictions groups added, and with inplace=True there is no returned object, the preditcions groups are added to idata_orig which is not returned.

      @@ -800,7 +794,7 @@

      Predictions -

      Extra: generating the post image#

      +

      Extra: generating the post image#

      Here is the code used to generate the summary image for this post. Take a look if you want to use matplotlib to create array diagrams!

      @@ -825,8 +819,8 @@

      Extra: generating the post image[-1, 1, 1] ]) -fig = plt.figure(dpi=300) -ax = fig.add_axes([0, .05, 1, .8], projection='3d') +fig = plt.figure(dpi=300) +ax = fig.add_axes([0, .05, 1, .8], projection='3d') side = 3 r = side * np.array([-1,1]) one_2d = side * np.ones((1,1)) @@ -964,21 +958,21 @@

      -python +pymc , - pymc + arviz , - arviz + python , @@ -992,8 +986,8 @@
      -data storage arviz converters +data storage

    @@ -1029,8 +1023,8 @@
    - - + + - - - - + + + + - - + + - - - - + + + + - - - - - - - - - - + + + + + + + + + + @@ -108,7 +110,7 @@ - @@ -174,7 +172,7 @@ - @@ -237,15 +231,15 @@
    -

    ArviZ customization with rcParams#

    +

    ArviZ customization with rcParams#

    -

    About#

    +

    About#

    ArviZ not only builds on top of matplotlib’s rcParams but also adds its own rcParams instance to handle specific settings. This post will only graze matplotlib’s rcParams, which are already detailed in matplotlib’s docs; it will dive into specific ArviZ rcParams.

    -

    Introduction#

    +

    Introduction#

    Paraphrasing the description on rcParams in the documentation of matplotlib:

    ArviZ uses arvizrc configuration files to customize all kinds of properties, which we call rcParams. You can control the defaults of many properties in ArviZ: data loading mode (lazy or eager), automatically showing generated plots, the default information criteria and so on.

    @@ -263,9 +257,9 @@

    Introduction -

    Customizing ArviZ#

    +

    Customizing ArviZ#

    -

    arvizrc file#

    +

    arvizrc file#

    To define default values on a per user or per project basis, arvizrc file should be used. When imported, ArviZ search for an arvizrc file in several locations sorted below by priority:

    -

    Dynamic rc settings#

    +

    Dynamic rc settings#

    To set default values on a per file or per project basis, rcParams can also be modified dynamically, either overwritting a specific key:

    @@ -333,7 +327,7 @@

    Dynamic rc settings -

    rc_context#

    +

    rc_context#

    And last but not least, to temporarily use a different set of defaults, ArviZ also has a rc_context function. Its main difference and advantage is that it is a context manager, therefore, all code executed inside the context will use the defaults defined by rc_context but once we exit the context, everything goes back to normal. Let’s generate 3 posterior plots with the same command to show this:

    @@ -355,10 +349,10 @@

    rc_context -

    ArviZ default settings#

    +

    ArviZ default settings#

    This section will describe ArviZ rcParams as version 0.8.3 (see GitHub for an up to date version).

    -

    Data#

    +

    Data#

    The rcParams in this section are related to the data module in ArviZ, that is, they are either related to from_xyz converter functions or to InferenceData class.

    data.http_protocol : {https, http}

    Only the first two example datasets centered_eight and non_centered_eight come as part of ArviZ. All the others are downloaded from figshare the first time and stored locally to help reloading them the next time. We can get the names of the data available by not passing any argument to az.load_arviz_data (you can also get the description of each of them with az.list_datasets):

    @@ -433,9 +427,9 @@

    Data#
    -

    Plot#

    +

    Plot#

    -

    General#

    +

    General#

    plot.backend : {matplotlib, bokeh}

    Default plotting backend.

    plot.max_subplots : int

    @@ -459,7 +453,7 @@

    Generalplot_posterior or plot_density.

    -

    Bokeh#

    +

    Bokeh#

    plot.bokeh.bounds_x_range, plot.bokeh.bounds_y_range : auto, None or tuple of (float, float), default auto

    plot.bokeh.figure.dpi : int, default 60

    plot.bokeh.figure.height, plot.bokeh.figure.width : int, default 500

    @@ -485,7 +479,7 @@

    Bokeh#

    Default tools in bokeh plots. More details on Configuring Plot Tools docs

    -

    Matplotlib#

    +

    Matplotlib#

    Matplotlib already has its own rcParams, which are actually the inspiration for ArviZ rcParams. Therefore, this section is minimalistic.

    plot.matplotlib.show : bool, default False

    Call plt.show from within ArviZ plotting functions. This generally makes no difference in jupyter like environments, but it can be useful for instance in the IPython terminal when we don’t want to customize the plots genereted by ArviZ by changing titles or labels.

    @@ -493,7 +487,7 @@

    Matplotlib
    -

    Stats#

    +

    Stats#

    stats.hdi_prob : float

    Default probability of the calculated HDI intervals.

    @@ -559,22 +553,22 @@
    -python +arviz , - arviz + python
  • -customization rcparams +customization
  • @@ -619,8 +613,8 @@

    - - + + - - - + + + - + - - + + - - - - + + + + - - - - - - - - - - - + + + + + + + + + + + @@ -176,7 +177,7 @@ @@ -211,18 +212,6 @@ GitHub - @@ -328,7 +317,7 @@ document.write(`
    - - + + - - - - + + + + - - + + - - - - + + + + - - - - - - - - - - + + + + + + + + + + @@ -110,7 +112,7 @@ - @@ -176,7 +174,7 @@ - @@ -239,7 +233,7 @@
    -

    Some dimensionality devils#

    +

    Some dimensionality devils#

    This blog post is a loosely connected collection of potentially bad practices that I have come accross while answering questions on discourse and reading the PyMC examples collection or similar blog posts and case studies. They are not necessarily the worst or most dangerous practices, they might not even be the most common ones! The main relation between the cases covered here is that they are related to my work and so it is much more easy for me to notice them and to remember them.

    In fact, all examples are related to «dimensionality» but not necessarly using the exact same definition for the term!

    @@ -261,7 +255,7 @@
    -

    Simulated data generation#

    +

    Simulated data generation#

    I initialize three distributions to use in the examples below. I will use 2d distributions with different shape but the same marginal means (2, 3) and standard deviations (0.4, 0.3). 2d is clearly not high dimensional and so the effects might not be of the same magnitude as what you will encounter in your real models, but it is much more convenient for visualization purposes and already serves to illustrate my points.

    To give it a feel of «MCMC output» I will generate 4000 samples per distribution in a 4 «chains» and 1000 «draws» shape. This also allows loading the data as InferenceData and taking advantage of ArviZ functions.

    For the purposes of the blog post, only the shape of the data is relevant, so the data generation is hidden inside the toggle button below and only the plots are visible by default.

    @@ -459,7 +453,7 @@

    Simulated data generation -

    Premature aggregation#

    +

    Premature aggregation#

    Now let’s get to work! It is very tempting to take the means and go with it instead of using the whole posterior, working with high dimensional arrays can be annoying or even borderline impossible unless we recurr to nested on nested loops. For the data generation to work we had to add these [..., i] clauses for example and it is also very common to need to reshape the data or use [None, :] for broadcasting to work.

    And in some cases, doing that won’t make any difference. If you were calculating the mean of a linear regression for example:

    -

    Pushforward computation examples#

    +

    Pushforward computation examples#

    In this section I will go over some pushforward computation examples. I’ll take a function that depends on two variables and apply it to each of the 3 distributions we generated. First I’ll compute the result using the post_summary with the already averaged data and then compare it to doing the operation first and averaging later.

    I will generate the same plot for each combination of function and distribution. That plot will have the following elements:

      @@ -606,7 +600,7 @@

      Pushforward computation examples -

      Golf putting example#

      +

      Golf putting example#

      I will also use the code from the golf putting case study (from PyMC examples because it already uses xarray). To illustrate two more points.

      The first is that averaging before operating is also dangerous when having a single variable: \(E[f(x)] \neq f(E[x])\) (except for linear functions as we have seen).

      And the second is that the «badness» of averaging before operating depends as we have seen on the distribution, on the function and can also depend on other constant inputs of the function. In this case, the effect of averaging before gets worse as we compute the pushforward operation on larger distances (we are modeling probabilities of making the putt as a function of the distance).

      @@ -716,7 +710,7 @@

      Golf putting example

    -

    A possible solution#

    +

    A possible solution#

    I know the fact that all posterior samples should be used is not a secret in any sense, it is mostly the challenge of working comfortably with them that motivates computing summary statistics earlier than one should. The Bayesian workflow paper (Gelman et al 2020) mentions this as one of the open challenges in using Bayesian workflow in practice:

    Probabilistic programming ultimately has the potential to allow random variables to manipulated like any other data objects, with uncertainty implicit in all the plots and calculations, but much more work needs to be done to turn this possibility into reality, going beyond point and interval estimation so that we can make full use of the models we fit.

    @@ -727,7 +721,7 @@

    A possible solution -

    Univariate priors#

    +

    Univariate priors#

    I recently collaborated a little to a paper on prior elicitation, where the current state and future research possibilities are discussed. One of the challenges mentioned is that most of the work so far has been done on eliciting the univariate marginal prior distributions. But what we really need to elicit are multivariate prior distributions because it is the joint prior what afects the model and the sampling.

    This section won’t have (yet) a possible solution section at the end :sweat_smile:. I realize that univariate priors are the default and that we need to develop better tools before this can actually change in practice. But I think it is still good to be aware of its limitations. I will use an extreme example to show some of its limitations. Hopefully this will motivate more thorough prior and prior predictive checks.

    I will use the updating priors notebook in the PyMC examples collection. It is a very popular example, there are often questions on discourse about adapting it to the specific situations of new users; and for good reason. It promises the philosophal stone of Bayesian statistics: using an old posterior as prior when we get new data so we can update our beliefs after seeing this new data and get an updated posterior. Again, this is very tempting, maybe even more so than premature averaging. But again, this is usually a bad idea, and more often than not a terrible one.

    @@ -803,23 +797,23 @@

    Univariate priors# Instantiate figure and grid widths = [6, 1, 6] heights = [1.4, 6] - fig = plt.figure(figsize=figsize, constrained_layout=True) + fig = plt.figure(figsize=figsize, constrained_layout=True) grid = plt.GridSpec( 2, 3, hspace=0.1, wspace=0.1, - figure=fig, + figure=fig, width_ratios=widths, height_ratios=heights, ) # Set up main plot - ax = fig.add_subplot(grid[1, 0]) + ax = fig.add_subplot(grid[1, 0]) # Set up top KDE - ax_hist_x = fig.add_subplot(grid[0, 0], sharex=ax) + ax_hist_x = fig.add_subplot(grid[0, 0], sharex=ax) ax_hist_x.set_yticks([]) # Set up right KDE - ax_hist_y = fig.add_subplot(grid[1, 1], sharey=ax) + ax_hist_y = fig.add_subplot(grid[1, 1], sharey=ax) ax_hist_y.set_xticks([]) x = idata_prior.prior[f"{var_name}_shot"].values.flatten() @@ -833,7 +827,7 @@

    Univariate priorsax_hist_x.tick_params(labelleft=False, labelbottom=False) ax_hist_y.tick_params(labelleft=False, labelbottom=False) - ax_zoom = fig.add_subplot(grid[1, -1]) + ax_zoom = fig.add_subplot(grid[1, -1]) ax_return = np.array([[ax_hist_x, None, None], [ax, ax_hist_y, ax_zoom]]) plot_prior_comparison(idata_prior, var_name, scatter=True, ax=ax_return[:, :-1]) @@ -846,7 +840,7 @@

    Univariate priors
    -
    with pm.Model():
    +
    with pm.Model():
         a_shot = from_posterior("a_shot", post["a"].sel(var="shot").values.flatten())
         a_distance = from_posterior("a_distance", post["a"].sel(var="distance").values.flatten())
         
    @@ -879,7 +873,7 @@ 

    Univariate priors
    -
    with pm.Model():
    +
    with pm.Model():
         b_shot = from_posterior("b_shot", post["b"].sel(var="shot").values.flatten())
         b_distance = from_posterior("b_distance", post["b"].sel(var="distance").values.flatten())
         
    @@ -911,7 +905,7 @@ 

    Univariate priorsa, so the isodensity regions differ even more from the original (red) distribution.

    -
    with pm.Model():
    +
    with pm.Model():
         c_shot = from_posterior("c_shot", post["c"].sel(var="shot").values.flatten())
         c_distance = from_posterior("c_distance", post["c"].sel(var="distance").values.flatten())
         
    @@ -999,28 +993,28 @@ 
    -python +arviz , - pymc + python , - xarray + pymc , - arviz + xarray , @@ -1068,8 +1062,8 @@
    - - + + - - - - + + + + - - + + - - - - + + + + - - - - - - - - - - + + + + + + + + + + @@ -108,7 +110,7 @@ - @@ -174,7 +172,7 @@ - @@ -237,10 +231,10 @@
    -

    An introduction to xarray#

    +

    An introduction to xarray#

    -

    Xarray is a Python library for N-D labeled arrays and datasets. It provides two data structures: xarray.DataArray and xarray.Dataset. Both support named dimensions, coordinates and, more recently, also explicit indexes. -A DataArray can be seen as an extension of an n-dimensional array like a numpy.ndarray. A DataSet can be seen as an extension of a flat dictionary of arrays.

    +

    Xarray is a Python library for N-D labeled arrays and datasets. It provides two data structures: xarray.DataArray and xarray.Dataset. Both support named dimensions, coordinates and, more recently, also explicit indexes. +A DataArray can be seen as an extension of an n-dimensional array like a numpy.ndarray. A DataSet can be seen as an extension of a flat dictionary of arrays.

    In this post we will cover dimensions, coordinates and indexes, especially for DataArray objects but also for Dataset objects. Xarray also supports attaching arbitrary metadata to DataArrays, Datasets and even coordinates. The arrays we’ll generate will have random values, so we won’t care much about the values themselves, and we won’t cover attributes in this post either, so we will configure the html view of xarray objects to show indexes by default and hide attributes:

    @@ -253,9 +247,9 @@
    -

    DataArray#

    +

    DataArray#

    -

    Dimensions#

    +

    Dimensions#

    For me, the most important feature is the ability to label dimensions. Given an array, we can assign a label to each of its dimensions (axes in NumPy terminology):

    -

    Coordinates and indexes#

    +

    Coordinates and indexes#

    In addition, it is also possible to use coordinates. For DataArrays, coordinates are kind of in between data and attributes. A DataArray is equivalent to a single array, however, it can have as many coordinates as desired. When creating a DataArray, the coords argument can be used to initialize the coordinates. It is a dictionary whose keys are coordinate names, @@ -2889,7 +2883,7 @@

    Coordinates and indexes

    • chain
      (chain)
      int64
      1 2 3 4
      array([1, 2, 3, 4])
    • gender
      (person)
      <U8
      'male' 'neutrois' ... 'female'
      array(['male', 'neutrois', 'female', 'male', 'NB', 'female', 'female'],
             dtype='<U8')
    • age
      (person)
      int64
      25 30 73 47 51 20 64
      array([25, 30, 73, 47, 51, 20, 64])
    • chain
      PandasIndex
      PandasIndex(Index([1, 2, 3, 4], dtype='int64', name='chain'))
  • -

    Alternatively, xarray.DataArray.assign_coords can be used to add coordinates to an existing DataArray:

    +

    Alternatively, xarray.DataArray.assign_coords can be used to add coordinates to an existing DataArray:

    da = da.assign_coords(city=("person", ["Lleida", "Leida", "Sau", "Lleida", "Reus", "Sau", "Reus"]))
    @@ -4158,7 +4152,7 @@ 

    Coordinates and indexes

    -

    Vectorized and outer indexing#

    +

    Vectorized and outer indexing#

    NumPy indexing is extremely powerful, especially what is often called «fancy» indexing. However, it can be confusing and inconsistent (see this NEP proposal for more background). With dimensions and coordinates, xarray allows being explicit and consistent when choosing between vectorized and outer indexing.

    Diagram showing visually the two indexing modes. With outer indexing, we select the intersection between the slice in each dimension. With vectorized indexing we select only the specific positions indicated by the pointwise combination of indexes.

    Outer indexing selects rectangular or hyper-rectangular slices. To use outer indexing with xarray, we can use lists, arrays or DataArrays that have as a dimension the one that is being indexed. Therefore, the output of outer indexing will have the same dimensions as the input minus those dimensions whose slice is a scalar, which are squeezed.

    @@ -5007,7 +5001,7 @@

    Vectorized and outer indexing -

    Plotting#

    +

    Plotting#

    Xarray also has some plotting support, which is very convenient for visualizing the multidimensional data. For example, we can facet over a 1st dimension (here chain, use a 2nd dimension (here time) as x values of the line plot and map the color of the lines to a 3rd dimension (here person). The y values are the actual values in the DataArray.

    @@ -5037,7 +5031,7 @@

    Plotting -

    Dataset#

    +

    Dataset#

    Datasets are a collection of DataArrays, each DataArray being a data variable and having a name/key. Thus, they are similar to a dictionary of arrays but with one important difference. Dimensions with the same name are shared between variables:

    @@ -5916,7 +5910,7 @@

    Dataset
    • -

      To apply arbitrary functions to all the data variables in a Dataset, we can use xarray.Dataset.map for functions that return a DataArray or xarray.apply_ufunc for functions that return arrays. apply_ufunc can be challenging to use, but there is a good chance that a library exists that already wraps and extends numpy/scipy/… functions to have an xarray-like API. Take a look at Xarray related projects to browse packages that extend xarray.

      +

      To apply arbitrary functions to all the data variables in a Dataset, we can use xarray.Dataset.map for functions that return a DataArray or xarray.apply_ufunc for functions that return arrays. apply_ufunc can be challenging to use, but there is a good chance that a library exists that already wraps and extends numpy/scipy/… functions to have an xarray-like API. Take a look at Xarray related projects to browse packages that extend xarray.

      And if this still doesn’t work, yet again, Datasets are quite like a dictionary. So much so that they even have a dict-like interface with .items(), .keys(), .get()

      I hope this introduction has been useful. I would like to continue exploring features of xarray as a series, also covering potential new features and extensions for ArviZ. You can leave your comments to this blog post below, only a GitHub account is needed for commenting.


      @@ -6018,22 +6012,22 @@
      -python +xarray , - xarray + python
    • -data storage recommendation +data storage
    • @@ -6069,8 +6063,8 @@
      - - + + - - - + + + - + - - + + - - - - + + + + - - - - - - - - - - - + + + + + + + + + + + @@ -167,7 +168,7 @@ @@ -202,18 +203,6 @@ GitHub - @@ -319,7 +308,7 @@ document.write(`

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