Introduction

Contains the observed data and the sampling of the PyMC3 model

In [1]:
import arviz as az
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pymc3 as pm
import theano.tensor as tt
import warnings

from scipy import stats
from scipy.special import expit as logistic
from scipy.special import softmax

warnings.simplefilter(action="ignore", category=FutureWarning)
RANDOM_SEED = 8927
np.random.seed(286)
In [2]:
az.style.use("arviz-darkgrid")
az.rcParams["stats.hdi_prob"] = 0.89 # name was changed in latest ArviZ
In [3]:
d = pd.read_csv(
    "https://raw.githubusercontent.com/pymc-devs/resources/master/Rethinking_2/Data/chimpanzees.csv", 
    sep=";"
)
# we change "actor" to zero-index
d.actor = d.actor - 1
d["treatment"] = d.prosoc_left + 2 * d.condition
d[["actor", "prosoc_left", "condition", "treatment"]]
Out[3]:
actor prosoc_left condition treatment
0 0 0 0 0
1 0 0 0 0
2 0 1 0 1
3 0 0 0 0
4 0 1 0 1
... ... ... ... ...
499 6 1 1 3
500 6 1 1 3
501 6 0 1 2
502 6 0 1 2
503 6 0 1 2

504 rows × 4 columns

In [4]:
actor_idx, actors = pd.factorize(d.actor)
treat_idx, treatments = pd.factorize(d.treatment)
In [5]:
with pm.Model() as m11_4:
    a = pm.Normal("a", 0.0, 1.5, shape=len(actors))
    b = pm.Normal("b", 0.0, 0.5, shape=len(treatments))

    actor_id = pm.intX(pm.Data("actor_id", actor_idx))
    treat_id = pm.intX(pm.Data("treat_id", treat_idx))
    p = pm.Deterministic("p", pm.math.invlogit(a[actor_id] + b[treat_id]))

    pulled_left = pm.Binomial("pulled_left", 1, p, observed=d.pulled_left)

    trace_11_4 = pm.sample(random_seed=RANDOM_SEED)
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [b, a]
Sampling 4 chains, 0 divergences: 100%|██████████| 4000/4000 [00:01<00:00, 2388.27draws/s]
In [6]:
treatment_names = [f"treatment {i+1}" for i in treatments]
# I have given some names to the treatments to show ArviZ capabilities with 
# labels thanks to xarray
dims = {
    "a": ["actor"], 
    "b": ["treatment"],
    "actor_id": ["experiment"],
    "treat_id": ["experiment"],
    "p": ["experiment"],
    "pulled_left": ["experiment"]
}
coords = {"actor": actors, "treatment": treatment_names} 

# also, it is highly recommended to either pass the model instance to `from_pymc3`
# or to call it from the corresponding model context
idata_11_4 = az.from_pymc3(trace_11_4, model=m11_4, dims=dims, coords=coords)
az.summary(idata_11_4, var_names=["a", "b"], round_to=2)
Out[6]:
mean sd hdi_5.5% hdi_94.5% mcse_mean mcse_sd ess_mean ess_sd ess_bulk ess_tail r_hat
a[0] -0.44 0.32 -0.97 0.05 0.01 0.01 696.64 696.64 697.77 1204.46 1.01
a[1] 3.90 0.76 2.82 5.27 0.02 0.01 1685.56 1590.31 1734.73 1307.42 1.00
a[2] -0.75 0.33 -1.31 -0.25 0.01 0.01 684.50 684.50 684.25 951.56 1.01
a[3] -0.74 0.33 -1.28 -0.24 0.01 0.01 746.43 746.43 758.53 1041.13 1.01
a[4] -0.44 0.33 -0.92 0.11 0.01 0.01 672.00 672.00 673.09 1275.21 1.00
a[5] 0.49 0.34 -0.03 1.03 0.01 0.01 623.04 623.04 622.09 1042.27 1.01
a[6] 1.95 0.41 1.34 2.65 0.01 0.01 978.12 974.13 995.21 1331.11 1.00
b[treatment 1] -0.04 0.29 -0.53 0.38 0.01 0.01 591.45 591.45 590.00 1137.32 1.01
b[treatment 2] 0.48 0.29 0.03 0.95 0.01 0.01 637.00 637.00 637.81 1418.87 1.01
b[treatment 3] -0.39 0.28 -0.84 0.05 0.01 0.01 596.72 596.72 595.32 989.79 1.01
b[treatment 4] 0.36 0.29 -0.07 0.82 0.01 0.01 580.24 580.24 577.46 931.29 1.01

Note: I am using this notebook also as a test for arviz-devs/arviz#1201 so I have coordinate values instead of indexes shown in the summary. This has no relation to the current quesion, it is only to prevent surprises when running the notebook on ArviZ<=0.8.3

In [7]:
idata_11_4.posterior["p"].shape
Out[7]:
(4, 500, 504)

We have 504 different $p$ but $n_{actors} \times n_{treatments} = 28$?!?! How do we get the 28 $p$ corresponding the each actor-treatment combination?

To the question at hand

As we have just seen, our values for $p$ correspond to each experiment, and there are 504 of them.

Each experiment was done for a specific combination of actor and treatment and different experiments correspond to the same combination of actor and treatment. Thus, to get the $p$ corresponding to each of the 28 actor-treatment combinations we have (at least) 3 options (we'll focus on the 2nd and 3dr ones):

  1. Group-by and average the original 504 $p$. This can be straighforward if there are the same number of experiments for each actor-treatment (a reshape could be enough if properly ordered) but with unsorted and ragged data things can get out of control.
  2. pm.sample_posterior_predictive: pm.Data containers are thought to allow changing the data in the model and get predictions for new values for example. In this particular case, we are modifying the data to contain only one experiment per actor-treatment combination which automatically gets us to the case in option 1 where only a reshape is needed.
  3. Calculate $p$ manually from $a$ and $b$. We can manually calculate $logistic(a+b)$ for every combination of actor-treatment

It should be noted that even though we are using pm.sample_posterior_predictive in option 2, we are not getting samples from the posterior predictive. We are using it to cleverly reevaluate a deterministic function from the posterior.

We would be sampling from the posterior predictive if we obtained values from pulled_left. The obtained values could then be averaged to estimate the probability, but given that we do know the probability it does not make much sense to estimate it.

pm.sample_posterior_predictive version

In [8]:
with m11_4:
    pm.set_data({"actor_id": np.repeat(range(7), 4), "treat_id": list(range(4)) * 7})
    p_post = pm.sample_posterior_predictive(
        trace_11_4, random_seed=RANDOM_SEED, var_names=["p"]
    )["p"]
p_mu = p_post.mean(0).reshape((7, 4))
100%|██████████| 2000/2000 [00:00<00:00, 3839.00it/s]
In [9]:
p_mu
Out[9]:
array([[0.38273298, 0.50794882, 0.3064966 , 0.48028027],
       [0.97383758, 0.9842027 , 0.96366044, 0.98230814],
       [0.31552197, 0.43399235, 0.24723306, 0.40704301],
       [0.31658471, 0.43514105, 0.24811081, 0.40830217],
       [0.38371248, 0.50898154, 0.30735674, 0.4813107 ],
       [0.60644722, 0.71919498, 0.52349316, 0.69665124],
       [0.8650691 , 0.91412716, 0.82050517, 0.90508358]])

Manual version

The manual version will use ArviZ and xarray to showcase its capabilities. The posterior group in the InferenceData object is an xarray.Dataset. As it can be seen below, the dataset stores both the data and its dimensions and coordinate values:

In [10]:
idata_11_4.posterior
Out[10]:
Show/Hide data repr Show/Hide attributes
xarray.Dataset
    • actor: 7
    • chain: 4
    • draw: 500
    • experiment: 504
    • treatment: 4
    • chain
      (chain)
      int64
      0 1 2 3
      array([0, 1, 2, 3])
    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499
      array([  0,   1,   2, ..., 497, 498, 499])
    • actor
      (actor)
      int64
      0 1 2 3 4 5 6
      array([0, 1, 2, 3, 4, 5, 6])
    • treatment
      (treatment)
      <U11
      'treatment 1' ... 'treatment 4'
      array(['treatment 1', 'treatment 2', 'treatment 3', 'treatment 4'],
            dtype='<U11')
    • experiment
      (experiment)
      int64
      0 1 2 3 4 5 ... 499 500 501 502 503
      array([  0,   1,   2, ..., 501, 502, 503])
    • a
      (chain, draw, actor)
      float64
      0.135 3.439 ... 0.8038 2.469
      array([[[ 0.1350494 ,  3.43949205, -0.12937185, ...,  0.03736965,
                1.13246861,  2.41149076],
              [-0.53867798,  5.54241401, -0.86097509, ..., -0.49340846,
                0.51538093,  2.39456749],
              [-0.6464498 ,  2.63123411, -0.15443548, ..., -0.12293604,
                0.72261353,  1.76719445],
              ...,
              [-0.22109826,  3.77049511, -0.65876488, ..., -0.36966607,
                0.3325513 ,  1.70170163],
              [-0.46268774,  4.32909982, -0.51364639, ..., -0.28914722,
                0.34148056,  2.02406726],
              [-0.79424648,  3.23830151, -1.2127418 , ..., -0.56576385,
                0.14399398,  2.40274617]],
      
             [[-0.44553248,  3.42886858, -0.63826118, ..., -0.67836183,
                0.81808415,  1.80385049],
              [-0.28375707,  3.41254227, -0.52666946, ..., -0.65795236,
                0.72161261,  2.03624599],
              [-0.24907328,  3.5322941 , -0.78412297, ..., -0.63089803,
                1.33693092,  1.96060643],
              ...,
              [-0.15288734,  4.08486494,  0.26401406, ..., -0.49760689,
                1.507072  ,  1.88346066],
              [-0.42494098,  4.82477725, -0.79238959, ...,  0.09061211,
                0.31683397,  2.04605659],
              [ 0.46118619,  4.64381499,  0.07416212, ...,  0.33530701,
                1.21827518,  2.91216765]],
      
             [[-0.78547128,  4.7450789 , -0.78546263, ..., -0.80163116,
                0.15630192,  1.24127972],
              [-0.33331993,  2.90132854, -0.76646069, ..., -0.30024591,
                0.74294793,  2.61416152],
              [-0.39723684,  3.41333113, -0.39619374, ..., -0.96907126,
                0.10858268,  1.1236944 ],
              ...,
              [ 0.05353087,  4.87493456,  0.11899031, ...,  0.15286503,
                0.89845667,  1.89079282],
              [-0.17776394,  5.24086845, -0.13968179, ..., -0.40650101,
                0.85596658,  2.32740041],
              [-0.06807385,  3.49187068, -0.7569612 , ...,  0.12827456,
                0.68496056,  2.1930579 ]],
      
             [[-0.72787785,  3.3199782 , -0.80540404, ..., -0.57141605,
                0.17284305,  1.1029963 ],
              [-0.44173558,  4.22527233, -1.24332166, ..., -0.65391359,
               -0.36336629,  2.39538558],
              [-0.3523625 ,  3.91915261, -1.2200635 , ..., -0.85952723,
               -0.54765908,  2.52172622],
              ...,
              [-0.5660457 ,  3.07675958, -0.39877395, ..., -0.48418973,
                0.88115401,  2.39811526],
              [-0.57515718,  4.85570589, -0.47318295, ..., -0.02808618,
                0.61239922,  1.81332135],
              [-0.32259427,  2.92729824, -0.54600485, ..., -0.38426948,
                0.80376838,  2.46907673]]])
    • b
      (chain, draw, treatment)
      float64
      -0.3593 0.08189 ... -0.4503 0.3017
      array([[[-0.35929964,  0.08188989, -0.90768709, -0.31891759],
              [-0.18308382,  0.38016992, -0.46203453,  0.55845587],
              [-0.40881454,  0.12135358, -0.43520694,  0.18602932],
              ...,
              [-0.13702956,  0.25173945, -0.42576259,  0.69042055],
              [-0.16249926,  0.23940038, -0.59371464,  0.60846425],
              [-0.15320059,  1.0583223 , -0.53275706,  0.76881312]],
      
             [[-0.4386647 ,  0.43428959, -0.69013596,  0.5368523 ],
              [-0.26414823,  0.30762992, -0.53558744,  0.52895948],
              [-0.22472049,  0.7230068 , -0.79167565,  0.47707052],
              ...,
              [-0.20719957,  0.03885995, -1.01523696, -0.38181753],
              [-0.52578112,  0.3888622 , -0.33594527,  0.36942624],
              [-1.17373519, -0.19527191, -0.96670953, -0.23657849]],
      
             [[ 0.21501781,  0.64151466, -0.2640097 ,  0.57598384],
              [ 0.0341824 ,  0.16604603, -0.65063801,  0.26403522],
              [-0.01247477,  0.82985674, -0.19416263,  0.54055417],
              ...,
              [-0.397266  ,  0.2877604 , -0.58344193,  0.12683765],
              [-0.5483128 ,  0.41723657, -0.50482686, -0.04789725],
              [-0.17635197, -0.10309123, -0.8953712 ,  0.13159195]],
      
             [[ 0.05935307,  1.01295935,  0.07383078,  0.56308356],
              [ 0.29942449,  0.78510956, -0.42217475,  0.66064565],
              [ 0.07936967,  0.63896814, -0.58651151,  0.71442086],
              ...,
              [-0.00976328,  0.44357886, -0.36715989,  0.28928022],
              [-0.52414581,  0.20999093, -0.66477251,  0.08737833],
              [-0.1322785 ,  0.55515128, -0.45029006,  0.30174006]]])
    • p
      (chain, draw, experiment)
      float64
      0.4442 0.4442 ... 0.8828 0.8828
      array([[[0.4441712 , 0.4441712 , 0.55402312, ..., 0.81814109,
               0.81814109, 0.81814109],
              [0.32700514, 0.32700514, 0.46045575, ..., 0.87352952,
               0.87352952, 0.87352952],
              [0.25821549, 0.25821549, 0.37166134, ..., 0.7911692 ,
               0.7911692 , 0.7911692 ],
              ...,
              [0.41141284, 0.41141284, 0.5076597 , ..., 0.78175772,
               0.78175772, 0.78175772],
              [0.34860267, 0.34860267, 0.44440894, ..., 0.80695625,
               0.80695625, 0.80695625],
              [0.27939853, 0.27939853, 0.56563795, ..., 0.86645702,
               0.86645702, 0.86645702]],
      
             [[0.29230878, 0.29230878, 0.49718931, ..., 0.75282097,
               0.75282097, 0.75282097],
              [0.36635053, 0.36635053, 0.50596793, ..., 0.81767268,
               0.81767268, 0.81767268],
              [0.3837187 , 0.3837187 , 0.61631435, ..., 0.7629517 ,
               0.7629517 , 0.7629517 ],
              ...,
              [0.41093853, 0.41093853, 0.471524  , ..., 0.70437595,
               0.70437595, 0.70437595],
              [0.27873963, 0.27873963, 0.49098128, ..., 0.84685072,
               0.84685072, 0.84685072],
              [0.32903585, 0.32903585, 0.56608959, ..., 0.87495055,
               0.87495055, 0.87495055]],
      
             [[0.3611322 , 0.3611322 , 0.46407287, ..., 0.72656619,
               0.72656619, 0.72656619],
              [0.42576834, 0.42576834, 0.45827876, ..., 0.87691377,
               0.87691377, 0.87691377],
              [0.39898127, 0.39898127, 0.6064991 , ..., 0.71698028,
               0.71698028, 0.71698028],
              ...,
              [0.41490246, 0.41490246, 0.58450415, ..., 0.78706953,
               0.78706953, 0.78706953],
              [0.32605625, 0.32605625, 0.55958368, ..., 0.86087465,
               0.86087465, 0.86087465],
              [0.43919597, 0.43919597, 0.4573129 , ..., 0.7854454 ,
               0.7854454 , 0.7854454 ]],
      
             [[0.33882725, 0.33882725, 0.57079158, ..., 0.76437682,
               0.76437682, 0.76437682],
              [0.46448215, 0.46448215, 0.58500987, ..., 0.87795557,
               0.87795557, 0.87795557],
              [0.43217251, 0.43217251, 0.57116494, ..., 0.87382549,
               0.87382549, 0.87382549],
              ...,
              [0.35989752, 0.35989752, 0.4694215 , ..., 0.88400907,
               0.88400907, 0.88400907],
              [0.24987052, 0.24987052, 0.40970954, ..., 0.75924576,
               0.75924576, 0.75924576],
              [0.38820285, 0.38820285, 0.55787864, ..., 0.88275549,
               0.88275549, 0.88275549]]])
  • created_at :
    2020-06-04T22:45:38.724507
    arviz_version :
    0.8.3
    inference_library :
    pymc3
    inference_library_version :
    3.8

As dimensions are named, xarray is able to automatically broadcast, here we are adding two 3d arrays with different shapes without any problem and getting the desired 4d output

In [11]:
p_mu_samples = logistic(idata_11_4.posterior["a"]+ idata_11_4.posterior["b"])
p_mu_samples
Out[11]:
Show/Hide data repr Show/Hide attributes
xarray.DataArray
  • chain: 4
  • draw: 500
  • actor: 7
  • treatment: 4
  • 0.4442 0.554 0.3159 0.4542 0.9561 ... 0.9119 0.9537 0.8828 0.9411
    array([[[[0.4441712 , 0.55402312, 0.3159088 , 0.45416202],
             [0.95606827, 0.97129007, 0.92634161, 0.95773349],
             [0.38020658, 0.48813174, 0.26171787, 0.38976755],
             ...,
             [0.42020547, 0.5297796 , 0.29518825, 0.43007432],
             [0.68420601, 0.77106923, 0.55595995, 0.69286569],
             [0.88616883, 0.92367647, 0.81814109, 0.89017923]],
    
            [[0.32700514, 0.46045575, 0.26880136, 0.50494431],
             [0.99531797, 0.99732888, 0.99382087, 0.99776409],
             [0.26036758, 0.38206201, 0.21031801, 0.42494175],
             ...,
             [0.33704464, 0.47172058, 0.27779151, 0.51625612],
             [0.58231819, 0.71003434, 0.51333344, 0.74532588],
             [0.90127602, 0.94129532, 0.87352952, 0.95040619]],
    
            [[0.25821549, 0.37166134, 0.25319262, 0.38688608],
             [0.90224481, 0.94005933, 0.89989218, 0.94360161],
             [0.3627958 , 0.49173028, 0.3567169 , 0.5078978 ],
             ...,
             [0.37010869, 0.49960439, 0.36397725, 0.51576809],
             [0.57781228, 0.69930008, 0.5713611 , 0.71272237],
             [0.79549626, 0.86858989, 0.7911692 , 0.87579774]],
    
            ...,
    
            [[0.41141284, 0.5076597 , 0.34369729, 0.61522334],
             [0.97425583, 0.98240233, 0.96593192, 0.98858014],
             [0.31092585, 0.39962558, 0.25265019, 0.50791326],
             ...,
             [0.37596846, 0.47055246, 0.31100422, 0.57950811],
             [0.54872531, 0.64205411, 0.47671404, 0.73555108],
             [0.82702274, 0.87582137, 0.78175772, 0.9162246 ]],
    
            [[0.34860267, 0.44440894, 0.25799757, 0.53637973],
             [0.98473185, 0.989733  , 0.97669224, 0.99287902],
             [0.3371221 , 0.431865  , 0.2483632 , 0.52368672],
             ...,
             [0.38896937, 0.48756585, 0.29258508, 0.5791578 ],
             [0.54462626, 0.64127009, 0.43727369, 0.72110408],
             [0.86547961, 0.90580591, 0.80695625, 0.93292613]],
    
            [[0.27939853, 0.56563795, 0.20965545, 0.493642  ],
             [0.95627397, 0.98656842, 0.93735302, 0.98213902],
             [0.20327621, 0.46147166, 0.14861582, 0.39080524],
             ...,
             [0.32762106, 0.62070895, 0.25001713, 0.55058863],
             [0.49769836, 0.76893658, 0.4040151 , 0.71357424],
             [0.90461133, 0.96955952, 0.86645702, 0.95974986]]],
    
    
           [[[0.29230878, 0.49718931, 0.24311653, 0.5228141 ],
             [0.9521296 , 0.97943043, 0.93927385, 0.98139822],
             [0.25408821, 0.44918316, 0.20942462, 0.47466948],
             ...,
             [0.24656325, 0.43928306, 0.20286266, 0.46468154],
             [0.59373307, 0.7777105 , 0.53194348, 0.79493551],
             [0.79660123, 0.9036226 , 0.75282097, 0.91219239]],
    
            [[0.36635053, 0.50596793, 0.30590282, 0.5609953 ],
             [0.9588454 , 0.9763434 , 0.9466954 , 0.98095088],
             [0.31199312, 0.44545801, 0.25687839, 0.5005725 ],
             ...,
             [0.28453008, 0.41330423, 0.23262644, 0.46779642],
             [0.61241248, 0.73676902, 0.54637264, 0.77739888],
             [0.85471835, 0.91244622, 0.81767268, 0.92858841]],
    
            [[0.3837187 , 0.61631435, 0.26100551, 0.55675367],
             [0.96468772, 0.98600969, 0.93938132, 0.98217845],
             [0.26720625, 0.48472571, 0.17139132, 0.42383437],
             ...,
             [0.29825557, 0.52301093, 0.19425843, 0.46161878],
             [0.75254097, 0.88694793, 0.63303408, 0.85984479],
             [0.85016375, 0.93605275, 0.7629517 , 0.91965561]],
    
            ...,
    
            [[0.41093853, 0.471524  , 0.23719419, 0.36942022],
             [0.97972067, 0.98407364, 0.9556224 , 0.97594463],
             [0.5141998 , 0.57514494, 0.3205549 , 0.47058315],
             ...,
             [0.33074744, 0.38728313, 0.18051772, 0.29329707],
             [0.78581351, 0.8243254 , 0.62053862, 0.75496207],
             [0.8424088 , 0.87239699, 0.70437595, 0.81781942]],
    
            [[0.27873963, 0.49098128, 0.31845388, 0.48612488],
             [0.98659982, 0.99458762, 0.98889104, 0.99448198],
             [0.2111228 , 0.40046514, 0.24446853, 0.39580787],
             ...,
             [0.3928927 , 0.61762373, 0.4389725 , 0.61302327],
             [0.44795244, 0.66944948, 0.49522232, 0.66513448],
             [0.82057904, 0.91945157, 0.84685072, 0.91800035]],
    
            [[0.32903585, 0.56608959, 0.37624354, 0.55591704],
             [0.96982435, 0.98843961, 0.97532802, 0.98795796],
             [0.2498199 , 0.46975951, 0.29058441, 0.45948493],
             ...,
             [0.30186593, 0.53495168, 0.34719259, 0.5246621 ],
             [0.51113316, 0.73555719, 0.56256182, 0.72744475],
             [0.85048785, 0.93801629, 0.87495055, 0.93557076]]],
    
    
           [[[0.3611322 , 0.46407287, 0.25932478, 0.44781883],
             [0.99303658, 0.99544332, 0.98880544, 0.99513622],
             [0.36113419, 0.46407502, 0.25932644, 0.44782097],
             ...,
             [0.35741229, 0.46005618, 0.25623296, 0.44382632],
             [0.59177783, 0.68950723, 0.47309906, 0.67530667],
             [0.81096574, 0.86793177, 0.72656619, 0.86023745]],
    
            [[0.42576834, 0.45827876, 0.27210715, 0.48268575],
             [0.94957421, 0.95552674, 0.90471008, 0.95950985],
             [0.32469497, 0.35424883, 0.19511682, 0.37697084],
             ...,
             [0.43387375, 0.46650029, 0.27870709, 0.49094832],
             [0.68506131, 0.71279425, 0.52306111, 0.73242933],
             [0.93390885, 0.94159686, 0.87691377, 0.94675804]],
    
            [[0.39898127, 0.6064991 , 0.35631382, 0.53576813],
             [0.96773129, 0.9858416 , 0.96154928, 0.98118091],
             [0.39923143, 0.60674802, 0.35655309, 0.53602756],
             ...,
             [0.27258513, 0.46525247, 0.23808017, 0.39448049],
             [0.5240085 , 0.71878432, 0.47861806, 0.65681593],
             [0.75235642, 0.87583334, 0.71698028, 0.8408075 ]],
    
            ...,
    
            [[0.41490246, 0.58450415, 0.37053763, 0.54497028],
             [0.98876773, 0.99430636, 0.98650025, 0.99331892],
             [0.43087656, 0.6003085 , 0.38593031, 0.56114936],
             ...,
             [0.43920209, 0.60840805, 0.39398858, 0.56947333],
             [0.6227391 , 0.76606381, 0.57810883, 0.73600259],
             [0.81660704, 0.89830698, 0.78706953, 0.88263577]],
    
            [[0.32605625, 0.55958368, 0.33568331, 0.44382289],
             [0.99091996, 0.99652301, 0.991303  , 0.99447522],
             [0.33447933, 0.56894664, 0.34422806, 0.45324226],
             ...,
             [0.27791776, 0.50268386, 0.28672819, 0.38831555],
             [0.57631247, 0.78129058, 0.58689393, 0.69169794],
             [0.85558417, 0.93960975, 0.86087465, 0.90716521]],
    
            [[0.43919597, 0.4573129 , 0.27618897, 0.51587419],
             [0.96495737, 0.96735202, 0.93063595, 0.97400374],
             [0.28225303, 0.29732839, 0.16079397, 0.34856129],
             ...,
             [0.48798296, 0.5062955 , 0.3171075 , 0.56460348],
             [0.62448024, 0.64149743, 0.44759056, 0.69350404],
             [0.88253997, 0.88992416, 0.7854454 , 0.91089806]]],
    
    
           [[[0.33882725, 0.57079158, 0.34207812, 0.45889441],
             [0.9670523 , 0.98704121, 0.96751049, 0.97982761],
             [0.32168238, 0.55170335, 0.32484958, 0.43971458],
             ...,
             [0.37471004, 0.60862671, 0.37810831, 0.49791689],
             [0.55778962, 0.76598949, 0.56135765, 0.67610448],
             [0.76175935, 0.89244434, 0.76437682, 0.84105246]],
    
            [[0.46448215, 0.58500987, 0.29652301, 0.55451001],
             [0.9892782 , 0.99337582, 0.97818493, 0.99250442],
             [0.28011381, 0.38741005, 0.15902555, 0.35831708],
             ...,
             [0.41229425, 0.53275203, 0.25424698, 0.50168301],
             [0.48401999, 0.60390032, 0.31312689, 0.5737773 ],
             [0.9367197 , 0.96009364, 0.87795557, 0.9550422 ]],
    
            [[0.43217251, 0.57116494, 0.28112784, 0.58953861],
             [0.98198767, 0.98962699, 0.96553177, 0.99037361],
             [0.242193  , 0.35868059, 0.14105258, 0.37621555],
             ...,
             [0.31428593, 0.44508267, 0.19061196, 0.46378693],
             [0.3850212 , 0.52281142, 0.24339225, 0.5415941 ],
             [0.93093208, 0.95932805, 0.87382549, 0.96217212]],
    
            ...,
    
            [[0.35989752, 0.4694215 , 0.28227482, 0.43124694],
             [0.95551066, 0.97126095, 0.93759073, 0.96662617],
             [0.39926292, 0.51119935, 0.31735935, 0.47265388],
             ...,
             [0.37896278, 0.48984868, 0.29914982, 0.4514263 ],
             [0.705035  , 0.78996805, 0.62574232, 0.7632235 ],
             [0.91593476, 0.94488775, 0.88400907, 0.93627877]],
    
            [[0.24987052, 0.40970954, 0.22444823, 0.38041695],
             [0.98702358, 0.99373005, 0.98509341, 0.99291795],
             [0.26946694, 0.4345792 , 0.24269594, 0.40472766],
             ...,
             [0.36534672, 0.5453512 , 0.33339745, 0.51481869],
             [0.52204904, 0.69474347, 0.48690967, 0.66813845],
             [0.78400761, 0.88322307, 0.75924576, 0.8699707 ]],
    
            [[0.38820285, 0.55787864, 0.3158555 , 0.49478664],
             [0.94240611, 0.97018426, 0.92251421, 0.96191253],
             [0.33664455, 0.50228659, 0.26967051, 0.43923563],
             ...,
             [0.37365979, 0.5426168 , 0.30268184, 0.47937935],
             [0.66183669, 0.79558406, 0.58746081, 0.7512908 ],
             [0.91187914, 0.95365674, 0.88275549, 0.94107829]]]])
    • chain
      (chain)
      int64
      0 1 2 3
      array([0, 1, 2, 3])
    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499
      array([  0,   1,   2, ..., 497, 498, 499])
    • actor
      (actor)
      int64
      0 1 2 3 4 5 6
      array([0, 1, 2, 3, 4, 5, 6])
    • treatment
      (treatment)
      <U11
      'treatment 1' ... 'treatment 4'
      array(['treatment 1', 'treatment 2', 'treatment 3', 'treatment 4'],
            dtype='<U11')

We can also use dimension names to indicate the dimensions along which the mean should be taken

In [12]:
p_mu_az = p_mu_samples.mean(dim=("chain", "draw"))
p_mu_az
Out[12]:
Show/Hide data repr Show/Hide attributes
xarray.DataArray
  • actor: 7
  • treatment: 4
  • 0.3827 0.5079 0.3065 0.4803 0.9738 ... 0.8651 0.9141 0.8205 0.9051
    array([[0.38273298, 0.50794882, 0.3064966 , 0.48028027],
           [0.97383758, 0.9842027 , 0.96366044, 0.98230814],
           [0.31552197, 0.43399235, 0.24723306, 0.40704301],
           [0.31658471, 0.43514105, 0.24811081, 0.40830217],
           [0.38371248, 0.50898154, 0.30735674, 0.4813107 ],
           [0.60644722, 0.71919498, 0.52349316, 0.69665124],
           [0.8650691 , 0.91412716, 0.82050517, 0.90508358]])
    • actor
      (actor)
      int64
      0 1 2 3 4 5 6
      array([0, 1, 2, 3, 4, 5, 6])
    • treatment
      (treatment)
      <U11
      'treatment 1' ... 'treatment 4'
      array(['treatment 1', 'treatment 2', 'treatment 3', 'treatment 4'],
            dtype='<U11')

Note how thanks to xarray, this option ends up being a one liner:

logistic(idata_11_4.posterior["a"]+ idata_11_4.posterior["b"]).mean(dim=("chain", "draw"))

It has been extended to show the intermediate steps.

Compare results

In [13]:
np.allclose(p_mu, p_mu_az.values) # compare means
Out[13]:
True
In [14]:
np.allclose(p_post.reshape((4,-1,7,4)), p_mu_samples) # compare all samples, requires reshaping p_post
Out[14]:
True

We can see that here there is actually NO random sampling involved and that both approaches return the same result up to machine error. To be extra sure, go back to the pm.sample_posterior_predictive call and change the random seed to see we still get the same result.

Groupby p in trace_11_4

Finally we'll consider the first option, due to its relation to the following question:

Am I correct thinking that since p is a deterministic function of the parameters a and b , there should be a value of p in trace_11_4 for every value returned by sample_posterior_predictive?

We will explore the values stored in p in trace_11_4 (or what is the same, in idata_11_4). p is defined in the following line:

p = pm.Deterministic("p", pm.math.invlogit(a[actor_id] + b[treat_id]))

Thus, at every sample, p will contain only 28 different values, these unique values will be equal to the values returned by pm.sample_posterior_predictive and will be equal to the values stored in p_mu_samples. To check this, we'll compare the values of p in each sample for a couple of actor-treatment combination with the corresponding values in the other alternatives.

In [15]:
def get_mask(actor, treatment):
    return (actor == actor_idx) & (treatment == treat_idx)

Example 1: actor 2 and treatment 1

In [16]:
mask_2_1 = get_mask(actor=2, treatment=1)
In [17]:
da_2_1 = idata_11_4.posterior.p.sel(experiment=mask_2_1) 
da_2_1 # the database icon can be used to explore the data
Out[17]:
Show/Hide data repr Show/Hide attributes
xarray.DataArray
'p'
  • chain: 4
  • draw: 500
  • experiment: 18
  • 0.4881 0.4881 0.4881 0.4881 0.4881 ... 0.5023 0.5023 0.5023 0.5023
    array([[[0.48813174, 0.48813174, 0.48813174, ..., 0.48813174,
             0.48813174, 0.48813174],
            [0.38206201, 0.38206201, 0.38206201, ..., 0.38206201,
             0.38206201, 0.38206201],
            [0.49173028, 0.49173028, 0.49173028, ..., 0.49173028,
             0.49173028, 0.49173028],
            ...,
            [0.39962558, 0.39962558, 0.39962558, ..., 0.39962558,
             0.39962558, 0.39962558],
            [0.431865  , 0.431865  , 0.431865  , ..., 0.431865  ,
             0.431865  , 0.431865  ],
            [0.46147166, 0.46147166, 0.46147166, ..., 0.46147166,
             0.46147166, 0.46147166]],
    
           [[0.44918316, 0.44918316, 0.44918316, ..., 0.44918316,
             0.44918316, 0.44918316],
            [0.44545801, 0.44545801, 0.44545801, ..., 0.44545801,
             0.44545801, 0.44545801],
            [0.48472571, 0.48472571, 0.48472571, ..., 0.48472571,
             0.48472571, 0.48472571],
            ...,
            [0.57514494, 0.57514494, 0.57514494, ..., 0.57514494,
             0.57514494, 0.57514494],
            [0.40046514, 0.40046514, 0.40046514, ..., 0.40046514,
             0.40046514, 0.40046514],
            [0.46975951, 0.46975951, 0.46975951, ..., 0.46975951,
             0.46975951, 0.46975951]],
    
           [[0.46407502, 0.46407502, 0.46407502, ..., 0.46407502,
             0.46407502, 0.46407502],
            [0.35424883, 0.35424883, 0.35424883, ..., 0.35424883,
             0.35424883, 0.35424883],
            [0.60674802, 0.60674802, 0.60674802, ..., 0.60674802,
             0.60674802, 0.60674802],
            ...,
            [0.6003085 , 0.6003085 , 0.6003085 , ..., 0.6003085 ,
             0.6003085 , 0.6003085 ],
            [0.56894664, 0.56894664, 0.56894664, ..., 0.56894664,
             0.56894664, 0.56894664],
            [0.29732839, 0.29732839, 0.29732839, ..., 0.29732839,
             0.29732839, 0.29732839]],
    
           [[0.55170335, 0.55170335, 0.55170335, ..., 0.55170335,
             0.55170335, 0.55170335],
            [0.38741005, 0.38741005, 0.38741005, ..., 0.38741005,
             0.38741005, 0.38741005],
            [0.35868059, 0.35868059, 0.35868059, ..., 0.35868059,
             0.35868059, 0.35868059],
            ...,
            [0.51119935, 0.51119935, 0.51119935, ..., 0.51119935,
             0.51119935, 0.51119935],
            [0.4345792 , 0.4345792 , 0.4345792 , ..., 0.4345792 ,
             0.4345792 , 0.4345792 ],
            [0.50228659, 0.50228659, 0.50228659, ..., 0.50228659,
             0.50228659, 0.50228659]]])
    • chain
      (chain)
      int64
      0 1 2 3
      array([0, 1, 2, 3])
    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499
      array([  0,   1,   2, ..., 497, 498, 499])
    • experiment
      (experiment)
      int64
      145 146 147 150 ... 173 176 177 179
      array([145, 146, 147, 150, 152, 153, 156, 160, 161, 162, 166, 167, 169, 170,
             173, 176, 177, 179])
In [18]:
np.allclose(da_2_1.values, p_post.reshape((4,-1,7,4))[:,:,2,1,None])
Out[18]:
True
In [19]:
np.allclose(da_2_1.values, p_mu_samples.isel(actor=2, treatment=1).values[:,:,None])
Out[19]:
True

As shown in this example, positional indexing, isel, can still be used with xarray. Below we use label based indexing, sel

Example 1: actor 5 and treatment 3

In [20]:
mask_5_3 = get_mask(actor=5, treatment=3)
da_5_3 = idata_11_4.posterior.p.sel(experiment=mask_5_3) 
print(np.allclose(da_5_3.values, p_post.reshape((4,-1,7,4))[:,:,5,3,None]))
print(np.allclose(da_5_3.values, p_mu_samples.sel(actor=5, treatment="treatment 4").values[:,:,None]))
True
True

A mixed pandas-xarray implementation of option 1

In [21]:
d["repetition"] = d.groupby(["actor", "treatment"]).cumcount()
d
Out[21]:
actor recipient condition block trial prosoc_left chose_prosoc pulled_left treatment repetition
0 0 NaN 0 1 2 0 1 0 0 0
1 0 NaN 0 1 4 0 0 1 0 1
2 0 NaN 0 1 6 1 0 0 1 0
3 0 NaN 0 1 8 0 1 0 0 2
4 0 NaN 0 1 10 1 1 1 1 1
... ... ... ... ... ... ... ... ... ... ...
499 6 4.0 1 6 64 1 1 1 3 16
500 6 6.0 1 6 66 1 1 1 3 17
501 6 3.0 1 6 68 0 0 1 2 15
502 6 7.0 1 6 70 0 0 1 2 16
503 6 2.0 1 6 72 0 0 1 2 17

504 rows × 10 columns

In [22]:
aux_names = {"actor": "actor_aux", "treatment": "treatment_aux"}
aux_names_inv = {v: k for k, v in aux_names.items()}
multi_idx = pd.MultiIndex.from_frame(
    d[["actor", "treatment", "repetition"]].rename(columns=aux_names)
)
idata_11_4.posterior["experiment"] = multi_idx
idata_11_4.posterior = (
    idata_11_4.posterior.unstack(
        "experiment"
    ).reset_index(
        tuple(aux_names.values()), drop=True
    ).rename(aux_names_inv)
)
idata_11_4.posterior
Out[22]:
Show/Hide data repr Show/Hide attributes
xarray.Dataset
    • actor: 7
    • chain: 4
    • draw: 500
    • repetition: 18
    • treatment: 4
    • chain
      (chain)
      int64
      0 1 2 3
      array([0, 1, 2, 3])
    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499
      array([  0,   1,   2, ..., 497, 498, 499])
    • actor
      (actor)
      int64
      0 1 2 3 4 5 6
      array([0, 1, 2, 3, 4, 5, 6])
    • treatment
      (treatment)
      <U11
      'treatment 1' ... 'treatment 4'
      array(['treatment 1', 'treatment 2', 'treatment 3', 'treatment 4'],
            dtype='<U11')
    • repetition
      (repetition)
      int64
      0 1 2 3 4 5 6 ... 12 13 14 15 16 17
      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17])
    • a
      (chain, draw, actor)
      float64
      0.135 3.439 ... 0.8038 2.469
      array([[[ 0.1350494 ,  3.43949205, -0.12937185, ...,  0.03736965,
                1.13246861,  2.41149076],
              [-0.53867798,  5.54241401, -0.86097509, ..., -0.49340846,
                0.51538093,  2.39456749],
              [-0.6464498 ,  2.63123411, -0.15443548, ..., -0.12293604,
                0.72261353,  1.76719445],
              ...,
              [-0.22109826,  3.77049511, -0.65876488, ..., -0.36966607,
                0.3325513 ,  1.70170163],
              [-0.46268774,  4.32909982, -0.51364639, ..., -0.28914722,
                0.34148056,  2.02406726],
              [-0.79424648,  3.23830151, -1.2127418 , ..., -0.56576385,
                0.14399398,  2.40274617]],
      
             [[-0.44553248,  3.42886858, -0.63826118, ..., -0.67836183,
                0.81808415,  1.80385049],
              [-0.28375707,  3.41254227, -0.52666946, ..., -0.65795236,
                0.72161261,  2.03624599],
              [-0.24907328,  3.5322941 , -0.78412297, ..., -0.63089803,
                1.33693092,  1.96060643],
              ...,
              [-0.15288734,  4.08486494,  0.26401406, ..., -0.49760689,
                1.507072  ,  1.88346066],
              [-0.42494098,  4.82477725, -0.79238959, ...,  0.09061211,
                0.31683397,  2.04605659],
              [ 0.46118619,  4.64381499,  0.07416212, ...,  0.33530701,
                1.21827518,  2.91216765]],
      
             [[-0.78547128,  4.7450789 , -0.78546263, ..., -0.80163116,
                0.15630192,  1.24127972],
              [-0.33331993,  2.90132854, -0.76646069, ..., -0.30024591,
                0.74294793,  2.61416152],
              [-0.39723684,  3.41333113, -0.39619374, ..., -0.96907126,
                0.10858268,  1.1236944 ],
              ...,
              [ 0.05353087,  4.87493456,  0.11899031, ...,  0.15286503,
                0.89845667,  1.89079282],
              [-0.17776394,  5.24086845, -0.13968179, ..., -0.40650101,
                0.85596658,  2.32740041],
              [-0.06807385,  3.49187068, -0.7569612 , ...,  0.12827456,
                0.68496056,  2.1930579 ]],
      
             [[-0.72787785,  3.3199782 , -0.80540404, ..., -0.57141605,
                0.17284305,  1.1029963 ],
              [-0.44173558,  4.22527233, -1.24332166, ..., -0.65391359,
               -0.36336629,  2.39538558],
              [-0.3523625 ,  3.91915261, -1.2200635 , ..., -0.85952723,
               -0.54765908,  2.52172622],
              ...,
              [-0.5660457 ,  3.07675958, -0.39877395, ..., -0.48418973,
                0.88115401,  2.39811526],
              [-0.57515718,  4.85570589, -0.47318295, ..., -0.02808618,
                0.61239922,  1.81332135],
              [-0.32259427,  2.92729824, -0.54600485, ..., -0.38426948,
                0.80376838,  2.46907673]]])
    • b
      (chain, draw, treatment)
      float64
      -0.3593 0.08189 ... -0.4503 0.3017
      array([[[-0.35929964,  0.08188989, -0.90768709, -0.31891759],
              [-0.18308382,  0.38016992, -0.46203453,  0.55845587],
              [-0.40881454,  0.12135358, -0.43520694,  0.18602932],
              ...,
              [-0.13702956,  0.25173945, -0.42576259,  0.69042055],
              [-0.16249926,  0.23940038, -0.59371464,  0.60846425],
              [-0.15320059,  1.0583223 , -0.53275706,  0.76881312]],
      
             [[-0.4386647 ,  0.43428959, -0.69013596,  0.5368523 ],
              [-0.26414823,  0.30762992, -0.53558744,  0.52895948],
              [-0.22472049,  0.7230068 , -0.79167565,  0.47707052],
              ...,
              [-0.20719957,  0.03885995, -1.01523696, -0.38181753],
              [-0.52578112,  0.3888622 , -0.33594527,  0.36942624],
              [-1.17373519, -0.19527191, -0.96670953, -0.23657849]],
      
             [[ 0.21501781,  0.64151466, -0.2640097 ,  0.57598384],
              [ 0.0341824 ,  0.16604603, -0.65063801,  0.26403522],
              [-0.01247477,  0.82985674, -0.19416263,  0.54055417],
              ...,
              [-0.397266  ,  0.2877604 , -0.58344193,  0.12683765],
              [-0.5483128 ,  0.41723657, -0.50482686, -0.04789725],
              [-0.17635197, -0.10309123, -0.8953712 ,  0.13159195]],
      
             [[ 0.05935307,  1.01295935,  0.07383078,  0.56308356],
              [ 0.29942449,  0.78510956, -0.42217475,  0.66064565],
              [ 0.07936967,  0.63896814, -0.58651151,  0.71442086],
              ...,
              [-0.00976328,  0.44357886, -0.36715989,  0.28928022],
              [-0.52414581,  0.20999093, -0.66477251,  0.08737833],
              [-0.1322785 ,  0.55515128, -0.45029006,  0.30174006]]])
    • p
      (chain, draw, actor, treatment, repetition)
      float64
      0.4442 0.4442 ... 0.9411 0.9411
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               ...,
      
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               ...,
      
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              ...,
      
      
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               ...,
      
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               ...,
      
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               ...,
      
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               ...,
      
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               ...,
      
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               ...,
      
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              ...,
      
      
              [[[0.41093853, 0.41093853, 0.41093853, ..., 0.41093853,
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               ...,
      
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               ...,
      
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               ...,
      
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               [[0.85048785, 0.85048785, 0.85048785, ..., 0.85048785,
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               ...,
      
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               ...,
      
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               [[0.68506131, 0.68506131, 0.68506131, ..., 0.68506131,
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               ...,
      
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              ...,
      
      
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               ...,
      
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               ...,
      
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               ...,
      
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               [[0.88253997, 0.88253997, 0.88253997, ..., 0.88253997,
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             [[[[0.33882725, 0.33882725, 0.33882725, ..., 0.33882725,
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               ...,
      
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               [[0.76175935, 0.76175935, 0.76175935, ..., 0.76175935,
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              [[[0.46448215, 0.46448215, 0.46448215, ..., 0.46448215,
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               [[0.9892782 , 0.9892782 , 0.9892782 , ..., 0.9892782 ,
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               ...,
      
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               [[0.48401999, 0.48401999, 0.48401999, ..., 0.48401999,
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               [[0.9367197 , 0.9367197 , 0.9367197 , ..., 0.9367197 ,
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              [[[0.43217251, 0.43217251, 0.43217251, ..., 0.43217251,
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               [[0.98198767, 0.98198767, 0.98198767, ..., 0.98198767,
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               [[0.242193  , 0.242193  , 0.242193  , ..., 0.242193  ,
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               ...,
      
               [[0.31428593, 0.31428593, 0.31428593, ..., 0.31428593,
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               [[0.3850212 , 0.3850212 , 0.3850212 , ..., 0.3850212 ,
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               [[0.93093208, 0.93093208, 0.93093208, ..., 0.93093208,
                 0.93093208, 0.93093208],
                [0.95932805, 0.95932805, 0.95932805, ..., 0.95932805,
                 0.95932805, 0.95932805],
                [0.87382549, 0.87382549, 0.87382549, ..., 0.87382549,
                 0.87382549, 0.87382549],
                [0.96217212, 0.96217212, 0.96217212, ..., 0.96217212,
                 0.96217212, 0.96217212]]],
      
      
              ...,
      
      
              [[[0.35989752, 0.35989752, 0.35989752, ..., 0.35989752,
                 0.35989752, 0.35989752],
                [0.4694215 , 0.4694215 , 0.4694215 , ..., 0.4694215 ,
                 0.4694215 , 0.4694215 ],
                [0.28227482, 0.28227482, 0.28227482, ..., 0.28227482,
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                [0.43124694, 0.43124694, 0.43124694, ..., 0.43124694,
                 0.43124694, 0.43124694]],
      
               [[0.95551066, 0.95551066, 0.95551066, ..., 0.95551066,
                 0.95551066, 0.95551066],
                [0.97126095, 0.97126095, 0.97126095, ..., 0.97126095,
                 0.97126095, 0.97126095],
                [0.93759073, 0.93759073, 0.93759073, ..., 0.93759073,
                 0.93759073, 0.93759073],
                [0.96662617, 0.96662617, 0.96662617, ..., 0.96662617,
                 0.96662617, 0.96662617]],
      
               [[0.39926292, 0.39926292, 0.39926292, ..., 0.39926292,
                 0.39926292, 0.39926292],
                [0.51119935, 0.51119935, 0.51119935, ..., 0.51119935,
                 0.51119935, 0.51119935],
                [0.31735935, 0.31735935, 0.31735935, ..., 0.31735935,
                 0.31735935, 0.31735935],
                [0.47265388, 0.47265388, 0.47265388, ..., 0.47265388,
                 0.47265388, 0.47265388]],
      
               ...,
      
               [[0.37896278, 0.37896278, 0.37896278, ..., 0.37896278,
                 0.37896278, 0.37896278],
                [0.48984868, 0.48984868, 0.48984868, ..., 0.48984868,
                 0.48984868, 0.48984868],
                [0.29914982, 0.29914982, 0.29914982, ..., 0.29914982,
                 0.29914982, 0.29914982],
                [0.4514263 , 0.4514263 , 0.4514263 , ..., 0.4514263 ,
                 0.4514263 , 0.4514263 ]],
      
               [[0.705035  , 0.705035  , 0.705035  , ..., 0.705035  ,
                 0.705035  , 0.705035  ],
                [0.78996805, 0.78996805, 0.78996805, ..., 0.78996805,
                 0.78996805, 0.78996805],
                [0.62574232, 0.62574232, 0.62574232, ..., 0.62574232,
                 0.62574232, 0.62574232],
                [0.7632235 , 0.7632235 , 0.7632235 , ..., 0.7632235 ,
                 0.7632235 , 0.7632235 ]],
      
               [[0.91593476, 0.91593476, 0.91593476, ..., 0.91593476,
                 0.91593476, 0.91593476],
                [0.94488775, 0.94488775, 0.94488775, ..., 0.94488775,
                 0.94488775, 0.94488775],
                [0.88400907, 0.88400907, 0.88400907, ..., 0.88400907,
                 0.88400907, 0.88400907],
                [0.93627877, 0.93627877, 0.93627877, ..., 0.93627877,
                 0.93627877, 0.93627877]]],
      
      
              [[[0.24987052, 0.24987052, 0.24987052, ..., 0.24987052,
                 0.24987052, 0.24987052],
                [0.40970954, 0.40970954, 0.40970954, ..., 0.40970954,
                 0.40970954, 0.40970954],
                [0.22444823, 0.22444823, 0.22444823, ..., 0.22444823,
                 0.22444823, 0.22444823],
                [0.38041695, 0.38041695, 0.38041695, ..., 0.38041695,
                 0.38041695, 0.38041695]],
      
               [[0.98702358, 0.98702358, 0.98702358, ..., 0.98702358,
                 0.98702358, 0.98702358],
                [0.99373005, 0.99373005, 0.99373005, ..., 0.99373005,
                 0.99373005, 0.99373005],
                [0.98509341, 0.98509341, 0.98509341, ..., 0.98509341,
                 0.98509341, 0.98509341],
                [0.99291795, 0.99291795, 0.99291795, ..., 0.99291795,
                 0.99291795, 0.99291795]],
      
               [[0.26946694, 0.26946694, 0.26946694, ..., 0.26946694,
                 0.26946694, 0.26946694],
                [0.4345792 , 0.4345792 , 0.4345792 , ..., 0.4345792 ,
                 0.4345792 , 0.4345792 ],
                [0.24269594, 0.24269594, 0.24269594, ..., 0.24269594,
                 0.24269594, 0.24269594],
                [0.40472766, 0.40472766, 0.40472766, ..., 0.40472766,
                 0.40472766, 0.40472766]],
      
               ...,
      
               [[0.36534672, 0.36534672, 0.36534672, ..., 0.36534672,
                 0.36534672, 0.36534672],
                [0.5453512 , 0.5453512 , 0.5453512 , ..., 0.5453512 ,
                 0.5453512 , 0.5453512 ],
                [0.33339745, 0.33339745, 0.33339745, ..., 0.33339745,
                 0.33339745, 0.33339745],
                [0.51481869, 0.51481869, 0.51481869, ..., 0.51481869,
                 0.51481869, 0.51481869]],
      
               [[0.52204904, 0.52204904, 0.52204904, ..., 0.52204904,
                 0.52204904, 0.52204904],
                [0.69474347, 0.69474347, 0.69474347, ..., 0.69474347,
                 0.69474347, 0.69474347],
                [0.48690967, 0.48690967, 0.48690967, ..., 0.48690967,
                 0.48690967, 0.48690967],
                [0.66813845, 0.66813845, 0.66813845, ..., 0.66813845,
                 0.66813845, 0.66813845]],
      
               [[0.78400761, 0.78400761, 0.78400761, ..., 0.78400761,
                 0.78400761, 0.78400761],
                [0.88322307, 0.88322307, 0.88322307, ..., 0.88322307,
                 0.88322307, 0.88322307],
                [0.75924576, 0.75924576, 0.75924576, ..., 0.75924576,
                 0.75924576, 0.75924576],
                [0.8699707 , 0.8699707 , 0.8699707 , ..., 0.8699707 ,
                 0.8699707 , 0.8699707 ]]],
      
      
              [[[0.38820285, 0.38820285, 0.38820285, ..., 0.38820285,
                 0.38820285, 0.38820285],
                [0.55787864, 0.55787864, 0.55787864, ..., 0.55787864,
                 0.55787864, 0.55787864],
                [0.3158555 , 0.3158555 , 0.3158555 , ..., 0.3158555 ,
                 0.3158555 , 0.3158555 ],
                [0.49478664, 0.49478664, 0.49478664, ..., 0.49478664,
                 0.49478664, 0.49478664]],
      
               [[0.94240611, 0.94240611, 0.94240611, ..., 0.94240611,
                 0.94240611, 0.94240611],
                [0.97018426, 0.97018426, 0.97018426, ..., 0.97018426,
                 0.97018426, 0.97018426],
                [0.92251421, 0.92251421, 0.92251421, ..., 0.92251421,
                 0.92251421, 0.92251421],
                [0.96191253, 0.96191253, 0.96191253, ..., 0.96191253,
                 0.96191253, 0.96191253]],
      
               [[0.33664455, 0.33664455, 0.33664455, ..., 0.33664455,
                 0.33664455, 0.33664455],
                [0.50228659, 0.50228659, 0.50228659, ..., 0.50228659,
                 0.50228659, 0.50228659],
                [0.26967051, 0.26967051, 0.26967051, ..., 0.26967051,
                 0.26967051, 0.26967051],
                [0.43923563, 0.43923563, 0.43923563, ..., 0.43923563,
                 0.43923563, 0.43923563]],
      
               ...,
      
               [[0.37365979, 0.37365979, 0.37365979, ..., 0.37365979,
                 0.37365979, 0.37365979],
                [0.5426168 , 0.5426168 , 0.5426168 , ..., 0.5426168 ,
                 0.5426168 , 0.5426168 ],
                [0.30268184, 0.30268184, 0.30268184, ..., 0.30268184,
                 0.30268184, 0.30268184],
                [0.47937935, 0.47937935, 0.47937935, ..., 0.47937935,
                 0.47937935, 0.47937935]],
      
               [[0.66183669, 0.66183669, 0.66183669, ..., 0.66183669,
                 0.66183669, 0.66183669],
                [0.79558406, 0.79558406, 0.79558406, ..., 0.79558406,
                 0.79558406, 0.79558406],
                [0.58746081, 0.58746081, 0.58746081, ..., 0.58746081,
                 0.58746081, 0.58746081],
                [0.7512908 , 0.7512908 , 0.7512908 , ..., 0.7512908 ,
                 0.7512908 , 0.7512908 ]],
      
               [[0.91187914, 0.91187914, 0.91187914, ..., 0.91187914,
                 0.91187914, 0.91187914],
                [0.95365674, 0.95365674, 0.95365674, ..., 0.95365674,
                 0.95365674, 0.95365674],
                [0.88275549, 0.88275549, 0.88275549, ..., 0.88275549,
                 0.88275549, 0.88275549],
                [0.94107829, 0.94107829, 0.94107829, ..., 0.94107829,
                 0.94107829, 0.94107829]]]]])
  • created_at :
    2020-06-04T22:45:38.724507
    arviz_version :
    0.8.3
    inference_library :
    pymc3
    inference_library_version :
    3.8

The code combines two stackoverflow answers: reshaping tricks and changing indexing dimensions. They are quite detailed and should help understanding what are the different steps doing.


With ArviZ>=0.8.0, we can also automatically reshape several groups at once. For instance, observed and constant data or log_likelihood could potentially benefit from the reshape too, so here we go. We start with

In [23]:
idata_11_4.log_likelihood
Out[23]:
Show/Hide data repr Show/Hide attributes
xarray.Dataset
    • chain: 4
    • draw: 500
    • experiment: 504
    • chain
      (chain)
      int64
      0 1 2 3
      array([0, 1, 2, 3])
    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499
      array([  0,   1,   2, ..., 497, 498, 499])
    • experiment
      (experiment)
      int64
      0 1 2 3 4 5 ... 499 500 501 502 503
      array([  0,   1,   2, ..., 501, 502, 503])
    • pulled_left
      (chain, draw, experiment)
      float64
      -0.5873 -0.8115 ... -0.1247 -0.1247
      array([[[-0.58729495, -0.8115452 , -0.80748816, ..., -0.20072047,
               -0.20072047, -0.20072047],
              [-0.39601759, -1.11777939, -0.61703047, ..., -0.13521336,
               -0.13521336, -0.13521336],
              [-0.29869649, -1.35396083, -0.46467599, ..., -0.23424343,
               -0.23424343, -0.23424343],
              ...,
              [-0.53003026, -0.88815809, -0.70858513, ..., -0.24621041,
               -0.24621041, -0.24621041],
              [-0.42863549, -1.05382248, -0.58772275, ..., -0.21448582,
               -0.21448582, -0.21448582],
              [-0.32766904, -1.27511611, -0.83387688, ..., -0.14334278,
               -0.14334278, -0.14334278]],
      
             [[-0.3457474 , -1.22994458, -0.68754153, ..., -0.28392784,
               -0.28392784, -0.28392784],
              [-0.45625937, -1.00416466, -0.70515484, ..., -0.20129317,
               -0.20129317, -0.20129317],
              [-0.48405177, -0.95784554, -0.95793167, ..., -0.27056056,
               -0.27056056, -0.27056056],
              ...,
              [-0.52922474, -0.88931164, -0.63775789, ..., -0.35044304,
               -0.35044304, -0.35044304],
              [-0.32675508, -1.27747718, -0.67527049, ..., -0.16623084,
               -0.16623084, -0.16623084],
              [-0.39903957, -1.11158857, -0.8349172 , ..., -0.13358791,
               -0.13358791, -0.13358791]],
      
             [[-0.44805773, -1.01851119, -0.62375708, ..., -0.31942569,
               -0.31942569, -0.31942569],
              [-0.55472237, -0.85385989, -0.61300373, ..., -0.13134661,
               -0.13134661, -0.13134661],
              [-0.50912919, -0.9188408 , -0.93267193, ..., -0.33270694,
               -0.33270694, -0.33270694],
              ...,
              [-0.5359767 , -0.87971183, -0.87828266, ..., -0.23943869,
               -0.23943869, -0.23943869],
              [-0.39460863, -1.12068537, -0.82003483, ..., -0.14980638,
               -0.14980638, -0.14980638],
              [-0.57838375, -0.82280957, -0.61122236, ..., -0.24150433,
               -0.24150433, -0.24150433]],
      
             [[-0.41374012, -1.0822649 , -0.84581265, ..., -0.26869439,
               -0.26869439, -0.26869439],
              [-0.62452106, -0.76683214, -0.87950054, ..., -0.13015929,
               -0.13015929, -0.13015929],
              [-0.56593762, -0.83893044, -0.8466829 , ..., -0.13487459,
               -0.13487459, -0.13487459],
              ...,
              [-0.44612699, -1.02193596, -0.63378736, ..., -0.12328795,
               -0.12328795, -0.12328795],
              [-0.28750944, -1.38681243, -0.52714056, ..., -0.27542976,
               -0.27542976, -0.27542976],
              [-0.4913545 , -0.94622727, -0.81617085, ..., -0.12470703,
               -0.12470703, -0.12470703]]])
  • created_at :
    2020-06-04T22:45:38.960981
    arviz_version :
    0.8.3
    inference_library :
    pymc3
    inference_library_version :
    3.8
In [24]:
# these do not have actor and treatment dims so we can skip all crazy renaming
def reshape_experiment_dim(ds, multi_idx):
    ds["experiment"] = multi_idx
    return ds.unstack("experiment")
In [25]:
multi_idx = pd.MultiIndex.from_frame(
    d[["actor", "treatment", "repetition"]] # no renamig here either
)
idata_11_4 = idata_11_4.map(
    reshape_experiment_dim, 
    groups=("constant_data", "observed_data", "log_likelihood"), 
    args=(multi_idx,)
)
In [26]:
idata_11_4.log_likelihood
Out[26]:
Show/Hide data repr Show/Hide attributes
xarray.Dataset
    • actor: 7
    • chain: 4
    • draw: 500
    • repetition: 18
    • treatment: 4
    • chain
      (chain)
      int64
      0 1 2 3
      array([0, 1, 2, 3])
    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499
      array([  0,   1,   2, ..., 497, 498, 499])
    • actor
      (actor)
      int64
      0 1 2 3 4 5 6
      array([0, 1, 2, 3, 4, 5, 6])
    • treatment
      (treatment)
      int64
      0 1 2 3
      array([0, 1, 2, 3])
    • repetition
      (repetition)
      int64
      0 1 2 3 4 5 6 ... 12 13 14 15 16 17
      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17])
    • pulled_left
      (chain, draw, actor, treatment, repetition)
      float64
      -0.5873 -0.8115 ... -0.06073
      array([[[[[-5.87294954e-01, -8.11545196e-01, -5.87294954e-01, ...,
                 -5.87294954e-01, -5.87294954e-01, -5.87294954e-01],
                [-8.07488156e-01, -5.90548869e-01, -5.90548869e-01, ...,
                 -5.90548869e-01, -5.90548869e-01, -5.90548869e-01],
                [-1.15230173e+00, -3.79664032e-01, -3.79664032e-01, ...,
                 -3.79664032e-01, -3.79664032e-01, -3.79664032e-01],
                [-6.05433084e-01, -6.05433084e-01, -6.05433084e-01, ...,
                 -6.05433084e-01, -6.05433084e-01, -7.89301276e-01]],
      
               [[-4.49259596e-02, -4.49259596e-02, -4.49259596e-02, ...,
                 -4.49259596e-02, -4.49259596e-02, -4.49259596e-02],
                [-2.91301267e-02, -2.91301267e-02, -2.91301267e-02, ...,
                 -2.91301267e-02, -2.91301267e-02, -2.91301267e-02],
                [-7.65122078e-02, -7.65122078e-02, -7.65122078e-02, ...,
                 -7.65122078e-02, -7.65122078e-02, -7.65122078e-02],
                [-4.31857355e-02, -4.31857355e-02, -4.31857355e-02, ...,
                 -4.31857355e-02, -4.31857355e-02, -4.31857355e-02]],
      
               [[-4.78369053e-01, -4.78369053e-01, -9.67040537e-01, ...,
                 -4.78369053e-01, -9.67040537e-01, -9.67040537e-01],
                [-6.69687994e-01, -6.69687994e-01, -6.69687994e-01, ...,
                 -7.17169948e-01, -7.17169948e-01, -7.17169948e-01],
                [-3.03429241e-01, -3.03429241e-01, -1.34048818e+00, ...,
                 -3.03429241e-01, -1.34048818e+00, -3.03429241e-01],
                [-4.93915321e-01, -4.93915321e-01, -4.93915321e-01, ...,
                 -9.42204755e-01, -4.93915321e-01, -9.42204755e-01]],
      
               ...,
      
               [[-5.45081494e-01, -8.67011478e-01, -5.45081494e-01, ...,
                 -5.45081494e-01, -8.67011478e-01, -5.45081494e-01],
                [-6.35294210e-01, -6.35294210e-01, -6.35294210e-01, ...,
                 -7.54553756e-01, -7.54553756e-01, -6.35294210e-01],
                [-1.22014198e+00, -3.49824539e-01, -3.49824539e-01, ...,
                 -1.22014198e+00, -3.49824539e-01, -3.49824539e-01],
                [-5.62249313e-01, -5.62249313e-01, -5.62249313e-01, ...,
                 -8.43797247e-01, -8.43797247e-01, -8.43797247e-01]],
      
               [[-1.15266520e+00, -1.15266520e+00, -3.79496228e-01, ...,
                 -3.79496228e-01, -1.15266520e+00, -3.79496228e-01],
                [-2.59977122e-01, -2.59977122e-01, -1.47433562e+00, ...,
                 -2.59977122e-01, -2.59977122e-01, -2.59977122e-01],
                [-8.11840527e-01, -8.11840527e-01, -8.11840527e-01, ...,
                 -5.87059012e-01, -5.87059012e-01, -8.11840527e-01],
                [-3.66919111e-01, -3.66919111e-01, -1.18047013e+00, ...,
                 -1.18047013e+00, -3.66919111e-01, -3.66919111e-01]],
      
               [[-1.20847792e-01, -2.17303891e+00, -1.20847792e-01, ...,
                 -1.20847792e-01, -2.17303891e+00, -1.20847792e-01],
                [-7.93934051e-02, -7.93934051e-02, -2.57277405e+00, ...,
                 -7.93934051e-02, -7.93934051e-02, -7.93934051e-02],
                [-2.00720471e-01, -2.00720471e-01, -2.00720471e-01, ...,
                 -2.00720471e-01, -2.00720471e-01, -2.00720471e-01],
                [-1.16332453e-01, -1.16332453e-01, -1.16332453e-01, ...,
                 -1.16332453e-01, -1.16332453e-01, -1.16332453e-01]]],
      
      
              [[[-3.96017588e-01, -1.11777939e+00, -3.96017588e-01, ...,
                 -3.96017588e-01, -3.96017588e-01, -3.96017588e-01],
                [-6.17030472e-01, -7.75538526e-01, -7.75538526e-01, ...,
                 -7.75538526e-01, -7.75538526e-01, -7.75538526e-01],
                [-1.31378262e+00, -3.13070115e-01, -3.13070115e-01, ...,
                 -3.13070115e-01, -3.13070115e-01, -3.13070115e-01],
                [-7.03085022e-01, -7.03085022e-01, -7.03085022e-01, ...,
                 -7.03085022e-01, -7.03085022e-01, -6.83307129e-01]],
      
               [[-4.69302641e-03, -4.69302641e-03, -4.69302641e-03, ...,
                 -4.69302641e-03, -4.69302641e-03, -4.69302641e-03],
                [-2.67469059e-03, -2.67469059e-03, -2.67469059e-03, ...,
                 -2.67469059e-03, -2.67469059e-03, -2.67469059e-03],
                [-6.19829993e-03, -6.19829993e-03, -6.19829993e-03, ...,
                 -6.19829993e-03, -6.19829993e-03, -6.19829993e-03],
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              ...,
      
      
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               ...,
      
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               ...,
      
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               ...,
      
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              ...,
      
      
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               ...,
      
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               ...,
      
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               ...,
      
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               ...,
      
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  • created_at :
    2020-06-04T22:45:38.960981
    arviz_version :
    0.8.3
    inference_library :
    pymc3
    inference_library_version :
    3.8
In [ ]: