# Prediction space [prediction_draws()](../../reference/prediction_draws.md#tidydraws.prediction_draws) joins posterior prediction draws such as `mu` to covariates, producing one tidy row per `chain × draw × observation`. Parameters are deliberately **excluded** -- prediction space stays separate from parameter space, so coefficients never get duplicated across observations. Pass a `DataFrame` when you want explicit control over the covariates used for plotting. With `newdata=None`, [prediction_draws()](../../reference/prediction_draws.md#tidydraws.prediction_draws) reads covariates from a constant-data group in the ArviZ object and fails loudly if that group is missing. # Full PyMC workflow The workflow starts from observed data with strong group differences, fits a PyMC model, asks PyMC for posterior expectations `mu[obs_ind]`, and then uses [prediction_draws()](../../reference/prediction_draws.md#tidydraws.prediction_draws) to attach those draws to `x`, `groups`, and observed `y`. 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 tidydraws import point_interval from _pymc_workflow import simulate_grouped_regression lp.LetsPlot.setup_html() workflow = simulate_grouped_regression(seed=2026) observed = workflow.observed coords = { "groups": workflow.group_names, "obs_ind": observed.get_column("obs_ind").to_numpy(), } ``` Build our PyMC model and fit. ``` python 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", ) dt = pm.sample( draws=400, tune=400, random_seed=2027, ) pm.sample_posterior_predictive( dt, var_names=["mu", "y"], predictions=True, extend_inferencedata=True, random_seed=2028, progressbar=False, ) ``` Initializing NUTS using jitter+adapt_diag... Multiprocess sampling (2 chains in 2 jobs) NUTS: [intercept, beta, sigma] /home/runner/work/tidydraws/tidydraws/.venv/lib/python3.12/site-packages/pymc/step_methods/hmc/quadpotential.py:321: RuntimeWarning: overflow encountered in dot ``` ``` Sampling 2 chains for 400 tune and 400 draw iterations (800 + 800 draws total) took 1 seconds. We recommend running at least 4 chains for robust computation of convergence diagnostics The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details Sampling: [y] ``` 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 -1.162 0.1217 1.137 ... 1.421 2.132 array([[[-1.16180363, 0.12165948, 1.13685363, 2.09451466],[-1.16180363, 0.12165948, 1.13685363, 2.09451466],[-1.14237852, 0.1802708 , 1.17342478, 2.05000919],...,[-1.14351437, -0.04006841, 1.19617868, 2.20578884],[-1.16535894, 0.125233 , 1.20554193, 2.20681107],[-1.34304983, 0.18108446, 1.24578869, 2.00856969]],[[-1.23238737, 0.24978378, 1.20391056, 2.14883688],[-1.1587664 , 0.08504497, 1.33494906, 2.21462924],[-1.190985 , 0.16655445, 1.28544246, 2.04903901],...,[-1.3359371 , 0.09150072, 1.28505032, 2.14298991],[-1.21628303, 0.25161209, 1.26266611, 2.00438611],[-1.19289148, 0.13303571, 1.42127857, 2.13236682]]],shape=(2, 400, 4)) beta (chain, draw, groups) float64 0.425 0.8192 ... 1.452 -0.5716 array([[[ 0.42500251, 0.81917069, 1.46394584, -0.660629 ],[ 0.42500251, 0.81917069, 1.46394584, -0.660629 ],[ 0.41046992, 0.95935876, 1.56343875, -0.60357372],...,[ 0.4799572 , 0.93393392, 1.38007521, -0.61505928],[ 0.45322836, 0.87400184, 1.33208426, -0.55708329],[ 0.4345777 , 0.73565538, 1.49922715, -0.61502422]],[[ 0.29567256, 0.8470685 , 1.48896285, -0.50996498],[ 0.46009295, 0.70798592, 1.44114432, -0.63691735],[ 0.46289473, 0.63265218, 1.62566111, -0.53096786],...,[ 0.41245857, 0.84043359, 1.44017683, -0.48047732],[ 0.45425777, 0.74458965, 1.37802207, -0.71126017],[ 0.44323747, 0.74728569, 1.45177169, -0.57160291]]],shape=(2, 400, 4)) sigma (chain, draw) float64 0.4078 0.4078 ... 0.4723 0.4386 array([[0.40784871, 0.40784871, 0.40844332, 0.4716976 , 0.36739459,0.45700686, 0.39478465, 0.38031989, 0.39628872, 0.46163666,0.45508543, 0.4324881 , 0.43048323, 0.46079233, 0.4062716 ,0.40688437, 0.41713052, 0.44049382, 0.45723196, 0.40909684,0.40909684, 0.41859895, 0.43336567, 0.40186198, 0.45613674,0.37132403, 0.45981708, 0.45164367, 0.45902187, 0.41083836,0.45323332, 0.44328014, 0.42940619, 0.43752915, 0.42232428,0.43718889, 0.44101446, 0.41774228, 0.41854904, 0.45721474,0.44232526, 0.4440114 , 0.41234937, 0.41459559, 0.45815798,0.43912628, 0.4375038 , 0.40826502, 0.41115106, 0.41090171,0.43716332, 0.44638677, 0.50745353, 0.46111823, 0.43058823,0.38170822, 0.46984462, 0.49391164, 0.41525091, 0.47302766,0.38854477, 0.42673319, 0.42940911, 0.39596013, 0.40735891,0.43745755, 0.4485982 , 0.40178539, 0.43209101, 0.43413064,0.40094399, 0.39621634, 0.46846407, 0.37735415, 0.39540802,0.41166324, 0.4273483 , 0.4471377 , 0.38542598, 0.4769186 ,0.4526407 , 0.40798816, 0.42873387, 0.45283258, 0.44096981,0.43094526, 0.40351506, 0.42273413, 0.45619468, 0.390293 ,0.4468297 , 0.40024526, 0.43631684, 0.40956313, 0.45189673,0.42341728, 0.44099565, 0.42671281, 0.42848408, 0.40352189,...0.36585034, 0.51214561, 0.36431792, 0.39057052, 0.44446685,0.43403389, 0.41721266, 0.42865574, 0.42036561, 0.40951798,0.40709996, 0.4054084 , 0.40003052, 0.43547068, 0.42184167,0.43072484, 0.41126791, 0.41301852, 0.40739292, 0.4641417 ,0.42425522, 0.4214677 , 0.41637008, 0.4248597 , 0.39172727,0.39172727, 0.41989216, 0.41477083, 0.40752174, 0.45544178,0.38670301, 0.45018523, 0.40951434, 0.41789062, 0.43662168,0.45037729, 0.47475451, 0.49292655, 0.42998205, 0.4066102 ,0.42696764, 0.4234316 , 0.41406098, 0.41756278, 0.39653328,0.37326933, 0.47924407, 0.38308855, 0.4341665 , 0.45348737,0.39746757, 0.4515601 , 0.37748996, 0.46639017, 0.41159723,0.38878857, 0.46641926, 0.4097142 , 0.46918031, 0.4673944 ,0.41035726, 0.44427704, 0.4468857 , 0.46833964, 0.41293333,0.42974877, 0.44925211, 0.39298837, 0.51423729, 0.36760511,0.45482145, 0.39025508, 0.44160115, 0.38937201, 0.43952068,0.38886119, 0.44943764, 0.39284305, 0.42630406, 0.39014305,0.46251461, 0.42479608, 0.36710223, 0.51823667, 0.39971104,0.46676101, 0.4065613 , 0.46917738, 0.41477787, 0.42782917,0.39151051, 0.41344169, 0.39195076, 0.47642198, 0.41264166,0.43861773, 0.4094865 , 0.37085284, 0.47229741, 0.43861019]]) mu (chain, draw, obs_ind) float64 -2.039 -1.93 ... 1.083 0.8962 array([[[-2.03877496, -1.92971569, -1.92845716, ..., 1.07077169,0.88195146, 0.66580285],[-2.03877496, -1.92971569, -1.92845716, ..., 1.07077169,0.88195146, 0.66580285],[-1.98936259, -1.88403251, -1.88281701, ..., 1.11468187,0.94216912, 0.7446882 ],...,[-2.13388196, -2.01072084, -2.00929957, ..., 1.25266293,1.07686738, 0.87562854],[-2.10057292, -1.98427065, -1.98292853, ..., 1.3435276 ,1.18430268, 1.00203279],[-2.2397791 , -2.12826275, -2.12697586, ..., 1.05549811,0.87971259, 0.67848522]],[[-1.84249286, -1.76662075, -1.7657452 , ..., 1.35857024,1.21281262, 1.04595918],[-2.10814511, -1.99008133, -1.98871889, ..., 1.227631 ,1.04558801, 0.83719752],[-2.14614503, -2.02736228, -2.02599155, ..., 1.22622528,1.07446464, 0.90073935],...,[-2.18702465, -2.08118426, -2.07996287, ..., 1.39841879,1.26108931, 1.10388381],[-2.15362113, -2.03705471, -2.03570954, ..., 0.9021826 ,0.69889102, 0.46617659],[-2.10748974, -1.99375122, -1.99243869, ..., 1.24658303,1.08320813, 0.89618762]]], shape=(2, 400, 96)) Attributes: (9) created_at : 2026-07-14T15:10:27.637544+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 : 0.7919321060180664 tuning_steps : 400 /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) acceptance_rate (chain, draw) float64 0.9216 0.7231 ... 0.9292 0.9916 array([[0.92159106, 0.72310732, 0.55875698, 0.94019669, 0.48163849,0.96729548, 0.82906683, 0.89183211, 0.80682785, 0.90801153,1. , 0.85373218, 0.84270659, 1. , 1. ,1. , 0.84709068, 0.84571296, 0.86947463, 0.71595642,0.60978232, 0.78881073, 0.7446277 , 0.99373438, 0.85723638,0.9494455 , 1. , 0.76069911, 0.94924997, 0.91017452,0.99263903, 0.87570787, 0.99560938, 0.89055009, 0.6435773 ,0.99789595, 0.63876785, 0.98609286, 1. , 0.47224758,0.86913068, 0.99162768, 0.99215198, 0.9962005 , 0.8287558 ,0.95652956, 1. , 1. , 0.97200439, 0.89298701,0.51415125, 0.77960279, 0.55424147, 0.92385059, 1. ,0.73757664, 0.8621926 , 0.95790827, 0.90671608, 0.34086113,0.88902883, 0.92587501, 0.85951284, 0.84792537, 0.74000907,0.75109033, 0.89234783, 1. , 0.90961132, 0.99835942,0.91749043, 0.67427906, 0.64967052, 0.91351249, 0.94354873,0.99455626, 0.86395496, 0.99640897, 0.86030099, 0.60506612,0.95898151, 1. , 0.98761598, 0.57480343, 0.95625809,0.76565441, 0.80948363, 0.90102523, 0.46060894, 0.85878889,1. , 0.85014754, 0.78997886, 0.60477847, 0.94058764,0.74420035, 0.77932333, 1. , 0.91919038, 0.73218165,...0.76275965, 0.49845143, 0.98490987, 0.64977545, 0.47220427,0.85125585, 0.78209333, 0.94831175, 0.903609 , 0.83630854,0.80842513, 0.75739923, 0.98106044, 0.80915687, 0.90490356,0.77120518, 0.92505173, 0.96083062, 0.61223803, 0.85707794,0.93336709, 0.97966405, 0.90360857, 0.88656404, 0.9856251 ,0.42650424, 0.96391758, 0.73436117, 0.86219236, 0.96363221,0.85858965, 1. , 0.97271927, 0.8626602 , 0.92456629,0.88647449, 0.92033142, 0.99097474, 0.96739982, 0.93173278,0.85689304, 0.8534021 , 0.78554758, 0.73982542, 1. ,0.48943559, 1. , 0.94511246, 0.68542651, 0.79944327,0.82107833, 0.73087173, 0.93014333, 0.49640345, 0.62973391,0.9240186 , 0.93903551, 1. , 0.54535625, 0.95390758,0.93759825, 0.83310005, 0.87298409, 0.96103294, 0.97450407,1. , 0.71056952, 0.97343585, 0.5804028 , 0.99794439,0.98993273, 0.99177762, 0.62223999, 0.89620615, 0.94702414,0.94222082, 0.87195163, 0.88013741, 0.71609109, 1. ,0.87298212, 1. , 0.60268075, 0.94700608, 0.99261548,1. , 0.7699768 , 0.93735865, 1. , 0.9937974 ,0.8393659 , 0.83447301, 0.72162678, 0.95666389, 0.91842942,0.64585867, 0.89531734, 0.72977562, 0.92919235, 0.99155154]]) lp (chain, draw) float64 -65.75 -65.75 ... -68.14 -67.35 array([[-65.75360243, -65.75360243, -69.81655157, -67.5488283 ,-71.71967279, -69.72245904, -66.22868691, -66.86527008,-68.51694666, -69.78351193, -68.74624876, -71.50274903,-73.75060826, -71.68220234, -69.03404239, -66.16067568,-66.35689298, -68.43432553, -69.34258516, -67.05313004,-67.05313004, -68.09202159, -68.81614849, -66.93564654,-67.76544972, -68.55840147, -67.68712244, -68.62383098,-70.28978483, -71.79910807, -70.16505946, -70.10187715,-70.07730183, -66.7760096 , -70.80577873, -67.07102396,-71.10028169, -70.94600899, -70.84924579, -73.49081218,-73.65742747, -71.56629453, -68.90488816, -69.52962128,-69.92435553, -70.0448361 , -70.12267345, -69.75642042,-68.22814641, -67.67874479, -73.51138617, -69.09014079,-79.02621087, -72.77189335, -69.76734109, -67.57679992,-68.97938315, -71.03192122, -65.04843193, -68.2062194 ,-69.68550553, -67.16573047, -67.97026557, -66.67756988,-65.80267611, -66.12563788, -67.09944631, -66.73534712,-66.42154762, -66.47524833, -66.12420753, -67.64939435,-70.18877034, -68.5899764 , -68.43323324, -66.88845746,-68.81754682, -67.11364304, -66.26564978, -69.25034288,...-67.78708705, -65.74739305, -66.73814766, -66.53869303,-66.98730288, -66.98730288, -66.65516393, -66.33667321,-68.41121695, -67.27706282, -69.70302458, -69.85315024,-67.83334186, -68.24940553, -67.15597924, -68.32451888,-69.85768707, -70.0648681 , -66.09528381, -66.03846364,-67.7774129 , -66.67400854, -67.63785215, -66.75295098,-64.83210505, -71.00583968, -71.45438122, -70.71697714,-66.38272969, -69.04434175, -64.97401374, -67.75808823,-67.41723149, -67.58268713, -74.57825078, -68.22726698,-69.72650242, -66.50920093, -72.55659264, -68.64665524,-68.66108124, -69.70286876, -69.84392029, -71.06655443,-72.21207267, -65.99558181, -67.46428125, -66.10119748,-70.12155219, -67.30485539, -67.80870943, -66.92301178,-67.97435489, -66.37963033, -66.44238386, -66.10139382,-67.284886 , -67.83139597, -71.32990758, -70.84653791,-74.12411484, -67.4623509 , -72.26912241, -74.40819066,-71.31700841, -66.65364804, -71.63079882, -72.220841 ,-69.47759172, -66.10331777, -65.02791174, -66.55117929,-70.49040292, -71.1184135 , -66.6575536 , -66.71039273,-66.35902871, -67.47829909, -68.14028232, -67.35263794]]) tree_depth (chain, draw) int64 3 3 2 2 2 3 3 3 ... 2 3 3 3 2 2 3 3 array([[3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 2, 3,3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3,3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 2, 2, 2, 2, 3, 2, 2, 3,2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3,3, 3, 2, 3, 2, 2, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 2, 2,2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 2,2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3,2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3,3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2,3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3,2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 3,3, 2, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2,3, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3,2, 3, 3, 3, 3, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 2,2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 2, 2,2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 2, 2, 2,3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3,2, 3, 3, 3, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2,3, 2, 2, 3],[3, 3, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3,3, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3,3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3,3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 3,2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3,3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3,3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2,3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3,3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3,3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 2, 3, 3, 3,3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2,3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 3,3, 2, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 2, 3, 3,3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3,3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2,3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2,3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3,2, 2, 3, 3]]) energy_error (chain, draw) float64 -0.08197 0.0 ... 0.1035 -0.2678 array([[-8.19685300e-02, 0.00000000e+00, 7.54325625e-01,-1.96963846e-01, 2.26737676e-01, -3.39642272e-01,-4.23096715e-01, 2.06533005e-01, 3.22192984e-01,2.02230745e-01, -1.29521885e-01, 4.51918017e-01,3.78386967e-01, -3.60097103e-01, -3.42686272e-01,-5.53715914e-01, 1.73557191e-02, 3.11737211e-01,1.87590919e-01, -2.58439673e-01, 0.00000000e+00,1.78601501e-01, 6.69042574e-02, -3.52435324e-01,1.65212354e-01, 4.91403836e-02, -2.51685434e-01,4.40761599e-02, 1.65169611e-01, 3.21131642e-01,-2.46501957e-01, -3.83819298e-02, 2.58853940e-02,-4.28725237e-01, 4.84702971e-01, -6.13708128e-01,5.96684229e-01, 9.12073330e-03, -2.44155179e-02,8.88461262e-01, 7.05556061e-02, -3.72627182e-01,-4.08380250e-01, 2.69565942e-02, 1.03114479e-01,-3.57667148e-03, -9.29136667e-03, -1.34533963e-02,-2.58855743e-01, -3.10574554e-01, 9.30346753e-01,-4.97278770e-01, 8.64753386e-01, -8.39666089e-01,-2.90849255e-01, -3.06772550e-01, 2.55307329e-01,2.24205901e-01, -1.02274395e+00, 9.98067316e-01,...1.92587702e-01, -1.64414928e-01, -3.56255441e-01,9.19887482e-01, -1.27622464e-01, -7.48002364e-02,-3.95831958e-01, 2.25089320e-01, -4.80835619e-01,4.42893807e-01, -8.30385269e-02, 4.36134916e-01,1.21162718e+00, -1.18488641e+00, 1.85203079e-01,-5.36256661e-01, 6.79380654e-01, -6.39970885e-01,-4.94382617e-02, 1.93407374e-01, 1.46091675e-01,1.52182169e-01, 1.10719740e-01, -9.12329521e-01,2.18821326e-01, -2.58927651e-01, 8.24194392e-01,-5.30170822e-01, -2.99102946e-02, -1.42688486e-01,1.64017658e-01, -1.54032734e-01, 4.86209898e-02,-2.30726078e-02, 1.43429089e-01, 8.50769063e-02,6.52415639e-01, -2.14677358e-03, 3.78136450e-01,-1.01080710e+00, 7.73369901e-01, 2.56862401e-01,-1.33879378e-01, -5.38958570e-01, 7.49093515e-01,-5.04240609e-02, -2.19978970e-01, -5.89966067e-01,-2.64082714e-01, 2.63303611e-01, 7.99688635e-01,7.41171932e-02, -4.92892178e-01, 1.38007631e-01,-8.94624356e-02, 1.41986040e-01, 1.03532374e-01,-2.67758719e-01]]) max_energy_error (chain, draw) float64 0.1748 0.664 ... 0.2981 -0.3591 array([[ 0.17480261, 0.66398651, 0.75432562, -0.39644166, 1.23474151,-0.66058543, 0.59497608, 0.25452074, 0.32219298, 0.20223074,-0.46827937, -0.62315842, 0.37838697, -0.52182558, -0.34268627,-0.7755284 , 0.33283415, 0.31173721, 0.29664147, 0.91507729,1.18417502, 0.49868866, 0.49868772, -0.36308483, 0.24061433,-0.56483229, -0.63853313, 0.56041369, -0.62195465, -0.45815358,-0.45641134, -0.36534523, -0.5136436 , -0.42872524, 1.10572378,-0.63133396, 0.67400086, -0.2911444 , -0.84042769, 1.49245686,-0.68609822, -0.80030165, -0.40838025, -0.58797956, 0.40988748,-0.36192732, -0.34462654, -0.46464844, -0.25885574, 0.42533078,0.93034675, 1.01604132, 1.42060013, -0.98119995, -0.98727224,1.23031996, 0.25530733, -0.45805472, -1.02274395, 1.96648044,-0.47602099, -0.42066393, 0.34001923, 0.6092177 , 0.8342718 ,0.54105145, -0.27197024, -0.15281191, -0.34337885, -0.27406676,0.15082992, 1.01028349, 0.67079984, -0.78690016, -0.52897069,-0.56924002, 0.35307704, -0.50399809, 0.41667128, 0.6138434 ,-0.44258655, -0.13021527, -0.35169536, 0.62866493, -0.36468072,0.8381103 , 0.45900044, 0.16239009, 1.51205069, 0.23869138,-0.62579196, 0.31881285, 0.381092 , 1.09076846, -0.62632652,0.52567327, 0.50089291, -0.67497183, 0.16775865, 0.75356368,...0.81832578, 1.05333201, -0.75499108, 1.32771 , 1.17192585,0.33858031, 0.64589717, 0.18126308, 0.34841661, 0.67545342,0.52234446, 0.7216009 , -0.12841942, 0.38109669, 0.2752456 ,0.44011517, -0.30250085, 0.07586525, 1.04110938, -0.7573495 ,-1.16205801, -0.33004304, 0.23271553, 0.34772197, -0.3001985 ,1.11424714, -0.17688439, 0.55549692, 0.39058737, -0.36357464,0.3914078 , -0.64543661, -0.34724948, 0.36347605, 0.27173953,0.22148269, -0.57237687, -0.2835299 , -0.47171743, 0.18806529,0.29778835, 0.43439245, 0.40093912, 0.50663675, -0.35625544,1.46587886, -0.87568304, -0.77884943, 0.92798479, 0.50606141,-0.48083562, 0.44289381, 0.2236243 , 1.54110312, 1.21162718,-1.18488641, 0.18520308, -0.53625666, 0.67938065, -0.85020955,0.37656944, 0.32678292, -0.35930068, -0.20799794, -0.5174273 ,-0.91232952, 0.44808079, -0.25892765, 1.11808633, -0.53017082,-0.34477201, -0.23533486, 0.8725151 , 0.37306795, -0.20574747,-0.14399682, 0.29301357, 0.32577087, 0.67251704, -0.60043046,-0.51319105, -1.0108071 , 0.7733699 , -0.37782835, -0.83241415,-0.53895857, 0.74909351, -0.73067452, -0.41868068, -0.65723989,0.32912244, 0.3253929 , 0.79968864, -0.69042159, -1.02483431,0.84438406, 0.37694759, 0.83295646, 0.29806006, -0.35906457]]) 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]]) perf_counter_start (chain, draw) float64 178.1 178.1 178.1 ... 178.3 178.3 array([[178.09057274, 178.09127397, 178.09196402, 178.09243461,178.09287078, 178.09333519, 178.09397488, 178.09462364,178.09543746, 178.09608799, 178.09673852, 178.09749049,178.09814051, 178.09879618, 178.09945613, 178.10012789,178.10058394, 178.10129839, 178.10199261, 178.10269326,178.10315985, 178.10361586, 178.10431621, 178.10508613,178.10585746, 178.10658177, 178.10705353, 178.10750071,178.1079265 , 178.10839405, 178.10905627, 178.10969218,178.11042202, 178.11111584, 178.1115232 , 178.11229226,178.11290063, 178.11335793, 178.11408545, 178.11471868,178.11542572, 178.11614947, 178.11686238, 178.11761459,178.11835784, 178.11904531, 178.11973107, 178.12042343,178.12125251, 178.1219581 , 178.12261661, 178.12330225,178.12399911, 178.12449831, 178.12521834, 178.12568065,178.12614596, 178.1268037 , 178.12750849, 178.12794282,178.12840531, 178.1288582 , 178.12930383, 178.13004297,178.13047934, 178.13166136, 178.13237987, 178.13285465,178.13354373, 178.13399294, 178.13467803, 178.13545837,178.1358809 , 178.1365794 , 178.13732655, 178.13796404,178.13868814, 178.13943861, 178.14016206, 178.14080843,...178.2559596 , 178.25674589, 178.25723366, 178.25792439,178.25863738, 178.25937331, 178.25980803, 178.26055353,178.26130393, 178.2619365 , 178.26720837, 178.26796704,178.26871819, 178.26948157, 178.27021234, 178.27093076,178.27168585, 178.27242657, 178.27322758, 178.27398849,178.27469105, 178.27539856, 178.27609145, 178.27676347,178.27721211, 178.27763622, 178.27808476, 178.27877241,178.27945933, 178.28016722, 178.28085249, 178.28132215,178.28170794, 178.2824078 , 178.28309556, 178.28353967,178.28395572, 178.28444261, 178.28470573, 178.28496754,178.28543036, 178.28584678, 178.28632522, 178.28659137,178.28700464, 178.28746979, 178.28773489, 178.28800021,178.28845793, 178.28884805, 178.28932595, 178.28974686,178.29023266, 178.29066905, 178.2909598 , 178.29146081,178.30318672, 178.30378278, 178.30410701, 178.30455432,178.30499615, 178.3054829 , 178.30576261, 178.3062339 ,178.30666704, 178.30715929, 178.30745756, 178.30789109,178.30838168, 178.30891458, 178.30941381, 178.30969311,178.31015621, 178.31042766, 178.31085624, 178.31139565,178.31182335, 178.31211756, 178.31239236, 178.31282018]]) n_steps (chain, draw) float64 7.0 7.0 3.0 3.0 ... 3.0 3.0 7.0 7.0 array([[7., 7., 3., 3., 3., 7., 7., 7., 7., 7., 7., 7., 7., 7., 7., 3.,7., 7., 7., 3., 3., 7., 7., 7., 7., 3., 3., 3., 3., 7., 7., 7.,7., 3., 7., 7., 3., 7., 7., 7., 7., 7., 7., 7., 7., 7., 7., 7.,7., 7., 7., 7., 3., 7., 3., 3., 7., 7., 3., 3., 3., 3., 7., 3.,3., 7., 3., 7., 3., 7., 7., 3., 7., 7., 7., 7., 7., 7., 7., 7.,7., 7., 7., 3., 7., 3., 3., 7., 7., 7., 3., 7., 3., 3., 7., 7.,7., 3., 7., 7., 3., 3., 7., 7., 7., 3., 7., 7., 3., 3., 3., 7.,3., 7., 7., 7., 7., 7., 3., 7., 7., 7., 7., 7., 7., 7., 7., 3.,7., 7., 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3., 7., 7.]]) step_size (chain, draw) float64 0.9673 0.9673 ... 0.813 0.813 array([[0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,0.96730073, 0.96730073, 0.96730073, 0.96730073, 0.96730073,...0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848,0.81301848, 0.81301848, 0.81301848, 0.81301848, 0.81301848]]) 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]]) process_time_diff (chain, draw) float64 0.0005804 0.0005636 ... 0.0003621 array([[0.00058041, 0.00056359, 0.00035282, 0.00031872, 0.00034941,0.00051012, 0.00052211, 0.00068705, 0.00048233, 0.00053284,0.00063623, 0.00049708, 0.00054361, 0.00052999, 0.0005078 ,0.00033154, 0.00058198, 0.00058186, 0.00055938, 0.0003527 ,0.00032177, 0.00058628, 0.00061455, 0.00065265, 0.00058599,0.00032852, 0.00033315, 0.00031482, 0.00035608, 0.00050768,0.00050745, 0.00061722, 0.00052765, 0.00027015, 0.00065434,0.00047819, 0.00033462, 0.00058455, 0.00049541, 0.00059424,0.00055276, 0.00058855, 0.00063613, 0.00063143, 0.00052884,0.00055461, 0.0005752 , 0.00067657, 0.0005813 , 0.00053181,0.00056742, 0.00058239, 0.00035115, 0.00060368, 0.00032252,0.0003201 , 0.0004952 , 0.00059003, 0.00032026, 0.00035017,0.00031696, 0.00031515, 0.00060437, 0.00031924, 0.00025125,0.00058244, 0.00031156, 0.0005682 , 0.00031483, 0.00057226,0.00064684, 0.00028855, 0.0005835 , 0.00061552, 0.00051371,0.00060857, 0.00063639, 0.00055671, 0.00053777, 0.00064995,0.00061644, 0.00052377, 0.00056643, 0.00031674, 0.00059452,0.00036051, 0.00032433, 0.00052873, 0.00069008, 0.00050492,0.00035147, 0.0005927 , 0.00031552, 0.00031499, 0.00061094,0.00056269, 0.00052689, 0.00031628, 0.00063818, 0.00050834,...0.00035451, 0.00049123, 0.00055541, 0.00035653, 0.00054787,0.00035613, 0.0005736 , 0.00056275, 0.00066419, 0.00031799,0.00059247, 0.00035182, 0.00057435, 0.00058689, 0.00064256,0.00061428, 0.00054009, 0.00057554, 0.00062082, 0.00061028,0.00065638, 0.00034848, 0.00056601, 0.00058088, 0.00060748,0.00032106, 0.00062537, 0.00063828, 0.00049068, 0.00056015,0.00060692, 0.00061388, 0.00062075, 0.00059584, 0.00059018,0.00062893, 0.00059169, 0.00065311, 0.00061846, 0.00059268,0.00057725, 0.00054071, 0.00054404, 0.00031012, 0.00028518,0.00028415, 0.00055985, 0.00056829, 0.00053162, 0.00054644,0.00033105, 0.00025816, 0.00057159, 0.00052342, 0.00034863,0.00033064, 0.00039081, 0.00018033, 0.00017391, 0.00037359,0.00032444, 0.00038319, 0.00017798, 0.00033127, 0.00037195,0.00017561, 0.00017587, 0.0003732 , 0.00030805, 0.0003849 ,0.00032999, 0.00038898, 0.0003354 , 0.00020157, 0.00041378,0.0003289 , 0.00048229, 0.00019487, 0.00035225, 0.00034465,0.00038689, 0.00018722, 0.00037694, 0.00033983, 0.00036973,0.00020241, 0.00033957, 0.00039259, 0.0004336 , 0.00040073,0.00018126, 0.00036885, 0.00018185, 0.00033627, 0.00044307,0.00033604, 0.00018046, 0.00018712, 0.00033376, 0.00036209]]) perf_counter_diff (chain, draw) float64 0.0005802 0.0005632 ... 0.0003618 array([[0.00058023, 0.00056323, 0.00035275, 0.00031851, 0.00034926,0.00050992, 0.00052218, 0.00068661, 0.00048215, 0.00053277,0.00063577, 0.00049661, 0.00054341, 0.00052958, 0.00050755,0.0003311 , 0.00058197, 0.00058147, 0.00055919, 0.00035276,0.00032149, 0.00058614, 0.00061425, 0.00065234, 0.00058553,0.00032837, 0.00033301, 0.00031469, 0.00035592, 0.00050707,0.00050735, 0.00061704, 0.00052734, 0.00027016, 0.0006543 ,0.00047807, 0.00033446, 0.00058453, 0.00049532, 0.00059397,0.00055224, 0.00058834, 0.00063617, 0.00063116, 0.00052855,0.00055447, 0.00057438, 0.00067598, 0.00058116, 0.00053167,0.00056709, 0.00058199, 0.00035085, 0.00060368, 0.00032232,0.00032019, 0.00049501, 0.00058986, 0.00032044, 0.00035012,0.00031712, 0.00031509, 0.00060412, 0.00031906, 0.00025128,0.00058243, 0.00031093, 0.00056801, 0.00031452, 0.00057208,0.0006466 , 0.0002883 , 0.00058335, 0.00061544, 0.00051363,0.0006085 , 0.00063617, 0.00055629, 0.00053738, 0.00064978,0.00061618, 0.00052342, 0.00056624, 0.00031685, 0.00059429,0.00036058, 0.00032413, 0.00052825, 0.00069033, 0.00050433,0.00035124, 0.00059266, 0.00031567, 0.00031489, 0.00061068,0.00056233, 0.00052682, 0.00031636, 0.00063813, 0.00050825,...0.0003545 , 0.00049094, 0.00055544, 0.00035646, 0.00054757,0.00035588, 0.00057333, 0.00056242, 0.00066399, 0.0003178 ,0.00059233, 0.00035149, 0.00057378, 0.00058618, 0.0006422 ,0.00061389, 0.00054001, 0.00057547, 0.00062008, 0.00061004,0.00065601, 0.0003484 , 0.00056573, 0.00058066, 0.00060738,0.00032094, 0.00062543, 0.00063818, 0.00048992, 0.00055986,0.00060718, 0.00061378, 0.00062078, 0.00059567, 0.00059004,0.00062887, 0.00059169, 0.00065297, 0.00061838, 0.00059293,0.00057696, 0.000541 , 0.00054403, 0.00031008, 0.00028489,0.00028419, 0.00055932, 0.00056834, 0.00053117, 0.00054617,0.0003311 , 0.00025826, 0.00057181, 0.00052324, 0.00034876,0.00033017, 0.00039052, 0.00018 , 0.00017349, 0.00037331,0.00032442, 0.00038287, 0.00017794, 0.00033067, 0.00037164,0.00017541, 0.00017574, 0.000373 , 0.00030776, 0.00038471,0.00032948, 0.00038865, 0.00033494, 0.00020101, 0.0004135 ,0.00032864, 0.00048315, 0.0001943 , 0.00035241, 0.00034453,0.00038668, 0.00018694, 0.00037688, 0.00033958, 0.00036932,0.00020281, 0.00033892, 0.00039225, 0.00043314, 0.00040027,0.00018131, 0.00036882, 0.00018177, 0.00033612, 0.00044262,0.00033597, 0.00018029, 0.00018711, 0.00033358, 0.00036178]]) step_size_bar (chain, draw) float64 0.7812 0.7812 ... 0.7753 0.7753 array([[0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 0.78119746, 0.78119746, 0.78119746, 0.78119746,0.78119746, 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nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,...nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]]) index_in_trajectory (chain, draw) int64 7 0 -1 2 1 -5 3 ... 2 -4 2 -2 -4 -2 array([[ 7, 0, -1, 2, 1, -5, 3, -6, -6, -3, 1, -1, -7, -3, 2, 1,4, -6, -6, -3, 0, -2, -3, -5, -4, 2, 3, -1, -1, 3, 5, -3,4, -3, -3, 2, 2, 3, -4, 4, -6, 5, 6, 3, 4, 5, -7, 4,5, 4, -2, 1, -2, -3, -1, -2, -4, 1, -1, 1, 2, -2, 4, 2,1, 4, -2, 4, -2, -7, 4, -2, -3, -4, -6, -2, -3, -6, 4, 3,-6, 4, -2, -3, 2, 1, 3, -3, 3, -5, -2, 4, 3, 2, -5, -4,3, -1, -2, 5, -2, -3, 2, 5, 1, 2, -3, 4, -2, -2, -3, -6,-1, 2, -2, -1, -4, -2, 3, -4, -4, -2, -2, -6, 5, 7, 5, -2,4, -3, -2, -1, -1, 1, -4, -4, -1, 1, 4, -2, -2, 1, -2, 2,-6, -2, -2, -1, -4, -1, 4, 4, -2, 4, 1, 5, -3, -2, 4, -5,4, 4, -1, -6, 4, -1, -4, -1, 5, -3, -2, 2, 4, 3, -1, -3,-5, 1, -1, -3, -2, 1, -2, -4, -4, 6, -3, 2, 4, 2, 2, -3,-4, -3, -4, 5, -1, -3, 3, -1, -2, -2, 2, -3, -2, 1, 2, 3,-4, -2, 5, -2, 3, 3, -3, 3, -2, 5, 5, 2, -1, -1, 1, 4,-2, -3, 3, 3, 5, 2, -1, -5, 2, -2, -2, -6, 2, 3, -2, 1,3, -3, 3, 2, 6, -2, -1, 2, -3, -3, 4, 1, -2, -6, 6, -5,-1, 5, 6, -2, -2, -1, 3, 1, 1, -3, 3, -1, -3, -2, 1, 1,-5, 3, 6, -3, -6, 2, 2, 2, 2, 2, 2, 3, -5, 3, 3, 2,-4, 5, -3, -2, 2, -6, 3, 3, 2, -3, 1, -2, -4, 5, -2, -2,3, -2, -2, 1, 1, -2, -1, -3, -3, -2, -4, 2, 5, -2, 1, 4,...2, 1, 1, 3, 1, -3, 6, 6, -2, -2, 5, 3, -1, 5, -4, -3,-1, 3, -3, 2, 2, -2, -2, -2, 2, -4, 3, 4, 6, -1, -5, -2,2, -5, -4, -3, 1, 6, -5, -3, 5, 1, 3, -6, 5, -1, -1, 5,1, 3, 2, -5, 3, 7, -2, -5, 5, 7, 2, -1, 2, 5, -3, -3,2, 3, 3, 6, -3, 6, -2, 7, -3, -2, -3, -3, -6, 6, 3, 1,0, -7, -5, -4, 5, -3, -6, 2, 3, -4, 1, -2, -3, 3, 2, -2,-3, -3, -2, 2, 1, 5, 4, 7, 2, -3, -2, 1, -4, 4, -1, -3,5, 3, 2, 4, -2, -7, 4, -4, -4, -2, 3, -6, 5, -4, -1, -4,3, 1, -2, -1, 3, 1, 4, -5, -4, 3, -2, -6, 2, 1, 7, 3,3, 4, 4, -4, -4, 1, -7, -2, 6, 1, -2, -7, -2, 3, -2, -4,3, -4, -2, 3, -4, 7, 2, 3, 4, 1, 5, -5, -2, 1, 4, 4,1, -1, 4, 7, -2, 7, -6, -3, -7, -2, 4, -2, -1, 2, 3, -7,2, -5, -4, 1, -5, 2, -2, -4, -1, -1, 3, 2, 5, -6, -5, 2,2, 4, 4, 1, -2, 1, 1, -2, -3, -4, -5, 1, -2, -4, 3, -2,-3, 2, 2, 1, 3, -2, 7, -1, -7, -4, -3, 3, -2, -3, 6, 4,-2, -3, 2, 3, 4, 0, -6, -7, -5, -3, -2, -3, 4, -6, -5, -5,-2, -1, -6, -4, 1, 7, 5, -1, -2, 2, 4, 5, -1, 3, -3, 3,-3, -3, 2, 6, -4, -3, 2, 5, 3, -2, -2, 1, -3, 2, -3, -5,2, -4, -3, 5, 5, 3, 2, 4, 2, -3, -2, -1, -3, 3, 2, -4,2, -2, 2, -4, -3, 6, -1, -5, 1, 4, 2, -4, 2, -2, -4, -2]]) energy (chain, draw) float64 69.05 70.69 72.67 ... 71.78 70.71 array([[69.04672341, 70.68829932, 72.67216853, 72.29431216, 77.62332964,76.73277983, 73.2577506 , 68.94663051, 71.56260558, 73.23788555,72.18109728, 72.91113228, 79.71907419, 79.08983531, 75.68012622,69.34624211, 69.99999113, 70.59301113, 73.15649454, 76.80675034,73.06174071, 71.58152141, 74.5917392 , 70.92747558, 71.09459688,71.14729113, 69.71049054, 73.76625669, 70.83547124, 75.77271092,76.62003904, 75.0997858 , 73.47258688, 73.79872238, 74.43234163,72.89906889, 73.68770338, 76.0615265 , 72.58387186, 81.35615183,79.64560672, 76.88428761, 76.29057142, 72.08150265, 76.34948118,74.24443384, 73.86812266, 73.34583999, 74.23969899, 72.26867144,77.4330788 , 82.0474721 , 81.67401572, 86.75403975, 74.70173333,75.49121084, 72.43801222, 73.35783124, 74.39367964, 75.60157325,72.68339362, 73.39472889, 71.15700466, 71.4236481 , 71.82536751,70.49368668, 68.87238103, 69.20821673, 68.65979521, 67.43204218,69.53069587, 71.49240464, 74.42085224, 74.42945641, 72.1189763 ,70.6695811 , 70.78822755, 70.48341908, 69.92987149, 72.50356197,71.84469177, 72.47348579, 70.45619165, 73.08347213, 74.77526878,75.03720275, 68.30967051, 67.33138216, 75.27953319, 75.62412785,70.6899632 , 69.78732854, 68.79341565, 74.7544205 , 73.62321006,78.27058643, 77.79068965, 71.7177758 , 74.88850039, 76.17157166,...71.52363457, 74.48729578, 72.25085674, 71.49495765, 74.90879611,71.3075095 , 75.69538433, 76.5229253 , 74.87292684, 73.68715627,73.92367618, 72.02712432, 67.92968177, 68.72151399, 69.12682132,70.28261832, 69.55130579, 69.03249992, 74.68174652, 80.47311484,81.05980362, 69.42891464, 68.83564821, 70.44107867, 67.55566031,75.5073511 , 69.59930779, 72.64840542, 69.87781424, 71.27813801,72.36584964, 72.67593452, 73.94064634, 72.94062823, 73.96858635,71.73735741, 72.67569315, 72.98672942, 72.42147632, 69.17260196,70.07956985, 71.68485263, 71.19083354, 73.20467673, 67.35870556,74.50718146, 73.91776526, 77.88753246, 75.62119577, 73.11278613,72.71639404, 68.61218047, 71.30904535, 74.81401492, 77.1975694 ,82.67579324, 72.71458332, 71.48545315, 74.9058645 , 78.1717475 ,74.35721945, 74.43706387, 73.9365943 , 75.41167859, 76.20313631,73.23744039, 70.97007807, 70.39865877, 72.05490788, 73.0457001 ,69.76187619, 70.12657679, 75.65925357, 71.06121734, 68.46385802,68.75201486, 69.72365857, 71.23687925, 74.70314097, 75.53522751,77.84468499, 76.02560486, 76.3969515 , 78.12083929, 78.56893944,72.57552954, 73.4955605 , 77.26066974, 76.88332257, 70.88066813,70.54059543, 67.93941551, 73.0473223 , 74.75157134, 73.01263075,72.06094512, 68.65805597, 71.52819872, 71.7778412 , 70.70515933]]) Attributes: (9) created_at : 2026-07-14T15:10:27.647195+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 : 0.7919321060180664 tuning_steps : 400 /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, -1.08498417, -1.05077865, -0.75935677, -1.37400442,-1.85496624, -0.94723062, -1.11395241, -0.86751337, -0.24945719,-1.13196713, -0.38567466, -0.28631984, -0.39290684, -1.11487725,-1.43852721, -1.54137305, -0.6511997 , -0.79023151, -0.31233874,-0.66827013, 0.14492886, -0.40941263, -0.51331568, -0.8449366 ,-0.26285375, 0.47509636, -0.17208811, 0.39568225, 1.46431253,1.12549655, 1.54718495, 0.70766728, 0.49591797, 1.97764339,1.10735944, 1.88247435, 1.87050395, -1.6056923 , -0.43149774,-0.36337803, -0.56331921, -0.69288407, -0.20167962, -0.5726829 ,0.00746766, 0.26016749, 0.29541562, 1.23416368, 0.47333713,1.00227105, 0.60534737, 1.80626905, 2.07709192, 2.32537719,3.60230735, 2.94093613, 2.60894045, 3.9464667 , 3.07664575,3.70327149, 4.03462903, 2.74289723, 3.56837051, 3.03352449,3.0428552 , 2.53761613, 3.15635351, 2.21813466, 1.86553389,2.81637037, 2.17141484, 2.20613488, 2.75030906, 2.38352684,2.1822572 , 2.21455817, 1.46921248, 1.92070899, 1.88258873,1.66678582, 1.34727329, 0.00479285, 1.39274901, 1.08069951,0.73119664]) Attributes: (7) created_at : 2026-07-14T15:10:27.651286+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, 0.08182629, 0.25403144, 0.44765591,0.55957418, 0.75030867, 1.00038255, 1.11999616, 1.19439373,1.44007857, 1.70470364, 1.80750433, 1.98810138, -1.94865307,-1.68011813, -1.70922901, -1.37040432, -1.40274885, -1.11643657,-1.0500841 , -0.67449204, -0.54198181, -0.34376527, -0.33171222,-0.03219212, 0.04543546, 0.22427874, 0.47530558, 0.67883311,0.79896231, 0.90628277, 1.06436946, 1.41989319, 1.52577654,1.70975215, 2.00076601, 1.93473096, -1.79524338, -1.57401431,-1.52270086, -1.41209235, -1.35745358, -1.05087593, -0.99193711,-0.78434076, -0.63193031, -0.41207621, -0.15782335, -0.13140325,0.00812422, 0.18063304, 0.35732042, 0.49420741, 0.70957397,1.05998299, 1.08296983, 1.32491644, 1.38090935, 1.66574596,1.68682444, 1.94409953, -1.81963689, -1.87272453, -1.5625758 ,-1.44185654, -1.31658669, -1.18260333, -0.85356899, -0.79679937,-0.48650169, -0.49230893, -0.25628245, -0.04971659, 0.11680934,0.16216544, 0.38165759, 0.59301724, 0.71431275, 1.01070775,1.17747632, 1.14778107, 1.33384054, 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 : 2026-07-14T15:10:27.652571+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 : \[\] /predictions(12) Dimensions: - chain: 2 - draw: 400 - obs_ind: 96 Coordinates: (3) 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,)) 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) y (chain, draw, obs_ind) float64 -1.592 -1.999 ... 0.9266 0.599 array([[[-1.59232841, -1.99857157, -1.89860109, ..., 1.31312381,0.84469588, 1.14861878],[-1.80852118, -1.85339561, -1.93880771, ..., 1.34463315,1.20951754, 0.43918698],[-2.48766068, -2.35957589, -1.2142934 , ..., 0.9216618 ,1.02215886, 0.72945998],...,[-1.56675657, -1.93194344, -2.66247233, ..., 1.49947661,1.16894795, 0.13852609],[-2.30154897, -1.68770376, -2.80316569, ..., 1.08146294,0.92143331, 0.98246151],[-2.20397071, -2.56016301, -2.91413958, ..., 0.97176682,-0.03493367, 1.17405254]],[[-1.39977247, -1.38636514, -2.08384791, ..., 1.71963274,1.43806255, 1.33038724],[-2.53145207, -2.11762042, -2.24088833, ..., 1.26368223,1.40735789, 1.1139017 ],[-2.64806931, -2.39433094, -1.96496679, ..., 1.79896161,1.10660571, 0.8866698 ],...,[-1.62073473, -2.16017782, -2.2474717 , ..., 0.86170744,1.68248274, 0.60262682],[-2.60083598, -2.27847453, -1.71777515, ..., 0.71905298,0.39211136, 1.12758547],[-2.59208925, -1.94839179, -2.1159875 , ..., 1.83510852,0.9266363 , 0.59902826]]], shape=(2, 400, 96)) mu (chain, draw, obs_ind) float64 -2.039 -1.93 ... 1.083 0.8962 array([[[-2.03877496, -1.92971569, -1.92845716, ..., 1.07077169,0.88195146, 0.66580285],[-2.03877496, -1.92971569, -1.92845716, ..., 1.07077169,0.88195146, 0.66580285],[-1.98936259, -1.88403251, -1.88281701, ..., 1.11468187,0.94216912, 0.7446882 ],...,[-2.13388196, -2.01072084, -2.00929957, ..., 1.25266293,1.07686738, 0.87562854],[-2.10057292, -1.98427065, -1.98292853, ..., 1.3435276 ,1.18430268, 1.00203279],[-2.2397791 , -2.12826275, -2.12697586, ..., 1.05549811,0.87971259, 0.67848522]],[[-1.84249286, -1.76662075, -1.7657452 , ..., 1.35857024,1.21281262, 1.04595918],[-2.10814511, -1.99008133, -1.98871889, ..., 1.227631 ,1.04558801, 0.83719752],[-2.14614503, -2.02736228, -2.02599155, ..., 1.22622528,1.07446464, 0.90073935],...,[-2.18702465, -2.08118426, -2.07996287, ..., 1.39841879,1.26108931, 1.10388381],[-2.15362113, -2.03705471, -2.03570954, ..., 0.9021826 ,0.69889102, 0.46617659],[-2.10748974, -1.99375122, -1.99243869, ..., 1.24658303,1.08320813, 0.89618762]]], shape=(2, 400, 96)) Attributes: (7) created_at : 2026-07-14T15:10:29.307367+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 : \['chain', 'draw'\] /predictions_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, 0.08182629, 0.25403144, 0.44765591,0.55957418, 0.75030867, 1.00038255, 1.11999616, 1.19439373,1.44007857, 1.70470364, 1.80750433, 1.98810138, -1.94865307,-1.68011813, -1.70922901, -1.37040432, -1.40274885, -1.11643657,-1.0500841 , -0.67449204, -0.54198181, -0.34376527, -0.33171222,-0.03219212, 0.04543546, 0.22427874, 0.47530558, 0.67883311,0.79896231, 0.90628277, 1.06436946, 1.41989319, 1.52577654,1.70975215, 2.00076601, 1.93473096, -1.79524338, -1.57401431,-1.52270086, -1.41209235, -1.35745358, -1.05087593, -0.99193711,-0.78434076, -0.63193031, -0.41207621, -0.15782335, -0.13140325,0.00812422, 0.18063304, 0.35732042, 0.49420741, 0.70957397,1.05998299, 1.08296983, 1.32491644, 1.38090935, 1.66574596,1.68682444, 1.94409953, -1.81963689, -1.87272453, -1.5625758 ,-1.44185654, -1.31658669, -1.18260333, -0.85356899, -0.79679937,-0.48650169, -0.49230893, -0.25628245, -0.04971659, 0.11680934,0.16216544, 0.38165759, 0.59301724, 0.71431275, 1.01070775,1.17747632, 1.14778107, 1.33384054, 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 : 2026-07-14T15:10:29.309915+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 : \[\] # Use tidydraws One call joins `mu` to the observed covariates and responses: ``` python pred = td.prediction_draws(dt, newdata=observed, var_name="mu") pred.head() ``` shape: (5, 9) | chain | draw | obs_ind | mu | groups | group_idx | x | mu_true | y | |-------|------|---------|-----------|---------|-----------|-----------|-----------|-----------| | i64 | i64 | i64 | f64 | str | i64 | f64 | f64 | f64 | | 0 | 0 | 0 | -2.038775 | "North" | 0 | -2.06345 | -1.972207 | -2.106032 | | 0 | 0 | 1 | -1.929716 | "North" | 0 | -1.806841 | -1.882394 | -1.794667 | | 0 | 0 | 2 | -1.928457 | "North" | 0 | -1.80388 | -1.881358 | -2.253447 | | 0 | 0 | 3 | -1.742612 | "North" | 0 | -1.366599 | -1.72831 | -2.094702 | | 0 | 0 | 4 | -1.694453 | "North" | 0 | -1.253284 | -1.688649 | -2.373679 | Note the columns: `chain`, `draw`, `obs_ind`, `mu`, `groups`, `group_idx`, `x`, `mu_true`, and `y`. No `beta`, no `intercept` -- parameters stay in their own frame. # Plotting ## Posterior expected fit by group Summarise `mu` per observation with 50%, 80%, and 95% intervals, then draw nested ribbons, a median line, the true generating line, and the raw observed `y` values. ``` python summary = td.point_interval( pred, "mu", group_by=["obs_ind", "x", "groups", "mu_true", "y"], probs=(0.50, 0.80, 0.95), ).sort(["groups", "x"]) fit_median = summary observed_points = ( summary.select("x", "y", "groups", "mu_true").unique().sort(["groups", "x"]) ) ``` - lets-plot - plotnine ``` python ( lp.ggplot(summary.to_pandas(), lp.aes("x")) + lp.geom_ribbon( mapping=lp.aes( ymin="mu_lower_0.95", ymax="mu_upper_0.95", fill=lp.as_discrete("groups"), group="groups", ), alpha=0.10, color="transparent", ) + lp.geom_ribbon( mapping=lp.aes( ymin="mu_lower_0.80", ymax="mu_upper_0.80", fill=lp.as_discrete("groups"), group="groups", ), alpha=0.18, color="transparent", ) + lp.geom_ribbon( mapping=lp.aes( ymin="mu_lower_0.50", ymax="mu_upper_0.50", fill=lp.as_discrete("groups"), group="groups", ), alpha=0.28, color="transparent", ) + lp.geom_line( mapping=lp.aes(y="mu", color=lp.as_discrete("groups")), size=0.9, ) + lp.geom_line( data=observed_points.to_pandas(), mapping=lp.aes(y="mu_true", color=lp.as_discrete("groups")), linetype="dashed", size=0.8, ) + lp.geom_point( data=observed_points.to_pandas(), mapping=lp.aes(y="y", color=lp.as_discrete("groups")), size=1.8, alpha=0.6, ) + lp.labs( x="x", y="mu / y", color="group", fill="group", title="Posterior expected fit with observed data", ) ) ``` Posterior expected fit by group with nested credible ribbons, true lines, and observed data. ``` python ( p9.ggplot(summary.to_pandas(), p9.aes("x")) + p9.geom_ribbon( mapping=p9.aes( ymin="mu_lower_0.95", ymax="mu_upper_0.95", fill="groups", group="groups", ), alpha=0.10, ) + p9.geom_ribbon( mapping=p9.aes( ymin="mu_lower_0.80", ymax="mu_upper_0.80", fill="groups", group="groups", ), alpha=0.18, ) + p9.geom_ribbon( mapping=p9.aes( ymin="mu_lower_0.50", ymax="mu_upper_0.50", fill="groups", group="groups", ), alpha=0.28, ) + p9.geom_line( mapping=p9.aes(y="mu", color="groups"), size=0.9, ) + p9.geom_line( data=observed_points.to_pandas(), mapping=p9.aes(y="mu_true", color="groups"), linetype="dashed", size=0.8, ) + p9.geom_point( data=observed_points.to_pandas(), mapping=p9.aes(y="y", color="groups"), size=1.8, alpha=0.6, ) + p9.labs( x="x", y="mu / y", color="group", fill="group", title="Posterior expected fit with observed data", ) ) ```

## Posterior predicted fit by group The same interval plot, now using posterior predictive draws of the observed outcome \\y\\ rather than the posterior expectation \\\mu\\. Because \\y\\ includes the observation noise (\\\sigma\\), the intervals are wider -- they represent the distribution of *new data*, not the mean. Code ``` python pred_y = td.prediction_draws(dt, newdata=observed, var_name="y").rename({ "y_right": "y_obs" }) summary_y = td.point_interval( pred_y, "y", group_by=["obs_ind", "x", "groups", "mu_true", "y_obs"], probs=(0.50, 0.80, 0.95), ).sort(["groups", "x"]) ``` - lets-plot - plotnine ``` python ( lp.ggplot(summary_y.to_pandas(), lp.aes("x")) + lp.geom_ribbon( mapping=lp.aes( ymin="y_lower_0.95", ymax="y_upper_0.95", fill=lp.as_discrete("groups"), group="groups", ), alpha=0.10, color="transparent", ) + lp.geom_ribbon( mapping=lp.aes( ymin="y_lower_0.80", ymax="y_upper_0.80", fill=lp.as_discrete("groups"), group="groups", ), alpha=0.18, color="transparent", ) + lp.geom_ribbon( mapping=lp.aes( ymin="y_lower_0.50", ymax="y_upper_0.50", fill=lp.as_discrete("groups"), group="groups", ), alpha=0.28, color="transparent", ) + lp.geom_line( mapping=lp.aes(y="y", color=lp.as_discrete("groups")), size=0.9, ) + lp.geom_line( data=observed_points.to_pandas(), mapping=lp.aes(y="mu_true", color=lp.as_discrete("groups")), linetype="dashed", size=0.8, ) + lp.geom_point( data=observed_points.to_pandas(), mapping=lp.aes(y="y", color=lp.as_discrete("groups")), size=1.8, alpha=0.6, ) + lp.labs( x="x", y="y", color="group", fill="group", title="Posterior predicted fit with observed data", ) ) ``` Posterior predicted fit by group with nested credible intervals, true lines, and observed data. ``` python ( p9.ggplot(summary_y.to_pandas(), p9.aes("x")) + p9.geom_ribbon( mapping=p9.aes( ymin="y_lower_0.95", ymax="y_upper_0.95", fill="groups", group="groups", ), alpha=0.10, ) + p9.geom_ribbon( mapping=p9.aes( ymin="y_lower_0.80", ymax="y_upper_0.80", fill="groups", group="groups", ), alpha=0.18, ) + p9.geom_ribbon( mapping=p9.aes( ymin="y_lower_0.50", ymax="y_upper_0.50", fill="groups", group="groups", ), alpha=0.28, ) + p9.geom_line( mapping=p9.aes(y="y", color="groups"), size=0.9, ) + p9.geom_line( data=observed_points.to_pandas(), mapping=p9.aes(y="mu_true", color="groups"), linetype="dashed", size=0.8, ) + p9.geom_point( data=observed_points.to_pandas(), mapping=p9.aes(y="y", color="groups"), size=1.8, alpha=0.6, ) + p9.labs( x="x", y="y", color="group", fill="group", title="Posterior predicted fit with observed data", ) ) ```

## Group-specific panels Faceting is optional; the tidy frame already contains the group label needed by any plotting backend. - lets-plot - plotnine ``` python ( lp.ggplot(summary.to_pandas(), lp.aes("x")) + lp.geom_ribbon( mapping=lp.aes(ymin="mu_lower_0.95", ymax="mu_upper_0.95", group="groups"), fill="steelblue", alpha=0.10, color="transparent", ) + lp.geom_ribbon( mapping=lp.aes(ymin="mu_lower_0.80", ymax="mu_upper_0.80", group="groups"), fill="steelblue", alpha=0.18, color="transparent", ) + lp.geom_ribbon( mapping=lp.aes(ymin="mu_lower_0.50", ymax="mu_upper_0.50", group="groups"), fill="steelblue", alpha=0.28, color="transparent", ) + lp.geom_line(mapping=lp.aes(y="mu"), color="navy", size=0.8) + lp.geom_line( data=observed_points.to_pandas(), mapping=lp.aes(y="mu_true"), color="firebrick", linetype="dashed", size=0.8, ) + lp.geom_point( data=observed_points.to_pandas(), mapping=lp.aes(y="y"), color="black", size=1.6, alpha=0.55, ) + lp.facet_wrap(facets="groups", ncol=2) + lp.labs(x="x", y="mu / y", title="Each group's fitted relationship") ) ``` Posterior expected fit faceted by group. ``` python ( p9.ggplot(summary.to_pandas(), p9.aes("x")) + p9.geom_ribbon( mapping=p9.aes(ymin="mu_lower_0.95", ymax="mu_upper_0.95", group="groups"), fill="steelblue", alpha=0.10, ) + p9.geom_ribbon( mapping=p9.aes(ymin="mu_lower_0.80", ymax="mu_upper_0.80", group="groups"), fill="steelblue", alpha=0.18, ) + p9.geom_ribbon( mapping=p9.aes(ymin="mu_lower_0.50", ymax="mu_upper_0.50", group="groups"), fill="steelblue", alpha=0.28, ) + p9.geom_line(mapping=p9.aes(y="mu"), color="navy", size=0.8) + p9.geom_line( data=observed_points.to_pandas(), mapping=p9.aes(y="mu_true"), color="firebrick", linetype="dashed", size=0.8, ) + p9.geom_point( data=observed_points.to_pandas(), mapping=p9.aes(y="y"), color="black", size=1.6, alpha=0.55, ) + p9.facet_wrap("~groups", ncol=2) + p9.labs(x="x", y="mu / y", title="Each group's fitted relationship") ) ```

## Spaghetti posterior expectation lines Intervals summarise the draw distribution. Spaghetti lines show individual posterior expectation draws directly; here the first 40 `(chain, draw)` pairs are plotted for stability. ``` python draw_ids = ( pred .select("chain", "draw") .unique() .sort(["chain", "draw"]) .head(40) .with_row_index("curve_id") ) spaghetti = ( pred .join(draw_ids, on=["chain", "draw"], how="inner") .with_columns( (pl.col("groups") + "_" + pl.col("curve_id").cast(pl.Utf8)).alias("curve") ) .sort(["curve", "x"]) ) ``` - lets-plot - plotnine ``` python ( lp.ggplot(spaghetti.to_pandas(), lp.aes("x")) + lp.geom_line( lp.aes(y="mu", group="curve", color=lp.as_discrete("groups")), alpha=0.10, size=0.5, ) + lp.geom_point( data=observed_points.to_pandas(), mapping=lp.aes(y="y", color=lp.as_discrete("groups")), size=1.7, alpha=0.55, ) + lp.labs( x="x", y="mu / y", color="group", title="Individual posterior expectation lines" ) ) ``` ``` python ( p9.ggplot(spaghetti.to_pandas(), p9.aes("x")) + p9.geom_line(p9.aes(y="mu", group="curve", color="groups"), alpha=0.10, size=0.5) + p9.geom_point( data=observed_points.to_pandas(), mapping=p9.aes(y="y", color="groups"), size=1.7, alpha=0.55, ) + p9.labs( x="x", y="mu / y", color="group", title="Individual posterior expectation lines" ) ) ```

## Filter before plotting Subset with `.filter()` before summarising -- useful when the full prediction space is large. ``` python west = td.prediction_draws(dt, newdata=observed, var_name="mu").filter( pl.col("groups") == "West" ) s_west = td.point_interval( west, "mu", group_by=["obs_ind", "x", "y", "mu_true"], probs=(0.89,) ).sort("x") ``` - lets-plot - plotnine ``` python ( lp.ggplot(s_west.to_pandas(), lp.aes("x")) + lp.geom_ribbon( lp.aes(ymin="mu_lower", ymax="mu_upper"), fill="steelblue", alpha=0.3, color="transparent", ) + lp.geom_line(lp.aes(y="mu"), color="navy", size=0.9) + lp.geom_line(lp.aes(y="mu_true"), color="firebrick", linetype="dashed", size=0.8) + lp.geom_point(lp.aes(y="y"), color="black", size=1.6, alpha=0.5) + lp.labs(x="x", y="mu / y", title="West fit with observed data") ) ``` ``` python ( p9.ggplot(s_west.to_pandas(), p9.aes("x")) + p9.geom_ribbon( p9.aes(ymin="mu_lower", ymax="mu_upper"), fill="steelblue", alpha=0.3, ) + p9.geom_line(p9.aes(y="mu"), color="navy", size=0.9) + p9.geom_line(p9.aes(y="mu_true"), color="firebrick", linetype="dashed", size=0.8) + p9.geom_point(p9.aes(y="y"), color="black", size=1.6, alpha=0.5) + p9.labs(x="x", y="mu / y", title="West fit with observed data") ) ```

See [`parameter_draws()`](../../docs/examples/parameter_draws.md) for parameter space, or [`compare_draws()`](../../docs/examples/compare_draws.md) for prior vs posterior.