# Prior/posterior comparison [compare_draws()](../../reference/compare_draws.md#tidydraws.compare_draws) is the prior/posterior comparison helper: it calls [parameter_draws()](../../reference/parameter_draws.md#tidydraws.parameter_draws) once per selected group in the ArviZ object, tags each result with a `source` column, and stacks them into a single `DataFrame`. By default it compares `posterior` against `prior`, which is the workflow most users need after fitting a PyMC model. # Full PyMC workflow This example uses the same grouped regression data as the other examples, samples from the model prior before fitting, then compares those prior draws with the fitted posterior. That gives [compare_draws()](../../reference/compare_draws.md#tidydraws.compare_draws) real prior draws and real posterior draws from the same PyMC model. Code ``` python from pathlib import Path import sys import polars as pl import pymc as pm import tidydraws as td import lets_plot as lp import plotnine as p9 for parent in [Path.cwd(), *Path.cwd().parents]: helper_dir = parent / "docs" / "examples" if (helper_dir / "_pymc_workflow.py").exists(): sys.path.insert(0, str(helper_dir)) break from _pymc_workflow import simulate_grouped_regression lp.LetsPlot.setup_html() workflow = simulate_grouped_regression(seed=2026) observed = workflow.observed truth = workflow.truth ``` /home/runner/work/tidydraws/tidydraws/.venv/lib/python3.12/site-packages/lets_plot/plot/annotation.py:551: SyntaxWarning: invalid escape sequence '\(' """ /home/runner/work/tidydraws/tidydraws/.venv/lib/python3.12/site-packages/lets_plot/plot/annotation.py:601: SyntaxWarning: invalid escape sequence '\(' """ Build our PyMC model and fit. ``` python coords = { "groups": workflow.group_names, "obs_ind": observed.get_column("obs_ind").to_numpy(), } with pm.Model(coords=coords) as model: x = pm.Data("x", observed.get_column("x").to_numpy(), dims="obs_ind") group_idx = pm.Data( "group_idx", observed.get_column("group_idx").to_numpy().astype("int64"), dims="obs_ind", ) intercept = pm.Normal("intercept", mu=0.0, sigma=2.0, dims="groups") beta = pm.Normal("beta", mu=0.0, sigma=1.5, dims="groups") sigma = pm.HalfNormal("sigma", sigma=1.0) mu = pm.Deterministic( "mu", intercept[group_idx] + beta[group_idx] * x, dims="obs_ind", ) pm.Normal( "y", mu=mu, sigma=sigma, observed=observed.get_column("y").to_numpy(), dims="obs_ind", ) prior = pm.sample_prior_predictive( draws=800, random_seed=2029, var_names=["intercept", "beta", "sigma"], ) dt = pm.sample( draws=400, random_seed=2030, ) # arviz 1.0+ uses .update(), 0.x uses .extend() try: dt.update(prior) except AttributeError: dt.extend(prior) ``` Sampling: [beta, intercept, sigma] Initializing NUTS using jitter+adapt_diag... Multiprocess sampling (2 chains in 2 jobs) NUTS: [intercept, beta, sigma] ``` ``` Sampling 2 chains for 1_000 tune and 400 draw iterations (2_000 + 800 draws total) took 1 seconds. We recommend running at least 4 chains for robust computation of convergence diagnostics ``` python dt ``` ![](data:image/svg+xml;base64,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) ``` xr-text-repr-fallback Group: / ├── Group: /posterior │ Dimensions: (chain: 2, draw: 400, groups: 4, obs_ind: 96) │ Coordinates: │ * chain (chain) int64 16B 0 1 │ * draw (draw) int64 3kB 0 1 2 3 4 5 6 7 ... 393 394 395 396 397 398 399 │ * groups (groups) array([0, 1]) draw (draw) int64 0 1 2 3 4 5 ... 395 396 397 398 399 array([ 0, 1, 2, ..., 397, 398, 399], shape=(400,)) groups (groups) \ array(['North', 'South', 'East', 'West'], dtype=' array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,90, 91, 92, 93, 94, 95]) Data variables: (4) intercept (chain, draw, groups) float64 -1.425 0.1027 1.356 ... 1.099 2.101 array([[[-1.42525975, 0.10268786, 1.35639638, 2.12421651],[-1.26399267, 0.27530509, 1.20418957, 2.29495807],[-1.16748149, 0.16397921, 1.36157583, 2.15731677],...,[-1.36177207, 0.07647794, 1.23747468, 2.16032094],[-1.32849801, 0.11116353, 1.252087 , 2.21027418],[-1.14555092, 0.24901594, 1.26292019, 1.99356634]],[[-1.23530867, 0.20819445, 1.21595423, 2.13653015],[-1.17972187, -0.03978308, 1.20099138, 2.05810261],[-1.28816385, 0.30912631, 1.14757991, 2.13322889],...,[-1.25701418, 0.20256368, 1.26329494, 1.98888929],[-1.32856911, 0.18058029, 1.17631225, 2.19238307],[-1.39934252, 0.26794775, 1.09949502, 2.1013183 ]]],shape=(2, 400, 4)) beta (chain, draw, groups) float64 0.3943 0.782 ... 1.594 -0.6559 array([[[ 0.3943028 , 0.78200012, 1.38425398, -0.40758734],[ 0.47331785, 0.85141293, 1.47369171, -0.74806885],[ 0.46295417, 0.80226356, 1.50486243, -0.67247063],...,[ 0.30299398, 0.91134107, 1.47359993, -0.59778857],[ 0.48262136, 0.81956869, 1.4233696 , -0.69800193],[ 0.3967954 , 0.80616665, 1.49438534, -0.53911894]],[[ 0.35676385, 0.56861808, 1.41117148, -0.444816 ],[ 0.27601621, 0.73885245, 1.35808901, -0.58269875],[ 0.46822379, 0.78632349, 1.46311471, -0.64377001],...,[ 0.52301078, 0.80054639, 1.40520347, -0.59973873],[ 0.41186177, 0.69630973, 1.41449837, -0.53261835],[ 0.39290277, 0.78616402, 1.59421804, -0.6558692 ]]],shape=(2, 400, 4)) sigma (chain, draw) float64 0.424 0.4397 ... 0.3836 0.5073 array([[0.4240445 , 0.439713 , 0.47616476, 0.39777364, 0.44532509,0.38432567, 0.49271752, 0.48065168, 0.38441036, 0.40927171,0.41082693, 0.40381442, 0.44579514, 0.45576501, 0.42174279,0.43082038, 0.39541882, 0.450192 , 0.45686736, 0.42212526,0.43812352, 0.39207842, 0.44087748, 0.45080686, 0.45636553,0.44077369, 0.42495448, 0.46180355, 0.46180355, 0.4120871 ,0.44046321, 0.44165686, 0.40183561, 0.43968707, 0.41096983,0.40730624, 0.42921844, 0.43127227, 0.43149535, 0.37856602,0.4075648 , 0.43056757, 0.45453049, 0.45073744, 0.47527872,0.40951609, 0.41658321, 0.44252059, 0.42829297, 0.41218125,0.4312769 , 0.45633683, 0.40768132, 0.43538382, 0.48935354,0.41310023, 0.39029743, 0.44545994, 0.45838326, 0.43897983,0.40598199, 0.4328862 , 0.43961603, 0.41442451, 0.37496585,0.44604783, 0.42305968, 0.47361374, 0.43764587, 0.41981994,0.44095389, 0.45959946, 0.48314187, 0.40253944, 0.41340018,0.42639703, 0.43584856, 0.38089662, 0.50712697, 0.46278337,0.46194619, 0.43822187, 0.41644335, 0.36709773, 0.42694708,0.41684698, 0.43597133, 0.36959323, 0.44686673, 0.3943001 ,0.40153176, 0.41924568, 0.39695372, 0.43462357, 0.42286698,0.46363979, 0.42008213, 0.40838297, 0.42478493, 0.4030556 ,...0.40678593, 0.3907325 , 0.39222552, 0.51718638, 0.43333282,0.43333282, 0.44051873, 0.45369008, 0.40799809, 0.51407377,0.46847627, 0.39458619, 0.44628131, 0.3883531 , 0.36697424,0.50362965, 0.43291232, 0.39681165, 0.40640236, 0.40640236,0.40268169, 0.39891569, 0.39337451, 0.38095698, 0.40570618,0.43689266, 0.43625456, 0.4173726 , 0.41188756, 0.44805698,0.43954824, 0.42370099, 0.45199701, 0.41338846, 0.3931166 ,0.41751802, 0.39967521, 0.4384639 , 0.4075343 , 0.45100924,0.39221364, 0.44551695, 0.41106404, 0.42997303, 0.42360003,0.43412439, 0.38204773, 0.38393072, 0.47744034, 0.37986178,0.38976778, 0.36518779, 0.45080071, 0.42172353, 0.42689627,0.45927763, 0.46600061, 0.43500277, 0.40231988, 0.40231988,0.39832815, 0.44696552, 0.36811112, 0.33968925, 0.54240654,0.36960217, 0.47952735, 0.52141767, 0.48251999, 0.50776568,0.44351706, 0.50469158, 0.36668666, 0.41261466, 0.41304503,0.40138721, 0.38628326, 0.49615586, 0.4632036 , 0.38484105,0.44265493, 0.43989783, 0.44669851, 0.47592233, 0.47868492,0.45191661, 0.39121736, 0.44360111, 0.4004799 , 0.42969191,0.42969191, 0.41256408, 0.3913762 , 0.40980777, 0.39891613,0.38539848, 0.49091821, 0.37639848, 0.3835729 , 0.50732525]]) mu (chain, draw, obs_ind) float64 -2.239 -2.138 ... 0.8975 0.6829 array([[[-2.23888378, -2.13770232, -2.13653469, ..., 1.49259925,1.3761031 , 1.2427462 ],[-2.24066029, -2.11920288, -2.11780128, ..., 1.13571403,0.92190184, 0.67714413],[-2.12276418, -2.00396619, -2.00259527, ..., 1.11522343,0.92301863, 0.7029956 ],...,[-1.98698493, -1.90923408, -1.90833685, ..., 1.23395856,1.06309931, 0.86751121],[-2.32436295, -2.20051819, -2.19908904, ..., 1.1286163 ,0.92911418, 0.70073766],[-1.9643183 , -1.86249721, -1.86132221, ..., 1.1581213 ,1.00403094, 0.82763872]],[[-1.97147297, -1.87992432, -1.87886786, ..., 1.44722155,1.32008474, 1.17454714],[-1.74926747, -1.67843935, -1.677622 , ..., 1.15512417,0.98857787, 0.79792695],[-2.25432013, -2.13416991, -2.13278339, ..., 1.13561144,0.95160982, 0.74097723],...,[-2.33622067, -2.20201163, -2.20046288, ..., 1.05950486,0.88808821, 0.69186205],[-2.17842519, -2.07273794, -2.07151833, ..., 1.36701166,1.21477929, 1.04051398],[-2.21007766, -2.10925546, -2.10809198, ..., 1.08495135,0.89749156, 0.68290029]]], shape=(2, 400, 96)) Attributes: (9) created_at : 2026-07-14T15:09:59.014481+00:00 creation_library : ArviZ creation_library_version : 1.2.0 creation_library_language : Python inference_library : pymc inference_library_version : 6.0.1 sample_dims : \['chain', 'draw'\] sampling_time : 0.9929232597351074 tuning_steps : 1000 /sample_stats(29) Dimensions: - chain: 2 - draw: 400 Coordinates: (2) chain (chain) int64 0 1 array([0, 1]) draw (draw) int64 0 1 2 3 4 5 ... 395 396 397 398 399 array([ 0, 1, 2, ..., 397, 398, 399], shape=(400,)) Data variables: (18) lp (chain, draw) float64 -70.2 -70.44 ... -66.69 -72.28 array([[-70.20290403, -70.44205833, -68.71021813, -67.37123104,-67.01993119, -67.45692333, -69.34371697, -67.31646091,-67.96692344, -68.68421005, -65.38822672, -66.65145447,-67.48032875, -67.25137851, -66.27925327, -67.70956398,-66.79085239, -67.73031826, -68.77982582, -73.43263691,-68.84839384, -70.09118801, -68.6164851 , -71.43579776,-68.15907512, -71.12824356, -72.40099518, -66.6419907 ,-66.6419907 , -64.47054908, -66.05814137, -66.28420882,-65.74490547, -65.86013129, -64.90070045, -66.05842214,-66.59434683, -65.98774631, -65.16350325, -74.48567726,-67.41864699, -66.81606048, -65.75437048, -68.11184059,-68.38248189, -64.56339709, -68.94583539, -67.81859052,-65.06663976, -66.17578771, -67.43470597, -67.2636774 ,-67.09594552, -71.94690822, -72.30850565, -68.52931163,-66.31409066, -66.6958543 , -65.82305151, -67.12850177,-70.79613591, -67.95138457, -66.38704008, -66.624966 ,-69.14368327, -66.92709618, -66.64294818, -69.01738988,-66.2735439 , -65.53982912, -69.14079686, -70.28197437,-70.15587605, -72.08431039, -66.34573992, -66.31882749,-67.60723563, -68.2835539 , -70.79378391, -73.42773146,...-65.82187959, -67.05110314, -64.92349353, -66.75394703,-66.82434681, -68.09924036, -71.57228984, -65.41621993,-69.2514816 , -72.76529188, -66.51394883, -66.668 ,-66.32238223, -64.87933547, -68.08806429, -66.35151272,-66.73282938, -67.94226464, -65.51125642, -68.63611884,-69.62086139, -68.38156846, -67.67142001, -65.53529364,-64.60639124, -64.3434201 , -64.45817082, -69.96561245,-69.63953267, -69.87353346, -67.88099398, -68.8254215 ,-69.18597684, -65.02181037, -71.89424676, -70.68152293,-68.73153801, -68.57708508, -65.71781335, -65.71781335,-64.89802758, -70.94261068, -70.62767006, -70.60561969,-74.07602083, -71.80883819, -72.29159445, -73.39869106,-75.56624005, -71.15368589, -68.19250438, -70.59967303,-68.87949425, -67.00576708, -68.92517099, -69.19725611,-71.50516009, -71.32069344, -67.30154524, -67.26648716,-66.37413784, -69.3350566 , -66.76136128, -70.73641875,-69.47626757, -68.27365904, -67.15443581, -67.71944872,-67.04166027, -66.03050034, -66.03050034, -67.0273003 ,-67.31939776, -66.48098042, -67.47544857, -68.19658786,-69.8997449 , -66.61320682, -66.6899584 , -72.27544956]]) max_energy_error (chain, draw) float64 -0.8613 0.4267 ... 0.5838 0.8733 array([[-0.86126044, 0.42669335, 0.67378125, 0.33808142, -0.29784549,-0.23255305, 0.74589927, 0.63077103, 0.46712863, 1.03862835,-0.67344442, 0.26929619, 1.49425919, -0.18844423, 0.41570799,0.43987336, 1.01940856, 0.2584372 , 0.7997954 , 0.82996337,-0.84937359, -0.27284842, -0.36476473, 1.43775203, -0.97397394,0.50871618, -0.70010645, -0.76282403, 0.97452159, -0.50236523,0.63327468, -0.13389152, 0.37296029, 0.55873847, -0.14094388,0.28079939, 0.27038343, -0.16548149, 0.23955659, 1.93737199,2.83873072, -0.21403179, 0.51114375, 0.89557177, -0.26147067,-0.76618342, 0.79858055, -0.50655497, -0.41866183, 0.36945427,0.73647336, -0.44984536, -0.13052881, 0.9287178 , -0.37415736,-1.29917638, -0.55252246, 0.11006113, -0.25929294, 0.6099425 ,0.63721043, -0.55451764, 1.22758048, 0.59933611, 0.94716624,-0.67515359, 0.41342495, 0.54109914, -0.46965742, 0.28894942,0.63404978, 1.29444259, -0.42328615, 0.43091185, -1.09550471,0.51831055, 1.14638435, 0.96247307, 0.71308061, -0.72965924,-1.38648102, 0.51655988, -0.29315613, -0.42190312, 1.23706979,-0.27676453, 0.26511081, -0.37088496, -0.37253212, 0.20747114,0.70411259, 0.43526297, -0.65156251, 0.61077391, -0.3595788 ,0.38038824, -0.66652476, -0.13890378, 0.2403979 , 0.36480563,...0.0710958 , 0.53569007, -0.45466375, 1.66805533, -0.63892578,1.39757369, 0.78212689, -0.48210142, 0.3778667 , 0.57315386,-1.02606438, -0.26941132, -0.54285991, -0.39059868, 1.20317562,-0.48451415, -0.69350405, 0.32611643, -0.17954852, 2.66251547,-0.34322345, 0.24464933, -0.48057945, 0.61950446, 0.3692648 ,0.30301429, 0.63580345, -1.22285914, 0.71839254, 0.90183294,-1.14336986, 0.10663473, -0.44900673, -0.23888021, 1.24102552,0.90558613, 0.22389473, 0.44855281, -0.48277642, 1.10305018,-0.33625325, 1.56906638, 0.24058249, -0.59637513, -0.19771847,1.13254029, 0.81443588, 2.72907233, 0.81690959, -0.4312268 ,-1.10461721, -0.53700291, 2.03625012, -0.75607405, 1.81460021,-0.53078426, 0.89154976, 0.32688055, -0.69065342, 0.79715739,0.22851183, 1.7931604 , -0.78063354, -0.94196794, 0.75211311,-1.09752756, -1.69851122, -0.66402386, 0.2571856 , -1.50957701,-0.39560018, 0.66366653, -0.59005278, -0.26953031, 1.22851544,0.23488299, 0.64739107, -0.60461 , -1.48417602, -0.32302959,-0.33741656, 0.53077414, -0.43009721, 0.69159536, -0.6430472 ,-0.30173357, 0.60103359, 0.37397744, -0.20603267, -0.15019669,0.70860767, 0.93936538, 0.37223678, 1.54724139, 0.21235561,0.40657688, 1.46424477, -0.93838839, 0.58383671, 0.87325621]]) step_size_bar (chain, draw) float64 0.8464 0.8464 ... 0.8697 0.8697 array([[0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 0.84637963, 0.84637963, 0.84637963,0.84637963, 0.84637963, 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0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326,0.86966326, 0.86966326, 0.86966326, 0.86966326, 0.86966326]]) tree_depth (chain, draw) int64 2 3 2 3 3 2 3 2 ... 2 2 2 3 2 3 3 3 array([[2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2,3, 3, 2, 2, 3, 2, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 2,2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 2, 3,3, 3, 3, 3, 2, 3, 3, 2, 2, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 2,2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2, 2, 3, 3,3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2,3, 3, 2, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3,3, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 3, 2, 2, 2, 3, 3, 2,2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2,2, 3, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3,2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 2, 2, 2, 3, 3, 3,2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3,3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 2,2, 2, 3, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3,3, 3, 2, 2, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,3, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3,3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3,3, 3, 2, 3, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3,2, 3, 2, 3],[2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2,2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3,3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2,3, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3,3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3,2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3,3, 3, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2,3, 3, 2, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3,2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3,2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3,2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3,3, 3, 3, 3, 3, 2, 3, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2,3, 3, 3, 2, 3, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2,2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3,3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3,2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3, 2,3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 2, 3, 2, 3, 3, 2,2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3,2, 3, 3, 3]]) divergences (chain, draw) int64 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0]]) reached_max_treedepth (chain, draw) bool False False False ... False False array([[False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,...False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False]]) perf_counter_start (chain, draw) float64 149.5 149.5 149.5 ... 149.8 149.8 array([[149.54704442, 149.54752501, 149.54825475, 149.54865769,149.54945085, 149.55012062, 149.55058966, 149.55132231,149.55176524, 149.55223754, 149.55266661, 149.55313094,149.55359978, 149.55428639, 149.55495282, 149.55544567,149.55613138, 149.55678056, 149.55745085, 149.55811518,149.55855841, 149.5593395 , 149.55981156, 149.56050111,149.56116245, 149.56161323, 149.56212833, 149.56289307,149.56339308, 149.56404668, 149.56451808, 149.56497062,149.56576732, 149.56648522, 149.56722244, 149.56768126,149.5684388 , 149.56910285, 149.56984673, 149.57038073,149.57115605, 149.57191573, 149.57257118, 149.57306802,149.57345951, 149.5738916 , 149.57436225, 149.57479582,149.5754559 , 149.57588582, 149.57634426, 149.57676814,149.5773959 , 149.57814403, 149.57876401, 149.57946799,149.58020176, 149.58095199, 149.58171789, 149.58243343,149.58288522, 149.58357082, 149.58405792, 149.58452124,149.58527273, 149.58571475, 149.58636179, 149.58711162,149.5877499 , 149.58846781, 149.58918869, 149.58963722,149.59038139, 149.5911049 , 149.59153665, 149.59197888,149.59243774, 149.5932112 , 149.59366431, 149.59441751,...149.76868897, 149.76895824, 149.76945581, 149.76973569,149.7700033 , 149.77032476, 149.77059673, 149.77095662,149.77127827, 149.77153726, 149.77194354, 149.77225754,149.77252755, 149.77294112, 149.77326226, 149.77352771,149.77388559, 149.77441284, 149.77469251, 149.77496256,149.77544128, 149.77580982, 149.77612058, 149.77655527,149.77697906, 149.77729821, 149.77755703, 149.77781685,149.77818444, 149.77862892, 149.77908098, 149.77951685,149.77978379, 149.78022715, 149.78049591, 149.78075981,149.78122634, 149.78149538, 149.78192226, 149.78224842,149.78251253, 149.78293283, 149.78325771, 149.7836832 ,149.78395116, 149.78443071, 149.78485713, 149.78534423,149.78561414, 149.78587822, 149.78635611, 149.78662811,149.78707919, 149.78750777, 149.78777267, 149.78806098,149.78849918, 149.78892144, 149.78939124, 149.78980755,149.79029406, 149.79073322, 149.7910029 , 149.7913246 ,149.79174681, 149.79219453, 149.79245141, 149.7927069 ,149.79316091, 149.7935887 , 149.7938474 , 149.79414905,149.79458266, 149.79484782, 149.79515147, 149.79541736,149.79582564, 149.79610835, 149.7965389 , 149.79694496]]) largest_eigval (chain, draw) float64 nan nan nan nan ... nan nan nan nan array([[nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,...nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]]) energy (chain, draw) float64 74.81 76.41 76.34 ... 70.49 74.05 array([[74.81052166, 76.41077639, 76.340561 , 74.26909258, 70.06366055,70.14910388, 74.82861905, 73.48191056, 72.28067376, 74.62012452,71.22862075, 68.57025767, 76.022543 , 70.25776208, 71.61320943,69.40451693, 73.74098989, 70.38334697, 73.78139596, 76.77064228,78.0003689 , 74.11768986, 74.95770369, 78.54881904, 72.08570129,73.94606283, 75.61301706, 75.20746787, 73.71542651, 69.36640092,68.27177027, 67.56454206, 69.99100954, 69.45665677, 67.55233427,67.36869307, 69.32320528, 68.27812367, 68.27471508, 76.08424022,83.76812117, 69.69534266, 70.03173093, 71.68685526, 71.12275411,72.68361582, 70.04501252, 73.06728679, 68.3690856 , 68.18717337,71.55539782, 70.14941857, 69.56981453, 75.34506381, 78.27415972,73.18700426, 71.06563022, 68.93109184, 68.25353361, 70.9787146 ,73.5030499 , 75.02252862, 74.86825983, 70.7331824 , 73.80712976,72.85300795, 70.48220628, 71.94001194, 71.70633263, 69.45985581,70.73130741, 79.00138928, 74.08096564, 76.95981981, 74.545379 ,71.10051721, 72.48386556, 74.48984006, 76.93537501, 77.26166069,75.43506331, 72.67915158, 71.18149938, 71.5404999 , 73.3103641 ,69.08381797, 70.30540245, 71.19993578, 69.12013222, 68.9131357 ,70.92848913, 71.49579862, 69.68331464, 70.26767438, 71.45183689,71.98450251, 70.74818939, 67.65310675, 68.28719161, 69.26276057,...68.41280845, 70.79441606, 70.25606252, 79.3080668 , 73.77648034,76.70164158, 73.15740032, 71.68792137, 73.41028578, 74.4244491 ,74.04702994, 76.32559929, 74.2014958 , 70.6662824 , 76.77225061,74.021474 , 70.64756309, 70.2121721 , 69.92057723, 83.41471016,69.90704324, 69.26173454, 69.0397911 , 69.28970575, 70.15767155,69.90370387, 74.58705937, 73.75162035, 71.33012708, 77.18808988,76.43968016, 68.89321762, 68.46864685, 68.64388833, 71.86095873,72.2707136 , 69.20455429, 71.40772881, 69.60183599, 72.50014535,73.07688517, 75.82632868, 71.94571862, 69.11925206, 66.86607163,70.41745534, 68.83148786, 75.11856056, 76.66320911, 72.90140669,70.43088786, 70.90796644, 78.91970192, 69.42902071, 76.78179921,76.47939933, 77.04442993, 73.24329813, 70.29645343, 70.73321645,67.22886552, 73.87630236, 75.31602752, 77.59372311, 77.84246157,77.14523397, 73.4921686 , 75.84006347, 79.16002339, 78.72865655,73.27716463, 75.3267611 , 73.92431188, 71.83890615, 73.85368508,73.79099364, 77.02978771, 76.97546002, 75.62999948, 70.42147045,69.14218521, 71.90796625, 71.90482816, 72.46586468, 74.25045676,74.1610808 , 72.11084236, 70.6766226 , 70.3098732 , 68.59366011,70.75891422, 70.25187841, 70.94065679, 72.53615679, 69.20225027,70.73697921, 76.34667944, 72.724118 , 70.49081268, 74.04768497]]) diverging (chain, draw) bool False False False ... False False array([[False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,...False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False, False, False, False, False, False,False, False, False, False]]) smallest_eigval (chain, draw) float64 nan nan nan nan ... nan nan nan nan array([[nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,...nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]]) energy_error (chain, draw) float64 0.1848 0.1389 ... 0.06755 0.8733 array([[ 1.84752815e-01, 1.38874632e-01, -9.38469212e-02,-3.37225179e-01, -1.06002363e-01, 9.73883828e-03,4.66819664e-01, -2.64918398e-01, 3.69730584e-02,4.62790712e-01, -6.73444418e-01, 2.17482732e-01,3.51756429e-01, -1.53958595e-02, -2.75479252e-01,2.78051426e-01, -3.61106003e-02, 2.05477945e-01,1.34810451e-01, 8.29963372e-01, -8.49373587e-01,1.25886643e-01, -3.32991828e-01, 5.43184565e-01,-4.49426588e-01, 5.08716178e-01, 2.35023480e-01,-7.62824026e-01, 0.00000000e+00, -5.02365231e-01,3.38707569e-01, 1.46670281e-02, -1.86305521e-01,7.63681552e-02, -1.40943882e-01, 2.01322940e-01,1.09072476e-01, -9.63425319e-02, -1.45866418e-01,1.93737199e+00, -5.98935580e-01, -7.50559511e-02,-6.52875818e-02, 3.04850803e-01, -1.79041869e-02,-7.66183425e-01, 7.98580548e-01, -2.81014969e-01,-4.18661835e-01, 1.53230304e-01, 2.35955614e-01,-3.54946567e-02, 4.11135678e-02, 8.86536458e-01,3.74763214e-02, -6.64223713e-01, -5.52522463e-01,7.78369410e-02, -9.73894464e-02, 2.93749831e-01,...-8.79138178e-02, -4.37549973e-01, -1.97718466e-01,3.17800744e-03, -1.60471753e-01, 7.95951541e-01,2.30719025e-01, 1.52476851e-01, -5.07894035e-01,2.83612618e-01, 5.74254568e-01, -7.56074046e-01,1.41334236e+00, -1.78768787e-01, -2.71445125e-01,7.09093634e-05, -6.90653421e-01, 0.00000000e+00,-1.12632095e-01, 1.08915795e+00, -1.30731342e-02,-9.41967940e-01, 6.77944752e-01, -7.43319527e-02,-3.41754784e-01, -9.15528179e-03, 2.48453248e-01,-5.67696079e-01, -2.25925848e-01, 4.26239102e-01,-5.90052776e-01, -2.69530314e-01, 3.52502519e-01,7.63643377e-02, 5.23592246e-01, -1.07888618e-01,-7.91947685e-01, -5.38316320e-02, -9.54416508e-02,5.30774136e-01, -4.30097206e-01, 4.56516158e-01,-1.83861453e-02, -3.01733571e-01, -2.64999215e-01,1.39945910e-01, -1.35072666e-01, -1.50196688e-01,0.00000000e+00, 3.62121147e-02, -2.18421403e-02,-1.49680976e-01, 2.12355613e-01, 3.44481841e-01,5.93400394e-01, -9.38388391e-01, 6.75539326e-02,8.73256210e-01]]) acceptance_rate (chain, draw) float64 0.8425 0.8179 ... 0.7391 0.5899 array([[0.84252097, 0.81793779, 0.83659244, 0.85409813, 0.99326785,0.93933833, 0.60696617, 0.84406044, 0.86350052, 0.57351619,0.91148942, 0.8128393 , 0.41852126, 0.97018486, 0.86632634,0.84249846, 0.65704535, 0.86167847, 0.68183231, 0.73788286,0.97653638, 0.91695921, 0.97317776, 0.46194962, 1. ,0.79249005, 0.94948722, 0.85450402, 0.62831936, 0.91112803,0.64553909, 0.98989284, 0.81255396, 0.78984377, 0.94714686,0.87612574, 0.84284051, 1. , 0.86265117, 0.40120734,0.39597244, 0.99075312, 0.78529759, 0.64336165, 0.97033022,0.72188771, 0.60477215, 0.97271101, 1. , 0.770714 ,0.65597714, 0.92251396, 0.97793091, 0.50695073, 0.96670137,0.96506709, 0.97383632, 0.94420224, 0.9829886 , 0.65149382,0.74053747, 0.88017964, 0.63807734, 0.81077179, 0.57489266,0.86784935, 0.88556928, 0.75629305, 0.95065771, 0.87678632,0.63272192, 0.50867465, 0.96594002, 0.78275828, 1. ,0.70287937, 0.66023103, 0.79398238, 0.5645933 , 0.86542203,0.95063539, 0.87125184, 0.92047573, 0.91449263, 0.54153054,1. , 0.87714021, 0.93822481, 1. , 0.92809575,0.6403442 , 0.74695183, 1. , 0.66299095, 0.92724805,0.85635034, 0.94242692, 0.98206877, 0.85159286, 0.83985579,...0.98125184, 0.62495682, 1. , 0.29725743, 1. ,0.31211662, 0.6515904 , 0.95193005, 0.82115477, 0.7687715 ,0.92714647, 0.96594038, 1. , 0.90346676, 0.58930389,0.97176833, 0.99295843, 0.90724038, 0.97374741, 0.17889744,0.91994282, 0.87272523, 0.92610665, 0.69735589, 0.841242 ,0.84258283, 0.69474913, 0.90847682, 0.63297926, 0.56113527,0.8969278 , 0.94018679, 0.97743278, 0.87531504, 0.58352778,0.62926779, 0.87512357, 0.7779887 , 0.94512344, 0.49843034,0.95152874, 0.64333455, 0.93758128, 0.97546374, 0.95724982,0.57259787, 0.68610787, 0.33656057, 0.68554365, 0.97070882,1. , 0.9176861 , 0.4610669 , 1. , 0.2085628 ,0.98010383, 0.80333994, 0.92597644, 0.95536926, 0.45372806,0.92467013, 0.34780128, 0.98084689, 0.86572746, 0.67984174,1. , 1. , 1. , 0.851077 , 1. ,0.97678692, 0.69751795, 0.98080836, 1. , 0.6123234 ,0.90684409, 0.66923244, 0.98161926, 0.83762015, 0.92699382,0.95339459, 0.72131348, 0.90744782, 0.76185881, 0.90486462,0.92593693, 0.84941489, 0.86242439, 0.98670698, 1. ,0.57654661, 0.78907126, 0.85808381, 0.6538115 , 0.93622569,0.88836862, 0.52436083, 0.8963412 , 0.73906767, 0.58992606]]) perf_counter_diff (chain, draw) float64 0.0003356 0.0005926 ... 0.0003956 array([[0.00033557, 0.00059258, 0.00028004, 0.00066851, 0.00051988,0.0003288 , 0.00061685, 0.0003298 , 0.00035557, 0.00031934,0.00032193, 0.00033677, 0.0005726 , 0.00055258, 0.00036561,0.00053038, 0.00053848, 0.00055602, 0.00050948, 0.00031386,0.00066122, 0.0003388 , 0.00057677, 0.00053102, 0.00033129,0.00035013, 0.00064479, 0.00038256, 0.0005033 , 0.00034233,0.00033284, 0.0006633 , 0.00058575, 0.00060389, 0.00034244,0.00064426, 0.00051952, 0.00061326, 0.00039836, 0.00061815,0.00058401, 0.00054044, 0.00032765, 0.00028258, 0.0003215 ,0.00035896, 0.00032261, 0.00054776, 0.00032165, 0.00034949,0.00031671, 0.00051837, 0.00059779, 0.0004923 , 0.00057803,0.00060156, 0.00062988, 0.00064167, 0.00057775, 0.00032702,0.00057387, 0.00032635, 0.00033613, 0.00061883, 0.00031544,0.00053647, 0.00059146, 0.00049887, 0.00058883, 0.00058443,0.00032855, 0.00062647, 0.000589 , 0.00032097, 0.00032709,0.00035039, 0.00064611, 0.00031953, 0.00064141, 0.00063551,0.0006137 , 0.00056107, 0.00031868, 0.00055326, 0.00064193,0.00063964, 0.00032327, 0.00032057, 0.00032482, 0.00063825,0.00032268, 0.00064066, 0.00033343, 0.00064586, 0.00063383,0.00064637, 0.00051645, 0.00060231, 0.00064135, 0.00063501,...0.00033794, 0.00018108, 0.00022917, 0.0003251 , 0.00018121,0.00023267, 0.00017655, 0.00032241, 0.00038758, 0.00034107,0.00059606, 0.00063852, 0.00032233, 0.00044575, 0.00034145,0.00039771, 0.00033576, 0.00017816, 0.00039018, 0.00017786,0.00018041, 0.00040233, 0.00018715, 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2026-07-14T15:09:59.026218+00:00 creation_library : ArviZ creation_library_version : 1.2.0 creation_library_language : Python inference_library : pymc inference_library_version : 6.0.1 sample_dims : \['chain', 'draw'\] sampling_time : 0.9929232597351074 tuning_steps : 1000 /observed_data(9) Dimensions: - obs_ind: 96 Coordinates: (1) obs_ind (obs_ind) int64 0 1 2 3 4 5 6 ... 90 91 92 93 94 95 array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,90, 91, 92, 93, 94, 95]) Data variables: (1) y (obs_ind) float64 -2.106 -1.795 ... 1.081 0.7312 array([-2.10603219, -1.79466675, -2.2534471 , -2.09470237, -2.37367922,-1.66374999, -1.26199135, -1.64025567, -0.98177939, -1.33925016,-1.33388682, 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1.39274901, 1.08069951,0.73119664]) Attributes: (7) created_at : 2026-07-14T15:09:46.859701+00:00 creation_library : ArviZ creation_library_version : 1.2.0 creation_library_language : Python inference_library : pymc inference_library_version : 6.0.1 sample_dims : \[\] /constant_data(10) Dimensions: - obs_ind: 96 Coordinates: (1) obs_ind (obs_ind) int64 0 1 2 3 4 5 6 ... 90 91 92 93 94 95 array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,90, 91, 92, 93, 94, 95]) Data variables: (2) x (obs_ind) float64 -2.063 -1.807 ... 1.835 2.163 array([-2.0634498 , -1.80684125, -1.80388002, -1.36659913, -1.25328425,-1.15379858, -0.98147769, -0.75830187, -0.63010848, -0.45285532,-0.20326414, -0.04578011, 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1.54964885, 1.83546772,2.1626538 ]) group_idx (obs_ind) int32 0 0 0 0 0 0 0 0 ... 3 3 3 3 3 3 3 3 array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,3, 3, 3, 3, 3, 3, 3, 3], dtype=int32) Attributes: (7) created_at : 2026-07-14T15:09:46.860851+00:00 creation_library : ArviZ creation_library_version : 1.2.0 creation_library_language : Python inference_library : pymc inference_library_version : 6.0.1 sample_dims : \[\] /prior(13) Dimensions: - chain: 1 - draw: 800 - groups: 4 Coordinates: (3) chain (chain) int64 0 array([0]) draw (draw) int64 0 1 2 3 4 5 ... 795 796 797 798 799 array([ 0, 1, 2, ..., 797, 798, 799], shape=(800,)) groups (groups) \ array(['North', 'South', 'East', 'West'], dtype=' array([[[-1.45677965, 1.44648249, -0.3248535 , -2.78314378],[-3.48613588, -2.72848537, 1.08008606, 0.11770342],[-0.187244 , -0.45170006, -1.54104664, -1.8327792 ],...,[ 0.46397585, -3.60632678, 0.38839175, -0.88072184],[ 0.19723876, 1.85621001, 2.07191875, -2.52842784],[-1.79765227, -1.64520139, -1.02255043, -0.55056527]]],shape=(1, 800, 4)) beta (chain, draw, groups) float64 -2.307 -0.09826 ... 0.6349 3.153 array([[[-2.30734786, -0.0982566 , -2.06626656, 0.19641394],[-2.82076793, 0.8176951 , 1.05571436, 0.73123794],[ 1.85451335, -1.4417889 , -1.17770994, -1.85756647],...,[-1.53219474, 2.70932537, 0.48351332, -2.26825199],[-0.78828509, -3.26580389, -0.84114311, 0.59252056],[ 1.17088835, 0.13880882, 0.6348729 , 3.15293988]]],shape=(1, 800, 4)) sigma (chain, draw) float64 1.121 1.051 ... 0.1778 0.07849 array([[1.12132323e+00, 1.05105774e+00, 8.45264927e-01, 1.20962340e+00,6.00588084e-01, 1.34200238e+00, 1.31086775e+00, 4.93977061e-01,4.02386052e-01, 9.61198738e-01, 2.15624859e+00, 4.70979116e-02,2.45313898e-01, 2.98163626e-01, 2.18168268e+00, 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8.19744794e-01, 4.58125439e-01, 7.80886824e-04,1.17768255e-01, 5.32613778e-01, 1.08965818e-01, 6.28659668e-01,5.78705930e-01, 7.54497182e-01, 8.16136405e-01, 2.42285586e-01,9.49540198e-01, 1.58872601e-01, 7.50485773e-01, 4.38542408e-02,2.81761498e-02, 1.00920728e+00, 1.77834679e-01, 7.84851791e-02]]) Attributes: (7) created_at : 2026-07-14T15:09:46.856860+00:00 creation_library : ArviZ creation_library_version : 1.2.0 creation_library_language : Python inference_library : pymc inference_library_version : 6.0.1 sample_dims : \['chain', 'draw'\] /prior_predictive(7) Attributes: (7) created_at : 2026-07-14T15:09:46.858772+00:00 creation_library : ArviZ creation_library_version : 1.2.0 creation_library_language : Python inference_library : pymc inference_library_version : 6.0.1 sample_dims : \['chain', 'draw'\] # Use tidydraws One call stacks both sources: ``` python compare = td.compare_draws(dt, "beta") compare.head() ``` shape: (5, 5) | chain | draw | groups | beta | source | |-------|------|---------|-----------|-------------| | i64 | i64 | str | f64 | str | | 0 | 0 | "North" | 0.394303 | "posterior" | | 0 | 0 | "South" | 0.782 | "posterior" | | 0 | 0 | "East" | 1.384254 | "posterior" | | 0 | 0 | "West" | -0.407587 | "posterior" | | 0 | 1 | "North" | 0.473318 | "posterior" | # Plotting ## Prior vs posterior (pooled) The prior is deliberately broad; after seeing the data, the posterior concentrates around the group-specific slopes. - lets-plot - plotnine ``` python ( lp.ggplot(compare.to_pandas(), lp.aes("beta", fill="source")) + lp.geom_density(alpha=0.5) + lp.geom_vline( data=truth.to_pandas(), mapping=lp.aes(xintercept="beta_true"), color="firebrick", linetype="dashed", size=0.7, ) + lp.labs(x="beta", y="density", fill="source", title="Prior vs posterior slopes") ) ``` Prior vs posterior density of group-specific slopes, pooled across groups. ``` python ( p9.ggplot(compare.to_pandas(), p9.aes("beta", fill="source")) + p9.geom_density(alpha=0.5) + p9.geom_vline( data=truth.to_pandas(), mapping=p9.aes(xintercept="beta_true"), color="firebrick", linetype="dashed", size=0.7, ) + p9.labs(x="beta", y="density", fill="source", title="Prior vs posterior slopes") ) ```

Prior vs posterior density of group-specific slopes, pooled across groups.
## Prior vs posterior by group - lets-plot - plotnine ``` python ( lp.ggplot(compare.to_pandas(), lp.aes("beta", fill="source")) + lp.geom_density(alpha=0.5) + lp.geom_vline( data=truth.to_pandas(), mapping=lp.aes(xintercept="beta_true"), color="firebrick", linetype="dashed", size=0.7, ) + lp.facet_wrap(facets="groups", ncol=2) + lp.labs(x="beta", y="density", fill="source", title="Prior vs posterior by group") ) ``` Prior vs posterior density of group-specific slopes, faceted by group. ``` python ( p9.ggplot(compare.to_pandas(), p9.aes("beta", fill="source")) + p9.geom_density(alpha=0.5) + p9.geom_vline( data=truth.to_pandas(), mapping=p9.aes(xintercept="beta_true"), color="firebrick", linetype="dashed", size=0.7, ) + p9.facet_wrap("~groups", ncol=2) + p9.labs(x="beta", y="density", fill="source", title="Prior vs posterior by group") ) ```

Prior vs posterior density of group-specific slopes, faceted by group.
## Credible-interval comparison A different cut: 89% intervals per group, dodged by source. The posterior intervals contract toward the true slopes while the prior intervals remain wide. ``` python ci = td.point_interval(compare, "beta", group_by=["groups", "source"], probs=(0.89,)) ``` - lets-plot - plotnine ``` python ( lp.ggplot(ci.to_pandas(), lp.aes("groups", "beta", color="source")) + lp.geom_pointrange( lp.aes(ymin="beta_lower", ymax="beta_upper"), position=lp.position_dodge(0.5), size=0.8, ) + lp.geom_pointrange( data=truth.to_pandas(), mapping=lp.aes("groups", "beta_true", ymin="beta_true", ymax="beta_true"), color="firebrick", size=0.7, ) + lp.geom_hline(yintercept=0, linetype="dashed", color="#888888") + lp.labs( x="group", y="beta (89% CrI)", color="source", title="Prior vs posterior credible intervals", ) ) ``` Prior vs posterior 89% credible intervals of group-specific slopes. ``` python ( p9.ggplot(ci.to_pandas(), p9.aes("groups", "beta", color="source")) + p9.geom_pointrange( p9.aes(ymin="beta_lower", ymax="beta_upper"), position=p9.position_dodge(0.5), size=0.8, ) + p9.geom_pointrange( data=truth.to_pandas(), mapping=p9.aes("groups", "beta_true", ymin="beta_true", ymax="beta_true"), color="firebrick", size=0.7, ) + p9.geom_hline(yintercept=0, linetype="dashed", color="#888888") + p9.labs( x="group", y="beta (89% CrI)", color="source", title="Prior vs posterior credible intervals", ) ) ```

Prior vs posterior 89% credible intervals of group-specific slopes.
`group_name` sets the source column's name, and `groups` can compare other ArviZ groups when needed. Next, join posterior expectations to covariates with [`prediction_draws()`](../../docs/examples/prediction_draws.md).