Original question: https://discourse.pymc.io/t/11-16-rethinking-code/5181
Contains the observed data and the sampling of the PyMC3 model
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)
az.style.use("arviz-darkgrid")
az.rcParams["stats.hdi_prob"] = 0.89 # name was changed in latest ArviZ
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"]]
| 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
actor_idx, actors = pd.factorize(d.actor)
treat_idx, treatments = pd.factorize(d.treatment)
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]
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)
| 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
idata_11_4.posterior["p"].shape
(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?
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):
actor-treatment (a reshape could be enough if properly ordered) but with unsorted and ragged data things can get out of control.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.actor-treatmentIt 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¶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]
p_mu
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]])
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:
idata_11_4.posterior
array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array([0, 1, 2, 3, 4, 5, 6])
array(['treatment 1', 'treatment 2', 'treatment 3', 'treatment 4'],
dtype='<U11')array([ 0, 1, 2, ..., 501, 502, 503])
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]]])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]]])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]]])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
p_mu_samples = logistic(idata_11_4.posterior["a"]+ idata_11_4.posterior["b"])
p_mu_samples
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]]]])array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array([0, 1, 2, 3, 4, 5, 6])
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
p_mu_az = p_mu_samples.mean(dim=("chain", "draw"))
p_mu_az
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]])array([0, 1, 2, 3, 4, 5, 6])
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.
np.allclose(p_mu, p_mu_az.values) # compare means
True
np.allclose(p_post.reshape((4,-1,7,4)), p_mu_samples) # compare all samples, requires reshaping p_post
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.
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.
def get_mask(actor, treatment):
return (actor == actor_idx) & (treatment == treat_idx)
Example 1: actor 2 and treatment 1
mask_2_1 = get_mask(actor=2, treatment=1)
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
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]]])array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array([145, 146, 147, 150, 152, 153, 156, 160, 161, 162, 166, 167, 169, 170,
173, 176, 177, 179])np.allclose(da_2_1.values, p_post.reshape((4,-1,7,4))[:,:,2,1,None])
True
np.allclose(da_2_1.values, p_mu_samples.isel(actor=2, treatment=1).values[:,:,None])
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
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
d["repetition"] = d.groupby(["actor", "treatment"]).cumcount()
d
| 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
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
array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array([0, 1, 2, 3, 4, 5, 6])
array(['treatment 1', 'treatment 2', 'treatment 3', 'treatment 4'],
dtype='<U11')array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17])
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]]])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]]])array([[[[[0.4441712 , 0.4441712 , 0.4441712 , ..., 0.4441712 ,
0.4441712 , 0.4441712 ],
[0.55402312, 0.55402312, 0.55402312, ..., 0.55402312,
0.55402312, 0.55402312],
[0.3159088 , 0.3159088 , 0.3159088 , ..., 0.3159088 ,
0.3159088 , 0.3159088 ],
[0.45416202, 0.45416202, 0.45416202, ..., 0.45416202,
0.45416202, 0.45416202]],
[[0.95606827, 0.95606827, 0.95606827, ..., 0.95606827,
0.95606827, 0.95606827],
[0.97129007, 0.97129007, 0.97129007, ..., 0.97129007,
0.97129007, 0.97129007],
[0.92634161, 0.92634161, 0.92634161, ..., 0.92634161,
0.92634161, 0.92634161],
[0.95773349, 0.95773349, 0.95773349, ..., 0.95773349,
0.95773349, 0.95773349]],
[[0.38020658, 0.38020658, 0.38020658, ..., 0.38020658,
0.38020658, 0.38020658],
[0.48813174, 0.48813174, 0.48813174, ..., 0.48813174,
0.48813174, 0.48813174],
[0.26171787, 0.26171787, 0.26171787, ..., 0.26171787,
0.26171787, 0.26171787],
[0.38976755, 0.38976755, 0.38976755, ..., 0.38976755,
0.38976755, 0.38976755]],
...,
[[0.42020547, 0.42020547, 0.42020547, ..., 0.42020547,
0.42020547, 0.42020547],
[0.5297796 , 0.5297796 , 0.5297796 , ..., 0.5297796 ,
0.5297796 , 0.5297796 ],
[0.29518825, 0.29518825, 0.29518825, ..., 0.29518825,
0.29518825, 0.29518825],
[0.43007432, 0.43007432, 0.43007432, ..., 0.43007432,
0.43007432, 0.43007432]],
[[0.68420601, 0.68420601, 0.68420601, ..., 0.68420601,
0.68420601, 0.68420601],
[0.77106923, 0.77106923, 0.77106923, ..., 0.77106923,
0.77106923, 0.77106923],
[0.55595995, 0.55595995, 0.55595995, ..., 0.55595995,
0.55595995, 0.55595995],
[0.69286569, 0.69286569, 0.69286569, ..., 0.69286569,
0.69286569, 0.69286569]],
[[0.88616883, 0.88616883, 0.88616883, ..., 0.88616883,
0.88616883, 0.88616883],
[0.92367647, 0.92367647, 0.92367647, ..., 0.92367647,
0.92367647, 0.92367647],
[0.81814109, 0.81814109, 0.81814109, ..., 0.81814109,
0.81814109, 0.81814109],
[0.89017923, 0.89017923, 0.89017923, ..., 0.89017923,
0.89017923, 0.89017923]]],
[[[0.32700514, 0.32700514, 0.32700514, ..., 0.32700514,
0.32700514, 0.32700514],
[0.46045575, 0.46045575, 0.46045575, ..., 0.46045575,
0.46045575, 0.46045575],
[0.26880136, 0.26880136, 0.26880136, ..., 0.26880136,
0.26880136, 0.26880136],
[0.50494431, 0.50494431, 0.50494431, ..., 0.50494431,
0.50494431, 0.50494431]],
[[0.99531797, 0.99531797, 0.99531797, ..., 0.99531797,
0.99531797, 0.99531797],
[0.99732888, 0.99732888, 0.99732888, ..., 0.99732888,
0.99732888, 0.99732888],
[0.99382087, 0.99382087, 0.99382087, ..., 0.99382087,
0.99382087, 0.99382087],
[0.99776409, 0.99776409, 0.99776409, ..., 0.99776409,
0.99776409, 0.99776409]],
[[0.26036758, 0.26036758, 0.26036758, ..., 0.26036758,
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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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0.48984868, 0.48984868],
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0.29914982, 0.29914982],
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0.705035 , 0.705035 ],
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0.62574232, 0.62574232],
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0.91593476, 0.91593476],
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0.88400907, 0.88400907],
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0.24987052, 0.24987052],
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0.22444823, 0.22444823],
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0.98702358, 0.98702358],
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0.98509341, 0.98509341],
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0.99291795, 0.99291795]],
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0.26946694, 0.26946694],
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0.4345792 , 0.4345792 ],
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0.24269594, 0.24269594],
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0.40472766, 0.40472766]],
...,
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0.36534672, 0.36534672],
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0.5453512 , 0.5453512 ],
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0.33339745, 0.33339745],
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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]]]]])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
idata_11_4.log_likelihood
array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array([ 0, 1, 2, ..., 501, 502, 503])
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]]])# 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")
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,)
)
idata_11_4.log_likelihood
array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array([0, 1, 2, 3, 4, 5, 6])
array([0, 1, 2, 3])
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17])
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],
[-2.23841044e-03, -2.23841044e-03, -2.23841044e-03, ...,
-2.23841044e-03, -2.23841044e-03, -2.23841044e-03]],
[[-3.01601949e-01, -3.01601949e-01, -1.34566087e+00, ...,
-3.01601949e-01, -1.34566087e+00, -1.34566087e+00],
[-4.81367172e-01, -4.81367172e-01, -4.81367172e-01, ...,
-9.62172345e-01, -9.62172345e-01, -9.62172345e-01],
[-2.36124954e-01, -2.36124954e-01, -1.55913458e+00, ...,
-2.36124954e-01, -1.55913458e+00, -2.36124954e-01],
[-5.53283945e-01, -5.53283945e-01, -5.53283945e-01, ...,
-8.55803170e-01, -5.53283945e-01, -8.55803170e-01]],
...,
[[-4.11047618e-01, -1.08753990e+00, -4.11047618e-01, ...,
-4.11047618e-01, -1.08753990e+00, -4.11047618e-01],
[-7.51368464e-01, -7.51368464e-01, -7.51368464e-01, ...,
-6.38129927e-01, -6.38129927e-01, -7.51368464e-01],
[-1.28088440e+00, -3.25441417e-01, -3.25441417e-01, ...,
-1.28088440e+00, -3.25441417e-01, -3.25441417e-01],
[-7.26199688e-01, -7.26199688e-01, -7.26199688e-01, ...,
-6.61152278e-01, -6.61152278e-01, -6.61152278e-01]],
[[-8.73035366e-01, -8.73035366e-01, -5.40738256e-01, ...,
-5.40738256e-01, -8.73035366e-01, -5.40738256e-01],
[-3.42441937e-01, -3.42441937e-01, -1.23799279e+00, ...,
-3.42441937e-01, -3.42441937e-01, -3.42441937e-01],
[-7.20176071e-01, -7.20176071e-01, -7.20176071e-01, ...,
-6.66829666e-01, -6.66829666e-01, -7.20176071e-01],
[-2.93933727e-01, -2.93933727e-01, -1.36777053e+00, ...,
-1.36777053e+00, -2.93933727e-01, -2.93933727e-01]],
[[-1.03943721e-01, -2.31542739e+00, -1.03943721e-01, ...,
-1.03943721e-01, -2.31542739e+00, -1.03943721e-01],
[-6.04983558e-02, -6.04983558e-02, -2.83523577e+00, ...,
-6.04983558e-02, -6.04983558e-02, -6.04983558e-02],
[-1.35213360e-01, -1.35213360e-01, -1.35213360e-01, ...,
-1.35213360e-01, -1.35213360e-01, -1.35213360e-01],
[-5.08658209e-02, -5.08658209e-02, -5.08658209e-02, ...,
-5.08658209e-02, -5.08658209e-02, -5.08658209e-02]]],
[[[-2.98696490e-01, -1.35396083e+00, -2.98696490e-01, ...,
-2.98696490e-01, -2.98696490e-01, -2.98696490e-01],
[-4.64675993e-01, -9.89772211e-01, -9.89772211e-01, ...,
-9.89772211e-01, -9.89772211e-01, -9.89772211e-01],
[-1.37360473e+00, -2.91947989e-01, -2.91947989e-01, ...,
-2.91947989e-01, -2.91947989e-01, -2.91947989e-01],
[-4.89204521e-01, -4.89204521e-01, -4.89204521e-01, ...,
-4.89204521e-01, -4.89204521e-01, -9.49624995e-01]],
[[-1.02869391e-01, -1.02869391e-01, -1.02869391e-01, ...,
-1.02869391e-01, -1.02869391e-01, -1.02869391e-01],
[-6.18122927e-02, -6.18122927e-02, -6.18122927e-02, ...,
-6.18122927e-02, -6.18122927e-02, -6.18122927e-02],
[-1.05480321e-01, -1.05480321e-01, -1.05480321e-01, ...,
-1.05480321e-01, -1.05480321e-01, -1.05480321e-01],
[-5.80512260e-02, -5.80512260e-02, -5.80512260e-02, ...,
-5.80512260e-02, -5.80512260e-02, -5.80512260e-02]],
[[-4.50665113e-01, -4.50665113e-01, -1.01391513e+00, ...,
-4.50665113e-01, -1.01391513e+00, -1.01391513e+00],
[-6.76743026e-01, -6.76743026e-01, -6.76743026e-01, ...,
-7.09824926e-01, -7.09824926e-01, -7.09824926e-01],
[-4.41170379e-01, -4.41170379e-01, -1.03081280e+00, ...,
-4.41170379e-01, -1.03081280e+00, -4.41170379e-01],
[-7.09068869e-01, -7.09068869e-01, -7.09068869e-01, ...,
-6.77475025e-01, -7.09068869e-01, -6.77475025e-01]],
...,
[[-4.62207992e-01, -9.93958570e-01, -4.62207992e-01, ...,
-4.62207992e-01, -9.93958570e-01, -4.62207992e-01],
[-6.93938723e-01, -6.93938723e-01, -6.93938723e-01, ...,
-6.92356264e-01, -6.92356264e-01, -6.93938723e-01],
[-1.01066392e+00, -4.52520942e-01, -4.52520942e-01, ...,
-1.01066392e+00, -4.52520942e-01, -4.52520942e-01],
[-7.25191336e-01, -7.25191336e-01, -7.25191336e-01, ...,
-6.62098051e-01, -6.62098051e-01, -6.62098051e-01]],
[[-8.62305228e-01, -8.62305228e-01, -5.48506239e-01, ...,
-5.48506239e-01, -8.62305228e-01, -5.48506239e-01],
[-3.57675335e-01, -3.57675335e-01, -1.20164244e+00, ...,
-3.57675335e-01, -3.57675335e-01, -3.57675335e-01],
[-8.47140450e-01, -8.47140450e-01, -8.47140450e-01, ...,
-5.59733862e-01, -5.59733862e-01, -8.47140450e-01],
[-3.38663320e-01, -3.38663320e-01, -1.24730617e+00, ...,
-1.24730617e+00, -3.38663320e-01, -3.38663320e-01]],
[[-2.28789127e-01, -1.58716904e+00, -2.28789127e-01, ...,
-2.28789127e-01, -1.58716904e+00, -2.28789127e-01],
[-1.40884200e-01, -1.40884200e-01, -2.02943223e+00, ...,
-1.40884200e-01, -1.40884200e-01, -1.40884200e-01],
[-2.34243425e-01, -2.34243425e-01, -2.34243425e-01, ...,
-2.34243425e-01, -2.34243425e-01, -2.34243425e-01],
[-1.32620110e-01, -1.32620110e-01, -1.32620110e-01, ...,
-1.32620110e-01, -1.32620110e-01, -1.32620110e-01]]],
...,
[[[-5.30030262e-01, -8.88158085e-01, -5.30030262e-01, ...,
-5.30030262e-01, -5.30030262e-01, -5.30030262e-01],
[-7.08585130e-01, -6.77943942e-01, -6.77943942e-01, ...,
-6.77943942e-01, -6.77943942e-01, -6.77943942e-01],
[-1.06799399e+00, -4.21133142e-01, -4.21133142e-01, ...,
-4.21133142e-01, -4.21133142e-01, -4.21133142e-01],
[-9.55092216e-01, -9.55092216e-01, -9.55092216e-01, ...,
-9.55092216e-01, -9.55092216e-01, -4.85769923e-01]],
[[-2.60813555e-02, -2.60813555e-02, -2.60813555e-02, ...,
-2.60813555e-02, -2.60813555e-02, -2.60813555e-02],
[-1.77543474e-02, -1.77543474e-02, -1.77543474e-02, ...,
-1.77543474e-02, -1.77543474e-02, -1.77543474e-02],
[-3.46619220e-02, -3.46619220e-02, -3.46619220e-02, ...,
-3.46619220e-02, -3.46619220e-02, -3.46619220e-02],
[-1.14855685e-02, -1.14855685e-02, -1.14855685e-02, ...,
-1.14855685e-02, -1.14855685e-02, -1.14855685e-02]],
[[-3.72406390e-01, -3.72406390e-01, -1.16820083e+00, ...,
-3.72406390e-01, -1.16820083e+00, -1.16820083e+00],
[-5.10201788e-01, -5.10201788e-01, -5.10201788e-01, ...,
-9.17227216e-01, -9.17227216e-01, -9.17227216e-01],
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-2.91221920e-01, -1.37574939e+00, -2.91221920e-01],
[-7.09100274e-01, -7.09100274e-01, -7.09100274e-01, ...,
-6.77444597e-01, -7.09100274e-01, -6.77444597e-01]],
...,
[[-4.71554374e-01, -9.78250010e-01, -4.71554374e-01, ...,
-4.71554374e-01, -9.78250010e-01, -4.71554374e-01],
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-6.35921198e-01, -6.35921198e-01, -7.53847823e-01],
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-5.45575615e-01, -5.45575615e-01, -5.45575615e-01]],
[[-7.95679052e-01, -7.95679052e-01, -6.00157312e-01, ...,
-6.00157312e-01, -7.95679052e-01, -6.00157312e-01],
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[-3.07135297e-01, -3.07135297e-01, -1.33010715e+00, ...,
-1.33010715e+00, -3.07135297e-01, -3.07135297e-01]],
[[-1.89923084e-01, -1.75459516e+00, -1.89923084e-01, ...,
-1.89923084e-01, -1.75459516e+00, -1.89923084e-01],
[-1.32593122e-01, -1.32593122e-01, -2.08603420e+00, ...,
-1.32593122e-01, -1.32593122e-01, -1.32593122e-01],
[-2.46210409e-01, -2.46210409e-01, -2.46210409e-01, ...,
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