Working with InferenceData#
Here we present a collection of common manipulations you can use while working with InferenceData
.
import arviz as az
import numpy as np
import xarray as xr
xr.set_options(display_expand_data=False, display_expand_attrs=False);
display_expand_data=False
makes the default view for xarray.DataArray
fold the data values to a single line. To explore the values, click on the icon on the left of the view, right under the xarray.DataArray
text. It has no effect on Dataset
objects that already default to folded views.
display_expand_attrs=False
folds the attributes in both DataArray
and Dataset
objects to keep the views shorter. In this page we print DataArrays and Datasets several times and they always have the same attributes.
idata = az.load_arviz_data("centered_eight")
idata
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: mu (chain, draw) float64 -3.477 -2.456 -2.826 ... 4.597 5.899 0.1614 theta (chain, draw, school) float64 1.669 -8.537 -2.623 ... 10.59 4.523 tau (chain, draw) float64 3.73 2.075 3.703 4.146 ... 8.346 7.711 5.407 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (chain, draw, school) float64 7.85 -19.03 -22.5 ... 4.698 -15.07 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tune (chain, draw) bool True False False ... False False False depth (chain, draw) int64 5 3 3 4 5 5 4 4 5 ... 4 4 4 5 5 5 5 5 tree_size (chain, draw) float64 31.0 7.0 7.0 15.0 ... 31.0 31.0 31.0 lp (chain, draw) float64 -59.05 -56.19 ... -63.62 -58.35 energy_error (chain, draw) float64 0.07387 -0.1841 ... -0.087 -0.003652 step_size_bar (chain, draw) float64 0.2417 0.2417 ... 0.1502 0.1502 max_energy_error (chain, draw) float64 0.131 -0.2067 ... -0.101 -0.1757 energy (chain, draw) float64 60.76 62.76 64.4 ... 67.77 67.21 mean_tree_accept (chain, draw) float64 0.9506 0.9906 ... 0.9875 0.9967 step_size (chain, draw) float64 0.1275 0.1275 ... 0.1064 0.1064 diverging (chain, draw) bool False False False ... False False False log_likelihood (chain, draw, school) float64 -5.168 -4.589 ... -3.896 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 1, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tau (chain, draw) float64 6.561 1.016 68.91 ... 1.56 5.949 0.7631 tau_log__ (chain, draw) float64 1.881 0.01593 4.233 ... 1.783 -0.2704 mu (chain, draw) float64 5.293 0.8137 0.7122 ... -1.658 -3.273 theta (chain, draw, school) float64 2.357 7.371 7.251 ... -3.775 -3.555 obs (chain, draw, school) float64 -3.54 6.769 19.68 ... -21.16 -6.071 Attributes: (3)
-
<xarray.Dataset> Dimensions: (school: 8) Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (school) float64 28.0 8.0 -3.0 7.0 -1.0 1.0 18.0 12.0 Attributes: (3)
Get the dataset corresponding to a single group#
post = idata.posterior
post
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: mu (chain, draw) float64 -3.477 -2.456 -2.826 ... 4.597 5.899 0.1614 theta (chain, draw, school) float64 1.669 -8.537 -2.623 ... 10.59 4.523 tau (chain, draw) float64 3.73 2.075 3.703 4.146 ... 8.346 7.711 5.407 Attributes: (3)
Tip
You’ll have noticed we stored the posterior group in a new variable: post
. As .copy()
was not called, now using idata.posterior
or post
is equivalent.
Use this to keep your code short yet easy to read. Store the groups you’ll need very often as separate variables to use explicitly, but don’t delete the InferenceData parent. You’ll need it for many ArviZ functions to work properly. For example: plot_pair()
needs data from sample_stats
group to show divergences, compare()
needs data from both log_likelihood
and posterior
groups, plot_loo_pit()
needs not 2 but 3 groups: log_likelihood
, posterior_predictive
and posterior
.
Add a new variable#
post["log_tau"] = np.log(post["tau"])
idata.posterior
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: mu (chain, draw) float64 -3.477 -2.456 -2.826 ... 4.597 5.899 0.1614 theta (chain, draw, school) float64 1.669 -8.537 -2.623 ... 10.59 4.523 tau (chain, draw) float64 3.73 2.075 3.703 4.146 ... 8.346 7.711 5.407 log_tau (chain, draw) float64 1.316 0.7301 1.309 ... 2.122 2.043 1.688 Attributes: (3)
Combine chains and draws#
stacked = az.extract_dataset(idata)
stacked
<xarray.Dataset> Dimensions: (school: 8, sample: 2000) Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' * sample (sample) MultiIndex - chain (sample) int64 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 - draw (sample) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 Data variables: mu (sample) float64 -3.477 -2.456 -2.826 -1.996 ... 4.597 5.899 0.1614 theta (school, sample) float64 1.669 -6.239 2.195 ... -1.095 4.013 4.523 tau (sample) float64 3.73 2.075 3.703 4.146 ... 8.589 8.346 7.711 5.407 log_tau (sample) float64 1.316 0.7301 1.309 1.422 ... 2.122 2.043 1.688 Attributes: (3)
You can also use xarray.Dataset.stack()
if you only want to combine the chain and draw dimensions. arviz.extract_dataset()
is a convenience function aimed at taking care of the most common subsetting operations with MCMC samples. It can:
Combine chains and draws
Return a subset of variables (with optional filtering with regular expressions or string matching)
Return a subset of samples. Moreover by default it returns a random subset to prevent getting non-representative samples due to bad mixing.
Acess any group
Get a random subset of the samples#
az.extract_dataset(idata, num_samples=100)
<xarray.Dataset> Dimensions: (school: 8, sample: 100) Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' * sample (sample) MultiIndex - chain (sample) int64 0 0 0 3 1 2 2 2 3 2 1 0 ... 3 3 3 1 1 0 1 1 1 1 2 3 - draw (sample) int64 419 274 161 193 178 203 ... 238 49 212 448 95 412 Data variables: mu (sample) float64 6.95 7.4 4.131 1.644 ... 5.142 1.917 8.56 3.486 theta (school, sample) float64 8.734 3.829 19.1 ... 3.086 11.3 3.606 tau (sample) float64 1.867 1.603 8.83 1.929 ... 1.636 5.707 5.941 1.582 log_tau (sample) float64 0.6243 0.4717 2.178 0.6572 ... 1.742 1.782 0.4588 Attributes: (3)
Tip
Use a random seed to get the same subset from multiple groups: az.extract_dataset(idata, num_samples=100, rng=3)
and az.extract_dataset(idata, group="log_likelihood", num_samples=100, rng=3)
will continue to have matching samples
Obtain a NumPy array for a given parameter#
Let’s say we want to get the values for mu
as a NumPy array.
stacked.mu.values
array([-3.47698606, -2.45587061, -2.82625433, ..., 4.59705819,
5.89850592, 0.16138927])
Get the dimension lengths#
Let’s check how many groups are in our hierarchical model.
len(idata.observed_data.school)
8
Get coordinate values#
What are the names of the groups in our hierarchical model? You can access them from the coordinate name school
in this case
idata.observed_data.school
<xarray.DataArray 'school' (school: 8)> 'Choate' 'Deerfield' 'Phillips Andover' ... "St. Paul's" 'Mt. Hermon' Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon'
Get a subset of chains#
Let’s keep only chain 0 and 2 here. For the subset to take effect on all relevant InferenceData groups: posterior, sample_stats, log_likelihood, posterior_predictive we will use the arviz.InferenceData.sel()
, the method of InferenceData instead of xarray.Dataset.sel()
.
idata.sel(chain=[0, 2])
-
<xarray.Dataset> Dimensions: (chain: 2, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 2 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: mu (chain, draw) float64 -3.477 -2.456 -2.826 ... -1.571 -4.435 9.763 theta (chain, draw, school) float64 1.669 -8.537 -2.623 ... 12.01 16.67 tau (chain, draw) float64 3.73 2.075 3.703 4.146 ... 2.812 12.18 4.453 log_tau (chain, draw) float64 1.316 0.7301 1.309 1.422 ... 1.034 2.5 1.494 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 2, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 2 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (chain, draw, school) float64 7.85 -19.03 -22.5 ... 9.892 17.29 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 2, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 2 * draw (draw) int64 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tune (chain, draw) bool True False False ... False False False depth (chain, draw) int64 5 3 3 4 5 5 4 4 5 ... 4 4 4 5 4 4 4 5 tree_size (chain, draw) float64 31.0 7.0 7.0 15.0 ... 15.0 15.0 31.0 lp (chain, draw) float64 -59.05 -56.19 ... -63.1 -61.91 energy_error (chain, draw) float64 0.07387 -0.1841 ... 1.118 -0.5052 step_size_bar (chain, draw) float64 0.2417 0.2417 ... 0.2501 0.2501 max_energy_error (chain, draw) float64 0.131 -0.2067 ... 4.38 -0.5052 energy (chain, draw) float64 60.76 62.76 64.4 ... 68.89 67.32 mean_tree_accept (chain, draw) float64 0.9506 0.9906 ... 0.1054 0.9791 step_size (chain, draw) float64 0.1275 0.1275 ... 0.2075 0.2075 diverging (chain, draw) bool False False False ... False False False log_likelihood (chain, draw, school) float64 -5.168 -4.589 ... -3.843 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 1, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tau (chain, draw) float64 6.561 1.016 68.91 ... 1.56 5.949 0.7631 tau_log__ (chain, draw) float64 1.881 0.01593 4.233 ... 1.783 -0.2704 mu (chain, draw) float64 5.293 0.8137 0.7122 ... -1.658 -3.273 theta (chain, draw, school) float64 2.357 7.371 7.251 ... -3.775 -3.555 obs (chain, draw, school) float64 -3.54 6.769 19.68 ... -21.16 -6.071 Attributes: (3)
-
<xarray.Dataset> Dimensions: (school: 8) Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (school) float64 28.0 8.0 -3.0 7.0 -1.0 1.0 18.0 12.0 Attributes: (3)
Remove the first n draws (burn-in)#
Let’s say we want to remove the first 100 samples, from all the chains and all InferenceData
groups with draws.
idata.sel(draw=slice(100, None))
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 400, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 100 101 102 103 104 105 ... 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: mu (chain, draw) float64 4.271 4.517 0.3265 ... 4.597 5.899 0.1614 theta (chain, draw, school) float64 32.74 1.796 2.199 ... 10.59 4.523 tau (chain, draw) float64 11.98 9.164 11.72 6.183 ... 8.346 7.711 5.407 log_tau (chain, draw) float64 2.483 2.215 2.462 1.822 ... 2.122 2.043 1.688 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 400, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 100 101 102 103 104 105 ... 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (chain, draw, school) float64 24.5 11.84 28.08 ... 4.698 -15.07 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 400, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 100 101 102 103 104 ... 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tune (chain, draw) bool False False False ... False False False depth (chain, draw) int64 5 5 5 5 5 5 4 4 4 ... 4 4 4 5 5 5 5 5 tree_size (chain, draw) float64 31.0 31.0 31.0 ... 31.0 31.0 31.0 lp (chain, draw) float64 -67.62 -66.08 ... -63.62 -58.35 energy_error (chain, draw) float64 0.003801 -0.0119 ... -0.003652 step_size_bar (chain, draw) float64 0.2417 0.2417 ... 0.1502 0.1502 max_energy_error (chain, draw) float64 -0.03831 -0.02486 ... -0.101 -0.1757 energy (chain, draw) float64 72.68 74.16 73.41 ... 67.77 67.21 mean_tree_accept (chain, draw) float64 0.9998 1.0 0.8716 ... 0.9875 0.9967 step_size (chain, draw) float64 0.1275 0.1275 ... 0.1064 0.1064 diverging (chain, draw) bool False False False ... False False False log_likelihood (chain, draw, school) float64 -3.677 -3.414 ... -3.896 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 1, draw: 400, school: 8) Coordinates: * chain (chain) int64 0 * draw (draw) int64 100 101 102 103 104 105 ... 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tau (chain, draw) float64 1.588 0.4472 1.197 ... 1.56 5.949 0.7631 tau_log__ (chain, draw) float64 0.4625 -0.8048 0.1801 ... 1.783 -0.2704 mu (chain, draw) float64 -1.087 -8.631 -0.7139 ... -1.658 -3.273 theta (chain, draw, school) float64 1.556 1.323 2.802 ... -3.775 -3.555 obs (chain, draw, school) float64 18.6 12.49 7.67 ... -21.16 -6.071 Attributes: (3)
-
<xarray.Dataset> Dimensions: (school: 8) Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (school) float64 28.0 8.0 -3.0 7.0 -1.0 1.0 18.0 12.0 Attributes: (3)
If you check the burnin
object you will see that the groups posterior
, posterior_predictive
, prior
and sample_stats
have 400 draws compared to idata
that has 500. The group observed_data
has not been affected because it does not have the draw
dimension. Alternatively, you can specify which group or groups you want to change.
idata.sel(draw=slice(100, None), groups="posterior")
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 400, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 100 101 102 103 104 105 ... 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: mu (chain, draw) float64 4.271 4.517 0.3265 ... 4.597 5.899 0.1614 theta (chain, draw, school) float64 32.74 1.796 2.199 ... 10.59 4.523 tau (chain, draw) float64 11.98 9.164 11.72 6.183 ... 8.346 7.711 5.407 log_tau (chain, draw) float64 2.483 2.215 2.462 1.822 ... 2.122 2.043 1.688 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (chain, draw, school) float64 7.85 -19.03 -22.5 ... 4.698 -15.07 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tune (chain, draw) bool True False False ... False False False depth (chain, draw) int64 5 3 3 4 5 5 4 4 5 ... 4 4 4 5 5 5 5 5 tree_size (chain, draw) float64 31.0 7.0 7.0 15.0 ... 31.0 31.0 31.0 lp (chain, draw) float64 -59.05 -56.19 ... -63.62 -58.35 energy_error (chain, draw) float64 0.07387 -0.1841 ... -0.087 -0.003652 step_size_bar (chain, draw) float64 0.2417 0.2417 ... 0.1502 0.1502 max_energy_error (chain, draw) float64 0.131 -0.2067 ... -0.101 -0.1757 energy (chain, draw) float64 60.76 62.76 64.4 ... 67.77 67.21 mean_tree_accept (chain, draw) float64 0.9506 0.9906 ... 0.9875 0.9967 step_size (chain, draw) float64 0.1275 0.1275 ... 0.1064 0.1064 diverging (chain, draw) bool False False False ... False False False log_likelihood (chain, draw, school) float64 -5.168 -4.589 ... -3.896 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 1, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tau (chain, draw) float64 6.561 1.016 68.91 ... 1.56 5.949 0.7631 tau_log__ (chain, draw) float64 1.881 0.01593 4.233 ... 1.783 -0.2704 mu (chain, draw) float64 5.293 0.8137 0.7122 ... -1.658 -3.273 theta (chain, draw, school) float64 2.357 7.371 7.251 ... -3.775 -3.555 obs (chain, draw, school) float64 -3.54 6.769 19.68 ... -21.16 -6.071 Attributes: (3)
-
<xarray.Dataset> Dimensions: (school: 8) Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (school) float64 28.0 8.0 -3.0 7.0 -1.0 1.0 18.0 12.0 Attributes: (3)
Compute posterior mean values along draw
and chain
dimensions#
To compute the mean value of the posterior samples, do the following:
post.mean()
<xarray.Dataset> Dimensions: () Data variables: mu float64 4.093 theta float64 4.56 tau float64 4.089 log_tau float64 1.15
This computes the mean along all dimensions. This is probably what you want for mu
and tau
, which have two dimensions (chain
and draw
), but maybe not what you expected for theta
, which has one more dimension school
.
You can specify along which dimension you want to compute the mean (or other functions).
post.mean(dim=['chain', 'draw'])
<xarray.Dataset> Dimensions: (school: 8) Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: mu float64 4.093 theta (school) float64 6.026 4.724 3.576 4.478 3.064 3.821 6.25 4.544 tau float64 4.089 log_tau float64 1.15
Compute and store posterior pushforward quantities#
We use “posterior pushfoward quantities” to refer to quantities that are not variables in the posterior but deterministic computations using posterior variables.
You can use xarray for these pushforward operations and store them as a new variable in the posterior group. You’ll then be able to plot them with ArviZ functions, calculate stats and diagnostics on them (like the mcse()
) or save and share the inferencedata object with the pushforward quantities included.
Compute the rolling mean of \(\log(\tau)\) with xarray.DataArray.rolling()
, storing the result in the posterior
post["mlogtau"] = post["log_tau"].rolling({'draw': 50}).mean()
Using xarray for pusforward calculations has all the advantages of working with xarray. It also inherits the disadvantages of working with xarray, but we believe those to be outweighed by the advantages, and we have already shown how to extract the data as NumPy arrays. Working with InferenceData is working mainly with xarray objects and this is what is shown in this guide.
Some examples of these advantages are specifying operations with named dimensions instead of positional ones (as seen in some previous sections), automatic alignment and broadcasting of arrays (as we’ll see now), or integration with Dask (as shown in the Dask for ArviZ guide).
In this cell you will compute pairwise differences between schools on their mean effects (variable theta
).
To do so, substract the variable theta after renaming the school dimension to the original variable.
Xarray then aligns and broadcasts the two variables because they have different dimensions, and
the result is a 4d variable with all the pointwise differences.
Eventually, store the result in the theta_school_diff
variable:
post['theta_school_diff'] = post.theta - post.theta.rename(school="school_bis")
Note
This same operation using NumPy would require manual alignment of the two arrays to make sure they broadcast correctly. The could would be something like:
theta_school_diff = theta[:, :, :, None] - theta[:, :, None, :]
The theta_shool_diff
variable in the posterior has kept the named dimensions and coordinates:
post
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8, school_bis: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 ... 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' * school_bis (school_bis) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: mu (chain, draw) float64 -3.477 -2.456 ... 5.899 0.1614 theta (chain, draw, school) float64 1.669 -8.537 ... 4.523 tau (chain, draw) float64 3.73 2.075 3.703 ... 7.711 5.407 log_tau (chain, draw) float64 1.316 0.7301 1.309 ... 2.043 1.688 mlogtau (chain, draw) float64 nan nan nan ... 0.9753 1.004 1.034 theta_school_diff (chain, draw, school, school_bis) float64 0.0 ... 0.0 Attributes: (3)
Advanced subsetting#
To select the value corresponding to the difference between the Choate and Deerfield schools do:
post['theta_school_diff'].sel(school="Choate", school_bis="Deerfield")
<xarray.DataArray 'theta_school_diff' (chain: 4, draw: 500)> 10.21 -7.311 5.116 2.606 -1.116 24.96 ... 3.128 -4.62 4.288 2.424 2.613 -0.1137 Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 school <U6 'Choate' school_bis <U9 'Deerfield'
For more advanced subsetting (the equivalent to what is sometimes called “fancy indexing” in NumPy) you need to provide the indices as DataArray
objects:
school_idx = xr.DataArray(["Choate", "Hotchkiss", "Mt. Hermon"], dims=["pairwise_school_diff"])
school_bis_idx = xr.DataArray(["Deerfield", "Choate", "Lawrenceville"], dims=["pairwise_school_diff"])
post['theta_school_diff'].sel(school=school_idx, school_bis=school_bis_idx)
<xarray.DataArray 'theta_school_diff' (chain: 4, draw: 500, pairwise_school_diff: 3)> 10.21 -5.673 2.356 -7.311 2.817 -1.51 ... 2.613 8.154 8.915 -0.1137 2.805 5.63 Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 school (pairwise_school_diff) object 'Choate' 'Hotchkiss' 'Mt. Hermon' school_bis (pairwise_school_diff) object 'Deerfield' ... 'Lawrenceville' Dimensions without coordinates: pairwise_school_diff
Using lists or NumPy arrays instead of DataArrays does colum/row based indexing. As you can see, the result has 9 values of theta_shool_diff
instead of the 3 pairs of difference we selected in the previous cell:
post['theta_school_diff'].sel(
school=["Choate", "Hotchkiss", "Mt. Hermon"],
school_bis=["Deerfield", "Choate", "Lawrenceville"]
)
<xarray.DataArray 'theta_school_diff' (chain: 4, draw: 500, school: 3, school_bis: 3)> 10.21 0.0 10.84 4.533 -5.673 5.169 1.719 ... 2.691 2.805 3.861 4.46 4.574 5.63 Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Hotchkiss' 'Mt. Hermon' * school_bis (school_bis) object 'Deerfield' 'Choate' 'Lawrenceville'
Add new chains using concat#
After checking the mcse()
and realizing you need more samples, you rerun the model with two chains
and obtain an idata_rerun
object.
idata_rerun = idata.sel(chain=[0, 1]).copy().assign_coords(coords={"chain":[4,5]},groups="posterior_groups")
You can combine the two into a single InferenceData object using arviz.concat()
:
idata_complete = az.concat(idata, idata_rerun, dim="chain")
idata_complete.posterior.dims["chain"]
6
Add groups to InferenceData objects#
You can also add new groups to InferenceData objects with the extend()
(if the new groups are already in an InferenceData object) or with add_groups()
(if the new groups are dictionaries or xarray.Dataset
objects).
rng = np.random.default_rng(3)
idata.add_groups(
{"predictions": {"obs": rng.normal(size=(4, 500, 2))}},
dims={"obs": ["new_school"]},
coords={"new_school": ["Essex College", "Moordale"]}
)
idata
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8, school_bis: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 ... 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' * school_bis (school_bis) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: mu (chain, draw) float64 -3.477 -2.456 ... 5.899 0.1614 theta (chain, draw, school) float64 1.669 -8.537 ... 4.523 tau (chain, draw) float64 3.73 2.075 3.703 ... 7.711 5.407 log_tau (chain, draw) float64 1.316 0.7301 1.309 ... 2.043 1.688 mlogtau (chain, draw) float64 nan nan nan ... 0.9753 1.004 1.034 theta_school_diff (chain, draw, school, school_bis) float64 0.0 ... 0.0 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (chain, draw, school) float64 7.85 -19.03 -22.5 ... 4.698 -15.07 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, new_school: 2) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 * new_school (new_school) <U13 'Essex College' 'Moordale' Data variables: obs (chain, draw, new_school) float64 2.041 -2.556 ... -0.2822 Attributes: (2)
-
<xarray.Dataset> Dimensions: (chain: 4, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 ... 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tune (chain, draw) bool True False False ... False False False depth (chain, draw) int64 5 3 3 4 5 5 4 4 5 ... 4 4 4 5 5 5 5 5 tree_size (chain, draw) float64 31.0 7.0 7.0 15.0 ... 31.0 31.0 31.0 lp (chain, draw) float64 -59.05 -56.19 ... -63.62 -58.35 energy_error (chain, draw) float64 0.07387 -0.1841 ... -0.087 -0.003652 step_size_bar (chain, draw) float64 0.2417 0.2417 ... 0.1502 0.1502 max_energy_error (chain, draw) float64 0.131 -0.2067 ... -0.101 -0.1757 energy (chain, draw) float64 60.76 62.76 64.4 ... 67.77 67.21 mean_tree_accept (chain, draw) float64 0.9506 0.9906 ... 0.9875 0.9967 step_size (chain, draw) float64 0.1275 0.1275 ... 0.1064 0.1064 diverging (chain, draw) bool False False False ... False False False log_likelihood (chain, draw, school) float64 -5.168 -4.589 ... -3.896 Attributes: (3)
-
<xarray.Dataset> Dimensions: (chain: 1, draw: 500, school: 8) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 * school (school) object 'Choate' 'Deerfield' ... 'Mt. Hermon' Data variables: tau (chain, draw) float64 6.561 1.016 68.91 ... 1.56 5.949 0.7631 tau_log__ (chain, draw) float64 1.881 0.01593 4.233 ... 1.783 -0.2704 mu (chain, draw) float64 5.293 0.8137 0.7122 ... -1.658 -3.273 theta (chain, draw, school) float64 2.357 7.371 7.251 ... -3.775 -3.555 obs (chain, draw, school) float64 -3.54 6.769 19.68 ... -21.16 -6.071 Attributes: (3)
-
<xarray.Dataset> Dimensions: (school: 8) Coordinates: * school (school) object 'Choate' 'Deerfield' ... "St. Paul's" 'Mt. Hermon' Data variables: obs (school) float64 28.0 8.0 -3.0 7.0 -1.0 1.0 18.0 12.0 Attributes: (3)