import numpy as np
import nutpie
import pandas as pd
from lifetimes import BetaGeoBetaBinomFitter

import pymc as pm
from pymc_marketing.clv import BetaGeoBetaBinomModel
from pymc_extras.prior import Prior

data = pd.read_csv("https://raw.githubusercontent.com/pymc-labs/pymc-marketing/main/data/bgbb_donations.csv") 
data.head()

model_config = {
    "alpha": Prior("HalfFlat"),
    "beta": Prior("HalfFlat"),
    "gamma": Prior("HalfFlat"),
    "delta": Prior("HalfFlat"),
}

model = BetaGeoBetaBinomModel(data=data,model_config=model_config)
model.build_model()
model

BG/BB
            alpha ~ HalfFlat()
             beta ~ HalfFlat()
            gamma ~ HalfFlat()
            delta ~ HalfFlat()
recency_frequency ~ BetaGeoBetaBinom(alpha, beta, gamma, delta, <constant>)

pm.model_to_graphviz(model.model)

model.fit(fit_method='map')

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 48B
  Dimensions:  (chain: 1, draw: 1)
  Coordinates:
    * chain    (chain) int64 8B 0
    * draw     (draw) int64 8B 0
  Data variables:
      alpha    (chain, draw) float64 8B 1.204
      beta     (chain, draw) float64 8B 0.7497
      delta    (chain, draw) float64 8B 2.784
      gamma    (chain, draw) float64 8B 0.6568
  Attributes:
      created_at:                 2024-09-12T21:32:31.746938+00:00
      arviz_version:              0.18.0
      inference_library:          pymc
      inference_library_version:  5.13.0

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 1
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0

      array([0])

  • Data variables: (4)
    • alpha
      (chain, draw)
      float64
      1.204

      array([[1.20350252]])

    • beta
      (chain, draw)
      float64
      0.7497

      array([[0.74970501]])

    • delta
      (chain, draw)
      float64
      2.784

      array([[2.78373359]])

    • gamma
      (chain, draw)
      float64
      0.6568

      array([[0.65676895]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Index([0], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([0], dtype='int64', name='draw'))

  • Attributes: (4)

    created_at :

    2024-09-12T21:32:31.746938+00:00

    arviz_version :

    0.18.0

    inference_library :

    pymc

    inference_library_version :

    5.13.0

  
  
• observed_data

  <xarray.Dataset> Size: 267kB
  Dimensions:            (customer_id: 11104, obs_var: 2)
  Coordinates:
    * customer_id        (customer_id) int64 89kB 0 1 2 3 ... 11101 11102 11103
    * obs_var            (obs_var) <U9 72B 'recency' 'frequency'
  Data variables:
      recency_frequency  (customer_id, obs_var) float64 178kB 0.0 0.0 ... 6.0 6.0
  Attributes:
      created_at:                 2024-09-12T21:32:31.749978+00:00
      arviz_version:              0.18.0
      inference_library:          pymc
      inference_library_version:  5.13.0

  xarray.Dataset

  • Dimensions:
    • customer_id: 11104
    • obs_var: 2
  • Coordinates: (2)
    • customer_id
      (customer_id)
      int64
      0 1 2 3 ... 11100 11101 11102 11103

      array([    0,     1,     2, ..., 11101, 11102, 11103])

    • obs_var
      (obs_var)
      <U9
      'recency' 'frequency'

      array(['recency', 'frequency'], dtype='<U9')

  • Data variables: (1)
    • recency_frequency
      (customer_id, obs_var)
      float64
      0.0 0.0 0.0 0.0 ... 6.0 6.0 6.0 6.0

      array([[0., 0.],
             [0., 0.],
             [0., 0.],
             ...,
             [6., 6.],
             [6., 6.],
             [6., 6.]])

  • Indexes: (2)
    • customer_id
      PandasIndex

      PandasIndex(Index([    0,     1,     2,     3,     4,     5,     6,     7,     8,     9,
             ...
             11094, 11095, 11096, 11097, 11098, 11099, 11100, 11101, 11102, 11103],
            dtype='int64', name='customer_id', length=11104))

    • obs_var
      PandasIndex

      PandasIndex(Index(['recency', 'frequency'], dtype='object', name='obs_var'))

  • Attributes: (4)

    created_at :

    2024-09-12T21:32:31.749978+00:00

    arviz_version :

    0.18.0

    inference_library :

    pymc

    inference_library_version :

    5.13.0

  
  
• fit_data

  <xarray.Dataset> Size: 444kB
  Dimensions:      (index: 11104)
  Coordinates:
    * index        (index) int64 89kB 0 1 2 3 4 ... 11099 11100 11101 11102 11103
  Data variables:
      customer_id  (index) int64 89kB 0 1 2 3 4 ... 11099 11100 11101 11102 11103
      frequency    (index) int64 89kB 0 0 0 0 0 0 0 0 0 0 ... 6 6 6 6 6 6 6 6 6 6
      recency      (index) int64 89kB 0 0 0 0 0 0 0 0 0 0 ... 6 6 6 6 6 6 6 6 6 6
      T            (index) int64 89kB 6 6 6 6 6 6 6 6 6 6 ... 6 6 6 6 6 6 6 6 6 6

  xarray.Dataset

  • Dimensions:
    • index: 11104
  • Coordinates: (1)
    • index
      (index)
      int64
      0 1 2 3 ... 11100 11101 11102 11103

      array([    0,     1,     2, ..., 11101, 11102, 11103])

  • Data variables: (4)
    • customer_id
      (index)
      int64
      0 1 2 3 ... 11100 11101 11102 11103

      array([    0,     1,     2, ..., 11101, 11102, 11103])

    • frequency
      (index)
      int64
      0 0 0 0 0 0 0 0 ... 6 6 6 6 6 6 6 6

      array([0, 0, 0, ..., 6, 6, 6])

    • recency
      (index)
      int64
      0 0 0 0 0 0 0 0 ... 6 6 6 6 6 6 6 6

      array([0, 0, 0, ..., 6, 6, 6])

    • T
      (index)
      int64
      6 6 6 6 6 6 6 6 ... 6 6 6 6 6 6 6 6

      array([6, 6, 6, ..., 6, 6, 6])

  • Indexes: (1)
    • index
      PandasIndex

      PandasIndex(RangeIndex(start=0, stop=11104, step=1, name='index'))

  • Attributes: (0)

  
  

model.fit_summary()

alpha    1.204
beta     0.750
delta    2.784
gamma    0.657
Name: value, dtype: float64

Compare to lifetimes

bgbb = BetaGeoBetaBinomFitter().fit(data['frequency'].values,
                             data['recency'].values,
                             data['T'].values
                                )
bgbb

<lifetimes.BetaGeoBetaBinomFitter: fitted with 22 subjects, alpha: 1.20, beta: 0.75, delta: 2.78, gamma: 0.66>

mcmc_model = BetaGeoBetaBinomModel(data=data)
mcmc_model.build_model()
pm.model_to_graphviz(mcmc_model.model)

with mcmc_model.model:
    prior_idata = pm.sample_prior_predictive()

Sampling: [kappa_dropout, kappa_purchase, phi_dropout, phi_purchase, recency_frequency]

prior_idata

arviz.InferenceData

• prior

  <xarray.Dataset> Size: 36kB
  Dimensions:         (chain: 1, draw: 500)
  Coordinates:
    * chain           (chain) int64 8B 0
    * draw            (draw) int64 4kB 0 1 2 3 4 5 6 ... 494 495 496 497 498 499
  Data variables:
      alpha           (chain, draw) float64 4kB 4.591 0.6012 ... 0.4558 1.681
      beta            (chain, draw) float64 4kB 0.2142 4.733 ... 6.893 0.1661
      delta           (chain, draw) float64 4kB 1.696 1.264 229.4 ... 0.1884 1.227
      gamma           (chain, draw) float64 4kB 0.8744 0.3572 ... 0.9208 0.9806
      kappa_dropout   (chain, draw) float64 4kB 2.571 1.621 263.1 ... 1.109 2.207
      kappa_purchase  (chain, draw) float64 4kB 4.805 5.335 3.053 ... 7.348 1.847
      phi_dropout     (chain, draw) float64 4kB 0.3401 0.2203 ... 0.8302 0.4443
      phi_purchase    (chain, draw) float64 4kB 0.9554 0.1127 ... 0.06203 0.9101
  Attributes:
      created_at:                 2024-09-12T21:43:04.658373+00:00
      arviz_version:              0.18.0
      inference_library:          pymc
      inference_library_version:  5.13.0

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

  • Data variables: (8)
    • alpha
      (chain, draw)
      float64
      4.591 0.6012 ... 0.4558 1.681

      array([[4.59120019e+00, 6.01186616e-01, 8.40457302e-01, 2.24198429e+00,
              5.43353336e-01, 9.36562830e-01, 3.45854514e-01, 2.70681628e+00,
              1.75975969e+01, 1.34388115e-01, 4.61431876e-03, 2.05853860e+00,
              7.55066159e+00, 1.29642161e+02, 3.48786682e+00, 1.78175739e+00,
              1.06194804e+01, 8.37511640e-01, 4.78342445e-01, 4.56178244e-01,
              7.64589323e-01, 8.90939121e-01, 1.24762907e+00, 5.86824101e+00,
              1.05207827e+00, 1.69747068e+00, 3.10340277e+00, 7.52096739e-01,
              2.14030942e-01, 1.11682628e+00, 1.33541549e+00, 9.63388864e-01,
              4.65181951e-03, 6.06299800e+00, 1.48277777e+00, 2.48060956e+00,
              2.89953997e-01, 4.17548616e-01, 3.59612777e-01, 6.54100629e+00,
              1.22519004e+00, 4.95530776e-01, 8.40284491e-01, 7.55663865e-02,
              4.63860715e-01, 1.03065812e+00, 4.90727714e-02, 1.12966062e+00,
              4.93780264e+00, 9.42256432e-01, 2.94908632e-01, 1.06231039e+00,
              1.20616490e+00, 5.64450274e-01, 6.02979127e-01, 7.81052086e+00,
              1.40412229e+00, 6.11885129e+00, 1.25547601e+00, 8.38947243e+00,
              1.09454830e+00, 1.79494556e+00, 1.43598862e-01, 3.11350895e-01,
              6.55920727e-01, 9.94006867e-01, 6.70665211e-01, 1.39570826e+00,
              1.83290130e+00, 7.24326376e+00, 6.12094471e-01, 1.14480677e+00,
              4.15707777e-01, 7.91868595e-01, 5.42763024e+00, 2.47598488e+00,
              1.53822645e+00, 4.15836239e-01, 4.26282873e-02, 8.41942467e-01,
      ...
              4.33566289e-01, 1.30261945e+00, 9.18080481e-01, 6.77551087e-01,
              9.64996860e-01, 1.29666169e-01, 1.17543496e+00, 3.27930876e-01,
              2.14517299e-01, 8.00759310e-01, 2.52142870e-02, 9.03126639e-01,
              5.04569450e-02, 1.04766145e+01, 5.44184689e+00, 1.34402732e+01,
              1.17869574e+00, 1.13424201e+00, 5.04610745e-01, 7.33007588e-01,
              1.25388973e+00, 3.77231293e+00, 3.93860954e+00, 3.38295080e+01,
              1.77951012e-02, 1.05598316e+00, 1.07353945e+00, 2.03403924e+00,
              2.08633537e+00, 5.33533622e+00, 5.20958848e+00, 7.94839034e-01,
              1.88337301e+00, 1.66516411e+00, 5.12605277e-01, 1.05507210e+00,
              2.54717208e+00, 1.10373275e+00, 1.80033751e-02, 1.08554089e+00,
              3.75257052e+01, 2.68076036e-01, 2.03115034e-01, 9.90722379e-01,
              1.18832527e+01, 1.49822369e+00, 1.90230431e+00, 7.56099526e-01,
              8.93838887e-01, 3.66868174e+00, 3.08298066e-01, 1.23134737e-01,
              5.37056130e+00, 9.21179785e-01, 8.11887990e-01, 1.41673387e+00,
              1.87638089e+00, 3.04431051e+00, 1.98064958e+00, 6.72049415e-01,
              2.18064752e+01, 8.26053893e-01, 2.19269493e-01, 1.00883125e-01,
              2.49225419e+00, 6.05880873e-01, 5.63106712e-01, 3.81910160e-01,
              1.12957191e+00, 1.08216659e+00, 6.89959253e-01, 1.13277877e+00,
              3.74883213e-02, 7.02151338e+00, 7.96646473e-01, 7.46432110e+00,
              7.15801526e-01, 1.13165973e-01, 4.55842440e-01, 1.68106605e+00]])

    • beta
      (chain, draw)
      float64
      0.2142 4.733 2.213 ... 6.893 0.1661

      array([[2.14194886e-01, 4.73344212e+00, 2.21275593e+00, 2.22038106e-01,
              9.26712549e-01, 4.40379746e-01, 6.77096592e-01, 6.18523967e-02,
              5.37016042e+00, 4.61976148e+00, 2.84072590e+00, 1.16413958e+00,
              2.27898041e+00, 2.37106945e+01, 9.56032495e-02, 2.27478095e+00,
              1.15784456e+01, 3.54565990e-01, 6.26863295e-01, 5.85950818e-01,
              2.61619293e-01, 1.24603083e-01, 3.09452022e+00, 4.64187086e-04,
              9.19251542e-01, 9.56248472e+00, 1.75151822e+00, 3.26922241e-01,
              1.40248949e+00, 2.32892561e-01, 2.57387820e+00, 2.85030153e-01,
              1.22615273e+00, 5.58862242e-01, 1.72541666e+00, 2.02982237e+00,
              7.83365210e-01, 9.53333697e-01, 4.08105750e+00, 3.71820778e+01,
              8.72768897e-02, 5.10173294e-01, 5.01476662e-01, 1.61633507e+00,
              8.63530239e-01, 3.73143380e+00, 1.71533967e+00, 4.80382630e-02,
              4.10450417e+00, 1.40515060e-01, 7.16026625e-01, 9.89807820e-01,
              1.36041189e+00, 1.73946996e+00, 7.28269955e-01, 2.61920343e+00,
              1.86817432e-02, 2.76209233e+01, 7.32663318e+00, 7.90097359e-01,
              4.73375795e-01, 3.90996806e-01, 1.92076846e+00, 1.39352897e+00,
              2.30611665e+00, 2.60914830e-02, 6.78499061e-01, 1.56722445e-01,
              2.35485630e-01, 1.69709557e+00, 7.67139739e-01, 4.25460491e-01,
              1.07804273e+00, 2.37344523e-01, 1.00080287e+00, 5.48046080e-01,
              5.52461043e-03, 2.17744258e+00, 1.27870359e+00, 1.93854590e-01,
      ...
              2.17494522e+00, 6.00122492e-01, 3.27811874e-01, 9.57361204e-01,
              9.08920548e-01, 1.10349551e+00, 1.66357710e-01, 7.06743871e-01,
              9.14022397e-01, 1.87152246e+00, 1.75347654e+00, 1.23292674e-01,
              1.03527915e+00, 2.23603114e+00, 1.58611783e+00, 9.26544626e+00,
              1.06789567e+00, 1.60193961e+00, 5.93155978e-01, 8.89817804e-01,
              2.97253849e-02, 4.23891940e-01, 9.79810429e-01, 1.55060674e+01,
              1.68404445e+00, 2.30595741e-01, 2.79619212e-01, 2.54381500e+00,
              2.80553198e-01, 5.19100081e+00, 8.48607284e-01, 3.54288867e-01,
              1.91711139e-01, 6.10331454e-01, 6.71692815e-01, 1.51079589e+00,
              2.75876406e-01, 1.73965641e+00, 2.05768705e+00, 1.62867973e-01,
              1.22179329e+01, 1.74426007e+00, 1.51521249e+00, 1.18695266e+00,
              5.37979551e+00, 2.33198002e+00, 2.74442313e+00, 5.41238394e-01,
              1.88392965e-01, 1.31073398e+00, 1.12712700e+00, 1.70886815e+00,
              4.64098844e-01, 4.59596438e-01, 3.48841111e+00, 7.86518412e+00,
              6.56086623e+00, 3.15342030e+00, 1.58639493e-01, 5.28447301e-01,
              1.31954244e+01, 2.73621010e-01, 8.56278876e-01, 1.25050687e+00,
              3.28930794e+00, 1.89656447e+00, 5.13933607e-01, 9.00062418e-01,
              1.21169879e+00, 7.97093588e-01, 6.71172509e-01, 4.43072475e-01,
              1.60406864e+00, 7.98027950e+00, 3.06342775e-01, 3.68944739e-01,
              1.58508080e+00, 1.34434296e+00, 6.89256790e+00, 1.66115591e-01]])

    • delta
      (chain, draw)
      float64
      1.696 1.264 229.4 ... 0.1884 1.227

      array([[1.69633164e+00, 1.26371927e+00, 2.29438073e+02, 2.87733242e+00,
              7.63820744e-01, 1.16244642e+00, 3.48775791e-01, 1.73707267e+00,
              6.83637017e-01, 4.47232545e-01, 5.25101296e+00, 5.69788070e-02,
              5.34291418e-01, 3.01766596e+00, 2.36107806e+00, 6.71283772e-01,
              2.23655511e-01, 4.17980224e-01, 6.71517138e-01, 1.11037521e+00,
              2.99348204e+00, 2.69861054e+00, 9.28808147e-01, 1.56231225e+00,
              2.15423793e+00, 4.30969961e+00, 8.92309453e-01, 6.76611430e+00,
              1.17933931e+00, 9.14452657e-01, 5.40311037e-01, 1.30098769e+00,
              5.62058521e-01, 2.17072979e+00, 3.69101744e-01, 6.43621044e-01,
              1.07834364e+00, 7.24712122e-01, 1.50010038e-01, 1.21442443e+01,
              2.00750254e+00, 2.77998612e+00, 4.27291905e-01, 5.93252213e-01,
              6.50269309e-01, 1.01171746e+00, 5.09271333e-01, 2.30694943e+00,
              4.15091112e-01, 2.97600932e+00, 8.47530965e-02, 1.17687750e+00,
              1.34939300e+00, 9.01786178e-01, 2.26806342e-01, 9.80699623e-01,
              1.68504524e+00, 3.20020387e-01, 8.48161780e-01, 7.40814915e-01,
              1.46065968e+01, 7.38088229e-01, 6.03617013e-01, 2.05282748e+00,
              1.00336124e+00, 2.68790362e+00, 2.34861436e-01, 5.50024890e+00,
              8.44313589e-02, 1.03390920e+00, 1.51814657e+00, 9.06950425e+00,
              7.63164091e+00, 7.84392679e-01, 2.10734418e+00, 8.58871353e-02,
              3.58892580e-01, 4.85176167e-01, 1.74730132e-01, 1.57566774e+00,
      ...
              2.50809793e+00, 6.86589534e+00, 1.61861619e+00, 8.16142271e-02,
              2.15321745e+00, 6.19389393e-01, 8.31531452e-01, 2.15538325e+00,
              1.12248787e+00, 3.61165827e+00, 7.39839727e-01, 7.19435150e-01,
              3.00553476e-01, 1.43554794e+00, 7.11082218e-01, 1.00798611e+00,
              4.26049124e-01, 2.00213748e-01, 5.82344168e-01, 3.72407036e+00,
              1.34123965e+00, 1.21295261e+00, 1.48580302e+00, 3.83209322e+01,
              6.24011062e-01, 9.40888514e+00, 8.20737724e-01, 7.00729021e-01,
              1.01793852e+00, 1.13330846e-01, 1.86851415e+00, 1.73467498e+00,
              2.27112123e+00, 6.94444979e+00, 5.71304522e-01, 1.71707520e-01,
              8.44818672e-02, 1.32352692e+00, 7.88442269e-01, 7.75926006e+00,
              7.03320859e-01, 9.10562047e-01, 1.60404268e+00, 2.16521378e+00,
              1.15788237e+00, 2.13101323e+00, 9.03456870e-01, 2.53117845e+00,
              8.89248971e-01, 6.58480486e+00, 4.05090225e+01, 4.85343576e-01,
              8.44216799e-03, 7.88290237e-02, 6.04877653e-01, 1.11808022e+00,
              2.06555664e+00, 5.08481478e-01, 5.69344698e-01, 6.78032172e-01,
              2.39327539e-01, 1.54925503e+00, 8.13406202e-01, 7.44782152e-01,
              1.07439633e+00, 1.01082292e+00, 6.81482654e+00, 1.09670644e+00,
              1.08104615e-01, 1.84759014e+01, 8.68775308e-01, 7.74334800e-01,
              8.75696649e-01, 7.36384717e-01, 5.91263970e+00, 9.18220911e-01,
              6.08363809e-02, 1.31272628e+00, 1.88390867e-01, 1.22668368e+00]])

    • gamma
      (chain, draw)
      float64
      0.8744 0.3572 ... 0.9208 0.9806

      array([[8.74372683e-01, 3.57152581e-01, 3.36667357e+01, 5.46447991e+00,
              9.78185103e-01, 5.86001453e-01, 1.25861437e+00, 1.59013527e+00,
              1.49379324e+00, 1.38352294e+00, 4.83734022e-01, 1.56889202e+00,
              4.85712793e-01, 7.94776216e-01, 2.01248270e+00, 5.51318919e-01,
              1.31209976e+00, 8.26122688e-01, 6.88068040e-01, 1.05956504e+00,
              2.02467719e+00, 1.09219955e+00, 1.61258066e+00, 1.63320924e-01,
              9.19321306e-01, 4.90928297e-01, 1.59572214e-01, 3.01730472e+00,
              2.43941173e+00, 2.07916047e+00, 1.71164811e+00, 7.28973784e-02,
              5.85148414e-01, 7.52814242e-01, 7.36045511e-01, 4.29432949e-01,
              3.42550287e-01, 4.99567996e-01, 8.91465651e+00, 8.59586553e+00,
              1.46433972e+00, 1.02013968e+00, 1.27587326e+00, 5.12825817e-01,
              4.97954171e-01, 9.39822987e-01, 6.74610576e-01, 1.25893341e+00,
              1.57946862e+00, 2.74724041e+00, 2.07312107e+00, 8.81330021e-01,
              1.90036523e-01, 9.65993894e-01, 1.54339332e+00, 3.80796570e-01,
              2.21257742e+00, 1.00991995e+00, 4.73995799e+00, 2.21347417e+00,
              2.92228047e+00, 2.94257283e+00, 5.19188294e-01, 1.06591279e+00,
              2.09370221e-01, 3.04235579e-01, 9.19474053e-01, 1.73437172e+00,
              6.20350986e+00, 1.30240423e+00, 9.80088978e-02, 6.87286719e+00,
              1.32711560e+00, 3.09442962e-01, 7.39271273e-02, 2.03537260e+00,
              7.48308502e-01, 2.19910422e+00, 1.42050072e+00, 1.27439862e+00,
      ...
              1.47564336e-01, 5.95601424e+00, 2.05213527e-01, 4.75236114e+00,
              1.36047911e-01, 1.49252874e+00, 6.11598533e-01, 2.79849207e-01,
              1.50644960e+00, 1.40980152e+00, 1.42073908e+00, 6.10751129e-01,
              1.94864181e+00, 1.33354903e+00, 7.68065301e-01, 3.30020152e-01,
              1.00588492e+00, 8.62338750e-01, 6.68140730e-01, 1.65200436e+00,
              1.44381824e+00, 1.96798742e+00, 4.25274952e-01, 2.12664560e-01,
              5.44148657e-01, 8.91741856e+01, 3.85682805e-01, 8.15427788e-01,
              1.25178817e+00, 9.04483515e-01, 2.38330812e-01, 2.03638713e+00,
              2.13533089e+00, 8.15810507e+00, 1.41233886e+00, 8.78879894e-01,
              1.24293853e+00, 8.03757100e-01, 2.62811325e-01, 7.59972859e-01,
              4.60079106e-01, 2.36200378e-01, 2.07833704e-02, 1.92245115e+00,
              1.12939667e+00, 1.55106484e+01, 7.00205752e-01, 6.87905725e-01,
              1.71559116e-01, 4.27430181e+00, 2.59623750e+00, 6.30024739e-01,
              9.20868885e+00, 1.03095332e+00, 4.27485817e-01, 3.93325483e+00,
              2.35599696e-02, 4.95247755e-01, 2.17281342e+00, 6.05288151e-01,
              7.78163584e-01, 5.23440287e-01, 6.80123806e-01, 4.32212993e-01,
              2.49359114e+00, 9.56328683e-03, 8.79293464e+00, 2.28163883e-01,
              1.20503898e+00, 1.67450296e+01, 3.98316074e-01, 1.82012610e+00,
              4.83708106e-01, 1.13688949e+00, 9.26990120e+00, 4.28193974e-01,
              1.77466073e+00, 2.51903906e-01, 9.20809879e-01, 9.80639812e-01]])

    • kappa_dropout
      (chain, draw)
      float64
      2.571 1.621 263.1 ... 1.109 2.207

      array([[  2.57070433,   1.62087186, 263.10480839,   8.34181233,
                1.74200585,   1.74844787,   1.60739016,   3.32720794,
                2.17743026,   1.83075548,   5.73474698,   1.62587083,
                1.02000421,   3.81244218,   4.37356076,   1.22260269,
                1.53575527,   1.24410291,   1.35958518,   2.16994024,
                5.01815923,   3.7908101 ,   2.54138881,   1.72563317,
                3.07355924,   4.8006279 ,   1.05188167,   9.78341902,
                3.61875105,   2.99361312,   2.25195914,   1.37388507,
                1.14720693,   2.92354403,   1.10514725,   1.07305399,
                1.42089393,   1.22428012,   9.06466655,  20.74010982,
                3.47184225,   3.8001258 ,   1.70316517,   1.10607803,
                1.14822348,   1.95154045,   1.18388191,   3.56588284,
                1.99455974,   5.72324973,   2.15787417,   2.05820752,
                1.53942952,   1.86778007,   1.77019966,   1.36149619,
                3.89762266,   1.32994034,   5.58811977,   2.95428909,
               17.52887726,   3.68066106,   1.12280531,   3.11874027,
                1.21273146,   2.9921392 ,   1.15433549,   7.23462062,
                6.28794122,   2.33631342,   1.61615547,  15.94237144,
                8.95875651,   1.09383564,   2.18127131,   2.12125973,
                1.10720108,   2.68428039,   1.59523085,   2.85006636,
      ...
                2.65566227,  12.82190957,   1.82382972,   4.83397536,
                2.28926536,   2.11191813,   1.44312999,   2.43523246,
                2.62893747,   5.02145978,   2.16057881,   1.33018628,
                2.24919528,   2.76909698,   1.47914752,   1.33800626,
                1.43193404,   1.0625525 ,   1.2504849 ,   5.37607472,
                2.78505789,   3.18094004,   1.91107797,  38.5335968 ,
                1.16815972,  98.58307078,   1.20642053,   1.51615681,
                2.26972669,   1.01781436,   2.10684496,   3.77106211,
                4.40645212,  15.10255486,   1.98364338,   1.05058741,
                1.3274204 ,   2.12728402,   1.05125359,   8.51923292,
                1.16339997,   1.14676243,   1.62482605,   4.08766492,
                2.28727903,  17.64166164,   1.60366262,   3.21908417,
                1.06080809,  10.85910667,  43.10525996,   1.11536831,
                9.21713102,   1.10978235,   1.03236347,   5.05133504,
                2.08911661,   1.00372923,   2.74215812,   1.28332032,
                1.01749112,   2.07269532,   1.49353001,   1.17699514,
                3.56798747,   1.0203862 ,  15.60776118,   1.32487032,
                1.3131436 ,  35.22093098,   1.26709138,   2.5944609 ,
                1.35940476,   1.87327421,  15.18254091,   1.34641489,
                1.83549711,   1.56463019,   1.10920075,   2.20732349]])

    • kappa_purchase
      (chain, draw)
      float64
      4.805 5.335 3.053 ... 7.348 1.847

      array([[4.80539507e+00, 5.33462874e+00, 3.05321323e+00, 2.46402239e+00,
              1.47006588e+00, 1.37694258e+00, 1.02295111e+00, 2.76866867e+00,
              2.29677573e+01, 4.75414960e+00, 2.84534021e+00, 3.22267818e+00,
              9.82964200e+00, 1.53352856e+02, 3.58347006e+00, 4.05653834e+00,
              2.21979261e+01, 1.19207763e+00, 1.10520574e+00, 1.04212906e+00,
              1.02620862e+00, 1.01554220e+00, 4.34214929e+00, 5.86870520e+00,
              1.97132981e+00, 1.12599554e+01, 4.85492098e+00, 1.07901898e+00,
              1.61652044e+00, 1.34971884e+00, 3.90929369e+00, 1.24841902e+00,
              1.23080455e+00, 6.62186025e+00, 3.20819443e+00, 4.51043193e+00,
              1.07331921e+00, 1.37088231e+00, 4.44067028e+00, 4.37230840e+01,
              1.31246693e+00, 1.00570407e+00, 1.34176115e+00, 1.69190145e+00,
              1.32739095e+00, 4.76209192e+00, 1.76441244e+00, 1.17769888e+00,
              9.04230681e+00, 1.08277149e+00, 1.01093526e+00, 2.05211821e+00,
              2.56657679e+00, 2.30392023e+00, 1.33124908e+00, 1.04297243e+01,
              1.42280404e+00, 3.37397746e+01, 8.58210919e+00, 9.17956979e+00,
              1.56792410e+00, 2.18594236e+00, 2.06436733e+00, 1.70487987e+00,
              2.96203738e+00, 1.02009835e+00, 1.34916427e+00, 1.55243070e+00,
              2.06838694e+00, 8.94035933e+00, 1.37923421e+00, 1.57026726e+00,
              1.49375051e+00, 1.02921312e+00, 6.42843311e+00, 3.02403096e+00,
              1.54375106e+00, 2.59327881e+00, 1.32133187e+00, 1.03579706e+00,
      ...
              2.60851151e+00, 1.90274194e+00, 1.24589236e+00, 1.63491229e+00,
              1.87391741e+00, 1.23316168e+00, 1.34179266e+00, 1.03467475e+00,
              1.12853970e+00, 2.67228177e+00, 1.77869083e+00, 1.02641931e+00,
              1.08573609e+00, 1.27126456e+01, 7.02796472e+00, 2.27057194e+01,
              2.24659140e+00, 2.73618163e+00, 1.09776672e+00, 1.62282539e+00,
              1.28361512e+00, 4.19620487e+00, 4.91841997e+00, 4.93355755e+01,
              1.70183955e+00, 1.28657890e+00, 1.35315866e+00, 4.57785424e+00,
              2.36688857e+00, 1.05263370e+01, 6.05819577e+00, 1.14912790e+00,
              2.07508415e+00, 2.27549556e+00, 1.18429809e+00, 2.56586799e+00,
              2.82304848e+00, 2.84338916e+00, 2.07569042e+00, 1.24840886e+00,
              4.97436381e+01, 2.01233611e+00, 1.71832753e+00, 2.17767504e+00,
              1.72630482e+01, 3.83020370e+00, 4.64672744e+00, 1.29733792e+00,
              1.08223185e+00, 4.97941572e+00, 1.43542506e+00, 1.83200288e+00,
              5.83466015e+00, 1.38077622e+00, 4.30029910e+00, 9.28191799e+00,
              8.43724712e+00, 6.19773082e+00, 2.13928907e+00, 1.20049672e+00,
              3.50018995e+01, 1.09967490e+00, 1.07554837e+00, 1.35139000e+00,
              5.78156213e+00, 2.50244534e+00, 1.07704032e+00, 1.28197258e+00,
              2.34127070e+00, 1.87926018e+00, 1.36113176e+00, 1.57585124e+00,
              1.64155696e+00, 1.50017929e+01, 1.10298925e+00, 7.83326584e+00,
              2.30088233e+00, 1.45750893e+00, 7.34841034e+00, 1.84718164e+00]])

    • phi_dropout
      (chain, draw)
      float64
      0.3401 0.2203 ... 0.8302 0.4443

      array([[3.40129619e-01, 2.20345970e-01, 1.27959409e-01, 6.55071067e-01,
              5.61528025e-01, 3.35155233e-01, 7.83017341e-01, 4.77918814e-01,
              6.86034942e-01, 7.55711481e-01, 8.43514149e-02, 9.64954899e-01,
              4.76187047e-01, 2.08469054e-01, 4.60147419e-01, 4.50938742e-01,
              8.54367740e-01, 6.64030829e-01, 5.06086747e-01, 4.88292264e-01,
              4.03470096e-01, 2.88117718e-01, 6.34527332e-01, 9.46440567e-02,
              2.99106422e-01, 1.02263351e-01, 1.51701678e-01, 3.08410047e-01,
              6.74103220e-01, 6.94532119e-01, 7.60070675e-01, 5.30592988e-02,
              5.10063525e-01, 2.57500566e-01, 6.66015780e-01, 4.00196963e-01,
              2.41080830e-01, 4.08050403e-01, 9.83451124e-01, 4.14456124e-01,
              4.21775993e-01, 2.68448924e-01, 7.49118927e-01, 4.63643435e-01,
              4.33673566e-01, 4.81580071e-01, 5.69829280e-01, 3.53049572e-01,
              7.91888353e-01, 4.80014072e-01, 9.60723800e-01, 4.28202702e-01,
              1.23446069e-01, 5.17188243e-01, 8.71875276e-01, 2.79689779e-01,
              5.67673583e-01, 7.59372373e-01, 8.48220544e-01, 7.49240886e-01,
              1.66712358e-01, 7.99468569e-01, 4.62402779e-01, 3.41776710e-01,
              1.72643515e-01, 1.01678284e-01, 7.96539707e-01, 2.39732227e-01,
              9.86572496e-01, 5.57461261e-01, 6.06432363e-02, 4.31106954e-01,
              1.48136139e-01, 2.82897129e-01, 3.38917616e-02, 9.59511259e-01,
              6.75856007e-01, 8.19252799e-01, 8.90467181e-01, 4.47146999e-01,
      ...
              5.55659269e-02, 4.64518503e-01, 1.12517920e-01, 9.83116541e-01,
              5.94286333e-02, 7.06717139e-01, 4.23800031e-01, 1.14916835e-01,
              5.73026030e-01, 2.80755314e-01, 6.57573367e-01, 4.59147067e-01,
              8.66372885e-01, 4.81582640e-01, 5.19262137e-01, 2.46650679e-01,
              7.02465958e-01, 8.11572842e-01, 5.34305317e-01, 3.07288207e-01,
              5.18415880e-01, 6.18681082e-01, 2.22531450e-01, 5.51893872e-03,
              4.65817001e-01, 9.04558815e-01, 3.19691845e-01, 5.37825496e-01,
              5.51514935e-01, 8.88652734e-01, 1.13122140e-01, 5.40003604e-01,
              4.84591875e-01, 5.40180462e-01, 7.11992323e-01, 8.36560463e-01,
              9.36356359e-01, 3.77832529e-01, 2.49998028e-01, 8.92067239e-02,
              3.95460822e-01, 2.05971501e-01, 1.27911356e-02, 4.70305464e-01,
              4.93773016e-01, 8.79205640e-01, 4.36629091e-01, 2.13696097e-01,
              1.61724932e-01, 3.93614497e-01, 6.02301785e-02, 5.64858021e-01,
              9.99084079e-01, 9.28968933e-01, 4.14084602e-01, 7.78656492e-01,
              1.12774794e-02, 4.93407722e-01, 7.92373498e-01, 4.71657886e-01,
              7.64786608e-01, 2.52540874e-01, 4.55380074e-01, 3.67217312e-01,
              6.98878895e-01, 9.37222278e-03, 5.63369374e-01, 1.72216012e-01,
              9.17674948e-01, 4.75428363e-01, 3.14354655e-01, 7.01543084e-01,
              3.55823462e-01, 6.06899666e-01, 6.10563229e-01, 3.18025282e-01,
              9.66855638e-01, 1.60999006e-01, 8.30156202e-01, 4.44266469e-01]])

    • phi_purchase
      (chain, draw)
      float64
      0.9554 0.1127 ... 0.06203 0.9101

      array([[9.55426165e-01, 1.12695118e-01, 2.75269770e-01, 9.09887951e-01,
              3.69611554e-01, 6.80175663e-01, 3.38094863e-01, 9.77659878e-01,
              7.66186992e-01, 2.82675403e-02, 1.62171073e-03, 6.38766420e-01,
              7.68152247e-01, 8.45384721e-01, 9.73321041e-01, 4.39230999e-01,
              4.78399667e-01, 7.02564681e-01, 4.32808506e-01, 4.37736803e-01,
              7.45062272e-01, 8.77303885e-01, 2.87329843e-01, 9.99920905e-01,
              5.33689625e-01, 1.50752878e-01, 6.39228276e-01, 6.97019008e-01,
              1.32402250e-01, 8.27451055e-01, 3.41600195e-01, 7.71687111e-01,
              3.77949489e-03, 9.15603438e-01, 4.62184509e-01, 5.49971621e-01,
              2.70147031e-01, 3.04583852e-01, 8.09816435e-02, 1.49600753e-01,
              9.33501646e-01, 4.92720265e-01, 6.26254896e-01, 4.46635862e-02,
              3.49452973e-01, 2.16429698e-01, 2.78125286e-02, 9.59210063e-01,
              5.46077759e-01, 8.70226487e-01, 2.91718614e-01, 5.17665302e-01,
              4.69950832e-01, 2.44995580e-01, 4.52942380e-01, 7.48871269e-01,
              9.86869771e-01, 1.81354243e-01, 1.46289913e-01, 9.13928716e-01,
              6.98087557e-01, 8.21131237e-01, 6.95607124e-02, 1.82623363e-01,
              2.21442421e-01, 9.74422581e-01, 4.97096777e-01, 8.99047059e-01,
              8.86150107e-01, 8.10175911e-01, 4.43792988e-01, 7.29052181e-01,
              2.78297998e-01, 7.69392249e-01, 8.44316203e-01, 8.18769686e-01,
              9.96421307e-01, 1.60351535e-01, 3.22616053e-02, 8.12845008e-01,
      ...
              1.66212144e-01, 6.84601217e-01, 7.36885877e-01, 4.14426566e-01,
              5.14962322e-01, 1.05149366e-01, 8.76018319e-01, 3.16941026e-01,
              1.90083964e-01, 2.99653772e-01, 1.41757559e-02, 8.79880793e-01,
              4.64725685e-02, 8.24109694e-01, 7.74313348e-01, 5.91933377e-01,
              5.24659596e-01, 4.14534621e-01, 4.59670287e-01, 4.51686048e-01,
              9.76842447e-01, 8.98982068e-01, 8.00787563e-01, 6.85702107e-01,
              1.04563919e-02, 8.20768286e-01, 7.93358148e-01, 4.44321538e-01,
              8.81467509e-01, 5.06855918e-01, 8.59924090e-01, 6.91688918e-01,
              9.07612837e-01, 7.31780864e-01, 4.32834673e-01, 4.11195005e-01,
              9.02277128e-01, 3.88175059e-01, 8.67343937e-03, 8.69539557e-01,
              7.54382000e-01, 1.33216333e-01, 1.18205075e-01, 4.54945004e-01,
              6.88363524e-01, 3.91160315e-01, 4.09385818e-01, 5.82808468e-01,
              8.25921807e-01, 7.36769522e-01, 2.14778238e-01, 6.72131786e-02,
              9.20458290e-01, 6.67146327e-01, 1.88798028e-01, 1.52633741e-01,
              2.22392548e-01, 4.91197602e-01, 9.25844761e-01, 5.59809457e-01,
              6.23008336e-01, 7.51180090e-01, 2.03867626e-01, 7.46513775e-02,
              4.31069344e-01, 2.42115527e-01, 5.22827885e-01, 2.97908213e-01,
              4.82461045e-01, 5.75847136e-01, 5.06901148e-01, 7.18836103e-01,
              2.28370518e-02, 4.68044949e-01, 7.22261323e-01, 9.52900266e-01,
              3.11098711e-01, 7.76434167e-02, 6.20327961e-02, 9.10070787e-01]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Index([0], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
            dtype='int64', name='draw', length=500))

  • Attributes: (4)

    created_at :

    2024-09-12T21:43:04.658373+00:00

    arviz_version :

    0.18.0

    inference_library :

    pymc

    inference_library_version :

    5.13.0

  
  
• prior_predictive

  <xarray.Dataset> Size: 89MB
  Dimensions:            (chain: 1, draw: 500, customer_id: 11104, obs_var: 2)
  Coordinates:
    * chain              (chain) int64 8B 0
    * draw               (draw) int64 4kB 0 1 2 3 4 5 ... 494 495 496 497 498 499
    * customer_id        (customer_id) int64 89kB 0 1 2 3 ... 11101 11102 11103
    * obs_var            (obs_var) <U9 72B 'recency' 'frequency'
  Data variables:
      recency_frequency  (chain, draw, customer_id, obs_var) float64 89MB 1.0 ....
  Attributes:
      created_at:                 2024-09-12T21:43:04.660348+00:00
      arviz_version:              0.18.0
      inference_library:          pymc
      inference_library_version:  5.13.0

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 500
    • customer_id: 11104
    • obs_var: 2
  • Coordinates: (4)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 495 496 497 498 499

      array([  0,   1,   2, ..., 497, 498, 499])

    • customer_id
      (customer_id)
      int64
      0 1 2 3 ... 11100 11101 11102 11103

      array([    0,     1,     2, ..., 11101, 11102, 11103])

    • obs_var
      (obs_var)
      <U9
      'recency' 'frequency'

      array(['recency', 'frequency'], dtype='<U9')

  • Data variables: (1)
    • recency_frequency
      (chain, draw, customer_id, obs_var)
      float64
      1.0 1.0 2.0 2.0 ... 1.0 1.0 6.0 0.0

      array([[[[1., 1.],
               [2., 2.],
               [1., 1.],
               ...,
               [7., 7.],
               [4., 4.],
               [5., 5.]],
      
              [[6., 0.],
               [6., 0.],
               [6., 0.],
               ...,
               [6., 0.],
               [3., 1.],
               [6., 0.]],
      
              [[6., 0.],
               [2., 2.],
               [6., 1.],
               ...,
      ...
               ...,
               [6., 0.],
               [6., 0.],
               [7., 7.]],
      
              [[6., 0.],
               [6., 0.],
               [6., 0.],
               ...,
               [6., 0.],
               [6., 0.],
               [6., 0.]],
      
              [[6., 0.],
               [6., 0.],
               [6., 0.],
               ...,
               [2., 2.],
               [1., 1.],
               [6., 0.]]]])

  • Indexes: (4)
    • chain
      PandasIndex

      PandasIndex(Index([0], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             490, 491, 492, 493, 494, 495, 496, 497, 498, 499],
            dtype='int64', name='draw', length=500))

    • customer_id
      PandasIndex

      PandasIndex(Index([    0,     1,     2,     3,     4,     5,     6,     7,     8,     9,
             ...
             11094, 11095, 11096, 11097, 11098, 11099, 11100, 11101, 11102, 11103],
            dtype='int64', name='customer_id', length=11104))

    • obs_var
      PandasIndex

      PandasIndex(Index(['recency', 'frequency'], dtype='object', name='obs_var'))

  • Attributes: (4)

    created_at :

    2024-09-12T21:43:04.660348+00:00

    arviz_version :

    0.18.0

    inference_library :

    pymc

    inference_library_version :

    5.13.0

  
  
• observed_data

  <xarray.Dataset> Size: 267kB
  Dimensions:            (customer_id: 11104, obs_var: 2)
  Coordinates:
    * customer_id        (customer_id) int64 89kB 0 1 2 3 ... 11101 11102 11103
    * obs_var            (obs_var) <U9 72B 'recency' 'frequency'
  Data variables:
      recency_frequency  (customer_id, obs_var) float64 178kB 0.0 0.0 ... 6.0 6.0
  Attributes:
      created_at:                 2024-09-12T21:43:04.661115+00:00
      arviz_version:              0.18.0
      inference_library:          pymc
      inference_library_version:  5.13.0

  xarray.Dataset

  • Dimensions:
    • customer_id: 11104
    • obs_var: 2
  • Coordinates: (2)
    • customer_id
      (customer_id)
      int64
      0 1 2 3 ... 11100 11101 11102 11103

      array([    0,     1,     2, ..., 11101, 11102, 11103])

    • obs_var
      (obs_var)
      <U9
      'recency' 'frequency'

      array(['recency', 'frequency'], dtype='<U9')

  • Data variables: (1)
    • recency_frequency
      (customer_id, obs_var)
      float64
      0.0 0.0 0.0 0.0 ... 6.0 6.0 6.0 6.0

      array([[0., 0.],
             [0., 0.],
             [0., 0.],
             ...,
             [6., 6.],
             [6., 6.],
             [6., 6.]])

  • Indexes: (2)
    • customer_id
      PandasIndex

      PandasIndex(Index([    0,     1,     2,     3,     4,     5,     6,     7,     8,     9,
             ...
             11094, 11095, 11096, 11097, 11098, 11099, 11100, 11101, 11102, 11103],
            dtype='int64', name='customer_id', length=11104))

    • obs_var
      PandasIndex

      PandasIndex(Index(['recency', 'frequency'], dtype='object', name='obs_var'))

  • Attributes: (4)

    created_at :

    2024-09-12T21:43:04.661115+00:00

    arviz_version :

    0.18.0

    inference_library :

    pymc

    inference_library_version :

    5.13.0

  
  

nutpie es aproximadamente 3 veces más rápido que el muestreador NUTS predeterminado en pymc.

# add warning supress here
mcmc_model.fit(nuts_sampler="nutpie")

/Users/coltallen/miniconda3/envs/pymc-marketing-dev/lib/python3.10/site-packages/nutpie/compile_pymc.py:554: NumbaWarning: Cannot cache compiled function "numba_funcified_fgraph" as it uses dynamic globals (such as ctypes pointers and large global arrays)
  return inner(x)
/Users/coltallen/miniconda3/envs/pymc-marketing-dev/lib/python3.10/site-packages/nutpie/compile_pymc.py:554: NumbaWarning: Cannot cache compiled function "scan" as it uses dynamic globals (such as ctypes pointers and large global arrays)
  return inner(x)
/Users/coltallen/miniconda3/envs/pymc-marketing-dev/lib/python3.10/site-packages/nutpie/compile_pymc.py:554: NumbaWarning: Cannot cache compiled function "numba_funcified_fgraph" as it uses dynamic globals (such as ctypes pointers and large global arrays)
  return inner(x)

Sampler Progress

Total Chains: 4

Active Chains: 0

Finished Chains: 4

Sampling for 6 minutes

Estimated Time to Completion: now

Progress	Draws	Divergences	Step Size	Gradients/Draw
	2000	0	0.68	7
	2000	0	0.69	3
	2000	0	0.66	3
	2000	0	0.64	7

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 392kB
  Dimensions:                    (chain: 4, draw: 1000)
  Coordinates:
    * chain                      (chain) int64 32B 0 1 2 3
    * draw                       (draw) int64 8kB 0 1 2 3 4 ... 996 997 998 999
  Data variables:
      alpha                      (chain, draw) float64 32kB 1.32 1.196 ... 1.15
      beta                       (chain, draw) float64 32kB 0.7781 ... 0.7317
      delta                      (chain, draw) float64 32kB 2.402 2.853 ... 2.966
      gamma                      (chain, draw) float64 32kB 0.6269 ... 0.6927
      kappa_dropout              (chain, draw) float64 32kB 3.029 3.539 ... 3.658
      kappa_dropout_interval__   (chain, draw) float64 32kB 0.7075 ... 0.9777
      kappa_purchase             (chain, draw) float64 32kB 2.098 1.946 ... 1.882
      kappa_purchase_interval__  (chain, draw) float64 32kB 0.09346 ... -0.1257
      phi_dropout                (chain, draw) float64 32kB 0.207 0.194 ... 0.1893
      phi_dropout_interval__     (chain, draw) float64 32kB -1.343 ... -1.454
      phi_purchase               (chain, draw) float64 32kB 0.6291 ... 0.6112
      phi_purchase_interval__    (chain, draw) float64 32kB 0.5284 ... 0.4523
  Attributes:
      created_at:                 2024-09-12T21:27:00.667319+00:00
      arviz_version:              0.18.0
      inference_library:          nutpie
      inference_library_version:  0.13.2
      sampling_time:              371.8816521167755

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

  • Data variables: (12)
    • alpha
      (chain, draw)
      float64
      1.32 1.196 1.116 ... 1.231 1.15

      array([[1.31983343, 1.19613816, 1.11633624, ..., 1.19530602, 1.20798819,
              1.1413295 ],
             [1.31337897, 1.30273396, 1.12029689, ..., 1.26978512, 1.2425516 ,
              1.17233724],
             [1.1111005 , 1.12419778, 1.20833662, ..., 1.18945544, 1.20810213,
              1.16681921],
             [1.19547515, 1.19547515, 1.19635735, ..., 1.2526484 , 1.23092149,
              1.15016888]])

    • beta
      (chain, draw)
      float64
      0.7781 0.7502 ... 0.7577 0.7317

      array([[0.77812916, 0.7501652 , 0.72231657, ..., 0.74079836, 0.7685355 ,
              0.73773858],
             [0.78587607, 0.8034402 , 0.72875225, ..., 0.7617708 , 0.75584112,
              0.7142414 ],
             [0.70999378, 0.69755146, 0.7521772 , ..., 0.78153389, 0.76418935,
              0.72404227],
             [0.74654241, 0.74654241, 0.74458659, ..., 0.74408205, 0.7576893 ,
              0.73170819]])

    • delta
      (chain, draw)
      float64
      2.402 2.853 3.144 ... 2.778 2.966

      array([[2.40191162, 2.85252164, 3.14430149, ..., 2.79563703, 2.75762327,
              2.56631528],
             [2.69298341, 2.5227949 , 3.2228197 , ..., 2.81440099, 2.90545405,
              2.69538079],
             [3.0922509 , 3.15725681, 2.56803316, ..., 2.69015088, 2.77207752,
              2.89446307],
             [2.65310196, 2.65310196, 2.66346954, ..., 2.61358616, 2.77801979,
              2.96559641]])

    • gamma
      (chain, draw)
      float64
      0.6269 0.6867 ... 0.6711 0.6927

      array([[0.62694209, 0.68667318, 0.7172625 , ..., 0.68890446, 0.64737674,
              0.60903177],
             [0.66937007, 0.61153642, 0.71574495, ..., 0.65894816, 0.69443912,
              0.64766217],
             [0.69141196, 0.72005855, 0.61733789, ..., 0.64905894, 0.65953668,
              0.66586959],
             [0.64730354, 0.64730354, 0.62594135, ..., 0.63460286, 0.67112469,
              0.69265589]])

    • kappa_dropout
      (chain, draw)
      float64
      3.029 3.539 3.862 ... 3.449 3.658

      array([[3.02885371, 3.53919482, 3.86156399, ..., 3.48454149, 3.40500001,
              3.17534705],
             [3.36235348, 3.13433131, 3.93856465, ..., 3.47334915, 3.59989318,
              3.34304295],
             [3.78366286, 3.87731535, 3.18537105, ..., 3.33920982, 3.43161421,
              3.56033266],
             [3.3004055 , 3.3004055 , 3.28941088, ..., 3.24818902, 3.44914448,
              3.6582523 ]])

    • kappa_dropout_interval__
      (chain, draw)
      float64
      0.7075 0.9318 ... 0.8957 0.9777

      array([[0.70747096, 0.93184703, 1.05136833, ..., 0.91008813, 0.87754991,
              0.77718821],
             [0.85965836, 0.7581534 , 1.07792125, ..., 0.90557316, 0.95547036,
              0.85145049],
             [1.02376764, 1.05685769, 0.78178563, ..., 0.84981319, 0.88855532,
              0.9401372 ],
             [0.83308541, 0.83308541, 0.82829453, ..., 0.81012501, 0.89573877,
              0.97766888]])

    • kappa_purchase
      (chain, draw)
      float64
      2.098 1.946 1.839 ... 1.989 1.882

      array([[2.09796259, 1.94630336, 1.83865281, ..., 1.93610438, 1.97652369,
              1.87906808],
             [2.09925504, 2.10617417, 1.84904914, ..., 2.03155592, 1.99839272,
              1.88657864],
             [1.82109428, 1.82174923, 1.96051382, ..., 1.97098933, 1.97229148,
              1.89086148],
             [1.94201756, 1.94201756, 1.94094394, ..., 1.99673045, 1.98861079,
              1.88187708]])

    • kappa_purchase_interval__
      (chain, draw)
      float64
      0.09346 -0.05519 ... -0.1257

      array([[ 0.09345627, -0.05519208, -0.17595847, ..., -0.06602829,
              -0.02375627, -0.12889294],
             [ 0.09463272,  0.10090736, -0.16363821, ...,  0.03106826,
              -0.00160858, -0.12038545],
             [-0.19711734, -0.19632   , -0.0402869 , ..., -0.0294398 ,
              -0.02809965, -0.11556633],
             [-0.05973136, -0.05973136, -0.06087172, ..., -0.00327491,
              -0.01145456, -0.1257026 ]])

    • phi_dropout
      (chain, draw)
      float64
      0.207 0.194 ... 0.1946 0.1893

      array([[0.20698989, 0.1940196 , 0.18574404, ..., 0.19770304, 0.19012533,
              0.19180006],
             [0.19907784, 0.19510905, 0.18172736, ..., 0.1897155 , 0.19290548,
              0.19373432],
             [0.18273614, 0.1857106 , 0.19380408, ..., 0.19437501, 0.1921943 ,
              0.18702454],
             [0.19612849, 0.19612849, 0.1902898 , ..., 0.19537128, 0.19457715,
              0.18934066]])

    • phi_dropout_interval__
      (chain, draw)
      float64
      -1.343 -1.424 ... -1.421 -1.454

      array([[-1.34316603, -1.42410021, -1.47790516, ..., -1.40071268,
              -1.44919605, -1.43835597],
             [-1.39206785, -1.41714814, -1.50468806, ..., -1.45185986,
              -1.43124046, -1.42592555],
             [-1.49791873, -1.47812631, -1.42547906, ..., -1.42182903,
              -1.43581473, -1.46946107],
             [-1.41066945, -1.41066945, -1.44812822, ..., -1.41547918,
              -1.42053869, -1.45430012]])

    • phi_purchase
      (chain, draw)
      float64
      0.6291 0.6146 ... 0.619 0.6112

      array([[0.62910246, 0.61456923, 0.60714901, ..., 0.61737685, 0.61116808,
              0.60739125],
             [0.6256405 , 0.61853098, 0.6058773 , ..., 0.62503085, 0.62177548,
              0.62140915],
             [0.61012794, 0.61709798, 0.6163367 , ..., 0.60348142, 0.61253732,
              0.61708339],
             [0.61558411, 0.61558411, 0.61637914, ..., 0.62734978, 0.61898562,
              0.61118173]])

    • phi_purchase_interval__
      (chain, draw)
      float64
      0.5284 0.4666 ... 0.4852 0.4523

      array([[0.5283683 , 0.46656   , 0.43534389, ..., 0.47842905, 0.45222485,
              0.43635956],
             [0.51355935, 0.48331762, 0.43001519, ..., 0.51095725, 0.49709109,
              0.49553367],
             [0.44785003, 0.47724869, 0.47402806, ..., 0.41999236, 0.45799032,
              0.47718692],
             [0.47084658, 0.47084658, 0.47420753, ..., 0.520864  , 0.48524494,
              0.45228227]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (5)

    created_at :

    2024-09-12T21:27:00.667319+00:00

    arviz_version :

    0.18.0

    inference_library :

    nutpie

    inference_library_version :

    0.13.2

    sampling_time :

    371.8816521167755

  
  
• sample_stats

  <xarray.Dataset> Size: 336kB
  Dimensions:               (chain: 4, draw: 1000)
  Coordinates:
    * chain                 (chain) int64 32B 0 1 2 3
    * draw                  (draw) int64 8kB 0 1 2 3 4 5 ... 995 996 997 998 999
  Data variables:
      depth                 (chain, draw) uint64 32kB 3 3 3 3 3 3 ... 2 3 3 2 2 3
      diverging             (chain, draw) bool 4kB False False ... False False
      energy                (chain, draw) float64 32kB 3.324e+04 ... 3.323e+04
      energy_error          (chain, draw) float64 32kB 0.637 -0.1158 ... 0.0765
      index_in_trajectory   (chain, draw) int64 32kB -5 4 3 4 -5 ... 4 -3 -3 -1 5
      logp                  (chain, draw) float64 32kB -3.324e+04 ... -3.323e+04
      maxdepth_reached      (chain, draw) bool 4kB False False ... False False
      mean_tree_accept      (chain, draw) float64 32kB 0.9861 0.724 ... 1.0 0.9373
      mean_tree_accept_sym  (chain, draw) float64 32kB 0.9656 0.8221 ... 0.9368
      n_steps               (chain, draw) uint64 32kB 7 11 15 11 7 ... 3 7 11 3 7
      step_size             (chain, draw) float64 32kB 0.6836 0.6836 ... 0.6418
      step_size_bar         (chain, draw) float64 32kB 0.6836 0.6836 ... 0.6418
  Attributes:
      created_at:     2024-09-12T21:27:00.659509+00:00
      arviz_version:  0.18.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

  • Data variables: (12)
    • depth
      (chain, draw)
      uint64
      3 3 3 3 3 3 3 3 ... 2 3 2 3 3 2 2 3

      array([[3, 3, 3, ..., 2, 2, 3],
             [2, 2, 3, ..., 3, 2, 1],
             [3, 2, 3, ..., 2, 2, 2],
             [3, 2, 2, ..., 2, 2, 3]], dtype=uint64)

    • 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]])

    • energy
      (chain, draw)
      float64
      3.324e+04 3.324e+04 ... 3.323e+04

      array([[33236.89277938, 33236.81522002, 33235.23400843, ...,
              33236.37792995, 33236.74324095, 33235.67353816],
             [33235.82548433, 33236.56732156, 33235.88504437, ...,
              33236.00234893, 33235.08077173, 33236.49390766],
             [33233.61812925, 33236.0787666 , 33234.74561625, ...,
              33240.28548206, 33237.50257315, 33233.10311566],
             [33235.77646771, 33235.32928411, 33233.48425607, ...,
              33234.11926054, 33235.78168823, 33233.07248326]])

    • energy_error
      (chain, draw)
      float64
      0.637 -0.1158 ... -0.08838 0.0765

      array([[ 0.63698811, -0.11577693, -0.32495473, ...,  1.24674281,
              -1.48710275,  0.13104669],
             [-0.15916115, -0.07368944, -0.28646397, ...,  0.10838389,
              -0.22449156,  0.10597123],
             [-0.05062632,  0.38416868, -0.47383985, ...,  1.26062246,
              -1.3902238 ,  0.0221264 ],
             [-0.43614587,  0.        , -0.10766014, ..., -0.08780076,
              -0.088376  ,  0.07650236]])

    • index_in_trajectory
      (chain, draw)
      int64
      -5 4 3 4 -5 -6 ... 2 4 -3 -3 -1 5

      array([[-5,  4,  3, ...,  3, -1, -2],
             [-2, -1, -5, ...,  4, -2,  1],
             [-3,  2,  5, ...,  1, -1, -2],
             [-4,  0,  2, ..., -3, -1,  5]])

    • logp
      (chain, draw)
      float64
      -3.324e+04 ... -3.323e+04

      array([[-33235.82821996, -33233.44717888, -33233.55327458, ...,
              -33235.44152001, -33232.68163013, -33234.24562686],
             [-33234.22922557, -33233.72349496, -33233.13873596, ...,
              -33234.10522967, -33233.09428379, -33233.70345947],
             [-33233.09061574, -33234.5248719 , -33232.21080879, ...,
              -33237.63567732, -33232.51853424, -33232.70673409],
             [-33232.87672752, -33232.87672752, -33232.42147547, ...,
              -33233.70048164, -33232.50229501, -33232.83757421]])

    • maxdepth_reached
      (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]])

    • mean_tree_accept
      (chain, draw)
      float64
      0.9861 0.724 0.9986 ... 1.0 0.9373

      array([[0.98611155, 0.72398087, 0.99861686, ..., 0.96379046, 0.48732534,
              0.90137048],
             [0.7081876 , 0.86264462, 0.87464825, ..., 0.81399272, 0.95460181,
              0.8684132 ],
             [0.12122987, 0.9929814 , 0.61874642, ..., 0.47417981, 0.34959915,
              1.        ],
             [0.67259234, 0.91737845, 0.65483721, ..., 0.93414242, 1.        ,
              0.9372976 ]])

    • mean_tree_accept_sym
      (chain, draw)
      float64
      0.9656 0.8221 ... 0.9163 0.9368

      array([[0.96560619, 0.82210711, 0.80398813, ..., 0.89257023, 0.60646967,
              0.58616941],
             [0.81009698, 0.89422607, 0.9175507 , ..., 0.88936433, 0.91678238,
              0.88518446],
             [0.18925095, 0.97459261, 0.76096058, ..., 0.55542519, 0.50288962,
              0.57446895],
             [0.78045642, 0.82931818, 0.7900454 , ..., 0.9356348 , 0.91633314,
              0.93681809]])

    • n_steps
      (chain, draw)
      uint64
      7 11 15 11 7 15 15 ... 7 3 7 11 3 7

      array([[ 7, 11, 15, ...,  7,  3,  7],
             [ 7,  3,  3, ..., 15,  7,  3],
             [ 3,  7,  3, ...,  3,  3,  3],
             [ 7, 11,  3, ..., 11,  3,  7]], dtype=uint64)

    • step_size
      (chain, draw)
      float64
      0.6836 0.6836 ... 0.6418 0.6418

      array([[0.68361932, 0.68361932, 0.68361932, ..., 0.68361932, 0.68361932,
              0.68361932],
             [0.68928774, 0.68928774, 0.68928774, ..., 0.68928774, 0.68928774,
              0.68928774],
             [0.6599716 , 0.6599716 , 0.6599716 , ..., 0.6599716 , 0.6599716 ,
              0.6599716 ],
             [0.64180785, 0.64180785, 0.64180785, ..., 0.64180785, 0.64180785,
              0.64180785]])

    • step_size_bar
      (chain, draw)
      float64
      0.6836 0.6836 ... 0.6418 0.6418

      array([[0.68361932, 0.68361932, 0.68361932, ..., 0.68361932, 0.68361932,
              0.68361932],
             [0.68928774, 0.68928774, 0.68928774, ..., 0.68928774, 0.68928774,
              0.68928774],
             [0.6599716 , 0.6599716 , 0.6599716 , ..., 0.6599716 , 0.6599716 ,
              0.6599716 ],
             [0.64180785, 0.64180785, 0.64180785, ..., 0.64180785, 0.64180785,
              0.64180785]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (2)

    created_at :

    2024-09-12T21:27:00.659509+00:00

    arviz_version :

    0.18.0

  
  
• observed_data

  <xarray.Dataset> Size: 267kB
  Dimensions:            (customer_id: 11104, obs_var: 2)
  Coordinates:
    * customer_id        (customer_id) int64 89kB 0 1 2 3 ... 11101 11102 11103
    * obs_var            (obs_var) <U9 72B 'recency' 'frequency'
  Data variables:
      recency_frequency  (customer_id, obs_var) float64 178kB 0.0 0.0 ... 6.0 6.0
  Attributes:
      created_at:                 2024-09-12T21:27:00.666769+00:00
      arviz_version:              0.18.0
      inference_library:          pymc
      inference_library_version:  5.13.0

  xarray.Dataset

  • Dimensions:
    • customer_id: 11104
    • obs_var: 2
  • Coordinates: (2)
    • customer_id
      (customer_id)
      int64
      0 1 2 3 ... 11100 11101 11102 11103

      array([    0,     1,     2, ..., 11101, 11102, 11103])

    • obs_var
      (obs_var)
      <U9
      'recency' 'frequency'

      array(['recency', 'frequency'], dtype='<U9')

  • Data variables: (1)
    • recency_frequency
      (customer_id, obs_var)
      float64
      0.0 0.0 0.0 0.0 ... 6.0 6.0 6.0 6.0

      array([[0., 0.],
             [0., 0.],
             [0., 0.],
             ...,
             [6., 6.],
             [6., 6.],
             [6., 6.]])

  • Indexes: (2)
    • customer_id
      PandasIndex

      PandasIndex(Index([    0,     1,     2,     3,     4,     5,     6,     7,     8,     9,
             ...
             11094, 11095, 11096, 11097, 11098, 11099, 11100, 11101, 11102, 11103],
            dtype='int64', name='customer_id', length=11104))

    • obs_var
      PandasIndex

      PandasIndex(Index(['recency', 'frequency'], dtype='object', name='obs_var'))

  • Attributes: (4)

    created_at :

    2024-09-12T21:27:00.666769+00:00

    arviz_version :

    0.18.0

    inference_library :

    pymc

    inference_library_version :

    5.13.0

  
  
• fit_data

  <xarray.Dataset> Size: 444kB
  Dimensions:      (index: 11104)
  Coordinates:
    * index        (index) int64 89kB 0 1 2 3 4 ... 11099 11100 11101 11102 11103
  Data variables:
      customer_id  (index) int64 89kB 0 1 2 3 4 ... 11099 11100 11101 11102 11103
      frequency    (index) int64 89kB 0 0 0 0 0 0 0 0 0 0 ... 6 6 6 6 6 6 6 6 6 6
      recency      (index) int64 89kB 0 0 0 0 0 0 0 0 0 0 ... 6 6 6 6 6 6 6 6 6 6
      T            (index) int64 89kB 6 6 6 6 6 6 6 6 6 6 ... 6 6 6 6 6 6 6 6 6 6

  xarray.Dataset

  • Dimensions:
    • index: 11104
  • Coordinates: (1)
    • index
      (index)
      int64
      0 1 2 3 ... 11100 11101 11102 11103

      array([    0,     1,     2, ..., 11101, 11102, 11103])

  • Data variables: (4)
    • customer_id
      (index)
      int64
      0 1 2 3 ... 11100 11101 11102 11103

      array([    0,     1,     2, ..., 11101, 11102, 11103])

    • frequency
      (index)
      int64
      0 0 0 0 0 0 0 0 ... 6 6 6 6 6 6 6 6

      array([0, 0, 0, ..., 6, 6, 6])

    • recency
      (index)
      int64
      0 0 0 0 0 0 0 0 ... 6 6 6 6 6 6 6 6

      array([0, 0, 0, ..., 6, 6, 6])

    • T
      (index)
      int64
      6 6 6 6 6 6 6 6 ... 6 6 6 6 6 6 6 6

      array([6, 6, 6, ..., 6, 6, 6])

  • Indexes: (1)
    • index
      PandasIndex

      PandasIndex(RangeIndex(start=0, stop=11104, step=1, name='index'))

  • Attributes: (0)

  
  
• warmup_posterior

  <xarray.Dataset> Size: 392kB
  Dimensions:                    (chain: 4, draw: 1000)
  Coordinates:
    * chain                      (chain) int64 32B 0 1 2 3
    * draw                       (draw) int64 8kB 0 1 2 3 4 ... 996 997 998 999
  Data variables:
      alpha                      (chain, draw) float64 32kB 1.217 1.217 ... 1.171
      beta                       (chain, draw) float64 32kB 0.2809 ... 0.7511
      delta                      (chain, draw) float64 32kB 1.244 1.244 ... 3.435
      gamma                      (chain, draw) float64 32kB 1.931 1.931 ... 0.7753
      kappa_dropout              (chain, draw) float64 32kB 3.175 3.175 ... 4.211
      kappa_dropout_interval__   (chain, draw) float64 32kB 0.7772 ... 1.166
      kappa_purchase             (chain, draw) float64 32kB 1.498 1.498 ... 1.922
      kappa_purchase_interval__  (chain, draw) float64 32kB -0.6972 ... -0.08079
      phi_dropout                (chain, draw) float64 32kB 0.6081 ... 0.1841
      phi_dropout_interval__     (chain, draw) float64 32kB 0.4393 ... -1.489
      phi_purchase               (chain, draw) float64 32kB 0.8125 ... 0.6093
      phi_purchase_interval__    (chain, draw) float64 32kB 1.466 1.466 ... 0.4444
  Attributes:
      created_at:     2024-09-12T21:27:00.655861+00:00
      arviz_version:  0.18.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

  • Data variables: (12)
    • alpha
      (chain, draw)
      float64
      1.217 1.217 1.665 ... 1.095 1.171

      array([[1.21707275, 1.21707275, 1.66509366, ..., 1.2158083 , 1.19561741,
              1.13703409],
             [0.79951514, 0.79951514, 0.80433485, ..., 1.17290895, 1.10250214,
              1.23125212],
             [4.56675682, 4.56675682, 2.62633019, ..., 1.15935429, 1.14421025,
              1.14421025],
             [0.34642776, 0.34642776, 0.40925366, ..., 1.21047375, 1.09511293,
              1.17130971]])

    • beta
      (chain, draw)
      float64
      0.2809 0.2809 ... 0.7067 0.7511

      array([[0.28092892, 0.28092892, 0.94093007, ..., 0.78204017, 0.75312438,
              0.72374677],
             [0.64748165, 0.64748165, 0.63712739, ..., 0.74264234, 0.70998883,
              0.76230147],
             [1.1422249 , 1.1422249 , 1.12732117, ..., 0.74118345, 0.74170373,
              0.74170373],
             [0.83103997, 0.83103997, 0.76024213, ..., 0.75068009, 0.70667046,
              0.75108199]])

    • delta
      (chain, draw)
      float64
      1.244 1.244 1.17 ... 3.059 3.435

      array([[1.24444206, 1.24444206, 1.17018001, ..., 3.5896128 , 3.34643296,
              2.92989088],
             [1.8250795 , 1.8250795 , 1.84812551, ..., 3.29118177, 2.93906414,
              2.45963629],
             [5.70513929, 5.70513929, 4.08724548, ..., 2.88284825, 3.06857185,
              3.06857185],
             [0.84151653, 0.84151653, 0.88081294, ..., 3.22637038, 3.05937138,
              3.43533465]])

    • gamma
      (chain, draw)
      float64
      1.931 1.931 ... 0.6838 0.7753

      array([[1.930939  , 1.930939  , 0.69705345, ..., 0.80509702, 0.75346888,
              0.66186684],
             [0.42839873, 0.42839873, 0.42349215, ..., 0.74004325, 0.66820096,
              0.58888999],
             [1.83098505, 1.83098505, 0.89635849, ..., 0.67069395, 0.68428187,
              0.68428187],
             [0.56607459, 0.56607459, 0.44550494, ..., 0.73779689, 0.68378246,
              0.77526473]])

    • kappa_dropout
      (chain, draw)
      float64
      3.175 3.175 1.867 ... 3.743 4.211

      array([[3.17538106, 3.17538106, 1.86723346, ..., 4.39470981, 4.09990184,
              3.59175772],
             [2.25347823, 2.25347823, 2.27161767, ..., 4.03122501, 3.6072651 ,
              3.04852628],
             [7.53612434, 7.53612434, 4.98360397, ..., 3.5535422 , 3.75285372,
              3.75285372],
             [1.40759112, 1.40759112, 1.32631788, ..., 3.96416727, 3.74315384,
              4.21059939]])

    • kappa_dropout_interval__
      (chain, draw)
      float64
      0.7772 0.7772 ... 1.009 1.166

      array([[ 0.77720385,  0.77720385, -0.14244706, ...,  1.22221828,
               1.13137045,  0.9523363 ],
             [ 0.22592227,  0.22592227,  0.24028984, ...,  1.10896683,
               0.95830182,  0.71712065],
             [ 1.87734438,  1.87734438,  1.38218693, ...,  0.93748149,
               1.01263809,  1.01263809],
             [-0.89749077, -0.89749077, -1.11988328, ...,  1.08659614,
               1.00910829,  1.16645765]])

    • kappa_purchase
      (chain, draw)
      float64
      1.498 1.498 2.606 ... 1.802 1.922

      array([[1.49800167, 1.49800167, 2.60602373, ..., 1.99784847, 1.9487418 ,
              1.86078086],
             [1.4469968 , 1.4469968 , 1.44146223, ..., 1.91555129, 1.81249096,
              1.99355359],
             [5.70898173, 5.70898173, 3.75365137, ..., 1.90053774, 1.88591398,
              1.88591398],
             [1.17746773, 1.17746773, 1.16949579, ..., 1.96115383, 1.80178339,
              1.9223917 ]])

    • kappa_purchase_interval__
      (chain, draw)
      float64
      -0.6972 -0.6972 ... -0.08079

      array([[-0.69715184, -0.69715184,  0.47376139, ..., -0.00215385,
              -0.0526186 , -0.14991532],
             [-0.80520385, -0.80520385, -0.81766281, ..., -0.08822889,
              -0.20765049, -0.00646728],
             [ 1.54947169,  1.54947169,  1.0129278 , ..., -0.1047632 ,
              -0.12113542, -0.12113542],
             [-1.72896652, -1.72896652, -1.77492722, ..., -0.03962081,
              -0.22091679, -0.08078531]])

    • phi_dropout
      (chain, draw)
      float64
      0.6081 0.6081 ... 0.1827 0.1841

      array([[0.60809678, 0.60809678, 0.37330814, ..., 0.18319686, 0.1837773 ,
              0.1842738 ],
             [0.19010555, 0.19010555, 0.18642757, ..., 0.18357776, 0.18523755,
              0.19317202],
             [0.2429611 , 0.2429611 , 0.1798615 , ..., 0.18873955, 0.18233641,
              0.18233641],
             [0.4021584 , 0.4021584 , 0.33589605, ..., 0.18611649, 0.18267549,
              0.18412218]])

    • phi_dropout_interval__
      (chain, draw)
      float64
      0.4393 0.4393 ... -1.498 -1.489

      array([[ 0.43931913,  0.43931913, -0.51805077, ..., -1.49483683,
              -1.49096255, -1.48765607],
             [-1.44932446, -1.44932446, -1.47339219, ..., -1.49229335,
              -1.48125752, -1.42952939],
             [-1.13651329, -1.13651329, -1.51728612, ..., -1.45822114,
              -1.50059761, -1.50059761],
             [-0.39647981, -0.39647981, -0.68163695, ..., -1.47544449,
              -1.49832492, -1.48866506]])

    • phi_purchase
      (chain, draw)
      float64
      0.8125 0.8125 ... 0.6078 0.6093

      array([[0.81246421, 0.81246421, 0.63894033, ..., 0.60855882, 0.61353301,
              0.61105212],
             [0.55253415, 0.55253415, 0.55799925, ..., 0.61230882, 0.60828007,
              0.61761676],
             [0.79992493, 0.79992493, 0.69967345, ..., 0.61001382, 0.60671391,
              0.60671391],
             [0.29421423, 0.29421423, 0.34994026, ..., 0.61722529, 0.60779389,
              0.60929815]])

    • phi_purchase_interval__
      (chain, draw)
      float64
      1.466 1.466 0.5708 ... 0.438 0.4444

      array([[ 1.46610218,  1.46610218,  0.57076784, ...,  0.44125829,
               0.4621876 ,  0.45173691],
             [ 0.21091501,  0.21091501,  0.23304605, ...,  0.45702767,
               0.44008832,  0.4794448 ],
             [ 1.38582526,  1.38582526,  0.84574333, ...,  0.44737031,
               0.43352006,  0.43352006],
             [-0.87500359, -0.87500359, -0.61930181, ...,  0.47778751,
               0.43804832,  0.44436299]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (2)

    created_at :

    2024-09-12T21:27:00.655861+00:00

    arviz_version :

    0.18.0

  
  
• warmup_sample_stats

  <xarray.Dataset> Size: 336kB
  Dimensions:               (chain: 4, draw: 1000)
  Coordinates:
    * chain                 (chain) int64 32B 0 1 2 3
    * draw                  (draw) int64 8kB 0 1 2 3 4 5 ... 995 996 997 998 999
  Data variables:
      depth                 (chain, draw) uint64 32kB 0 0 2 1 0 0 ... 3 2 3 2 3 3
      diverging             (chain, draw) bool 4kB True True False ... False False
      energy                (chain, draw) float64 32kB 4.085e+04 ... 3.324e+04
      energy_error          (chain, draw) float64 32kB 0.0 0.0 ... -0.0498 0.6378
      index_in_trajectory   (chain, draw) int64 32kB 0 0 2 -1 0 ... -3 -4 -3 4 -5
      logp                  (chain, draw) float64 32kB -4.084e+04 ... -3.323e+04
      maxdepth_reached      (chain, draw) bool 4kB False False ... False False
      mean_tree_accept      (chain, draw) float64 32kB 0.0 0.0 ... 0.9126 0.867
      mean_tree_accept_sym  (chain, draw) float64 32kB 0.0 0.0 ... 0.9539 0.918
      n_steps               (chain, draw) uint64 32kB 0 1 1 3 1 1 ... 15 7 11 3 15
      step_size             (chain, draw) float64 32kB 3.2 7.472 ... 0.6007 0.6479
      step_size_bar         (chain, draw) float64 32kB 3.2 7.472 ... 0.6418 0.6418
  Attributes:
      created_at:     2024-09-12T21:27:00.663215+00:00
      arviz_version:  0.18.0

  xarray.Dataset

  • Dimensions:
    • chain: 4
    • draw: 1000
  • Coordinates: (2)
    • chain
      (chain)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 995 996 997 998 999

      array([  0,   1,   2, ..., 997, 998, 999])

  • Data variables: (12)
    • depth
      (chain, draw)
      uint64
      0 0 2 1 0 0 1 1 ... 4 3 3 2 3 2 3 3

      array([[0, 0, 2, ..., 2, 2, 2],
             [1, 0, 2, ..., 3, 3, 2],
             [0, 0, 2, ..., 3, 3, 2],
             [0, 0, 1, ..., 2, 3, 3]], dtype=uint64)

    • diverging
      (chain, draw)
      bool
      True True False ... False False

      array([[ True,  True, False, ..., False, False, False],
             [ True,  True, False, ..., False, False, False],
             [ True,  True, False, ..., False, False, False],
             [ True,  True, False, ..., False, False, False]])

    • energy
      (chain, draw)
      float64
      4.085e+04 4.084e+04 ... 3.324e+04

      array([[40845.73560011, 40843.88666491, 40159.73039306, ...,
              33239.23790435, 33237.55197086, 33234.54845529],
             [33348.36745812, 33344.94077975, 33342.30948872, ...,
              33236.14780697, 33233.96195927, 33236.82191709],
             [34413.93369618, 34413.20194373, 34376.0118327 , ...,
              33234.42473858, 33234.32832627, 33239.44221622],
             [38027.901997  , 38028.55690914, 37762.83278886, ...,
              33234.75477534, 33235.3482773 , 33235.87265263]])

    • energy_error
      (chain, draw)
      float64
      0.0 0.0 -685.4 ... -0.0498 0.6378

      array([[ 0.00000000e+00,  0.00000000e+00, -6.85431882e+02, ...,
               1.45985833e-01, -1.09164905e+00, -1.19703877e-02],
             [ 0.00000000e+00,  0.00000000e+00, -8.89973058e-01, ...,
              -2.52637650e-01, -1.25145454e-02,  5.46192764e-01],
             [ 0.00000000e+00,  0.00000000e+00, -3.76809131e+01, ...,
              -3.69815684e-01,  8.16725273e-02,  0.00000000e+00],
             [ 0.00000000e+00,  0.00000000e+00, -2.66741285e+02, ...,
               4.03055055e-02, -4.98011899e-02,  6.37757442e-01]])

    • index_in_trajectory
      (chain, draw)
      int64
      0 0 2 -1 0 0 -1 ... 5 -3 -4 -3 4 -5

      array([[ 0,  0,  2, ..., -2,  1, -2],
             [ 0,  0,  1, ...,  4,  4,  3],
             [ 0,  0,  3, ...,  7,  2,  0],
             [ 0,  0,  1, ..., -3,  4, -5]])

    • logp
      (chain, draw)
      float64
      -4.084e+04 ... -3.323e+04

      array([[-40842.99343658, -40842.99343658, -34101.27613639, ...,
              -33237.8906471 , -33233.74905263, -33232.86880348],
             [-33342.33374297, -33342.33374297, -33331.36848403, ...,
              -33233.10193884, -33233.25974033, -33233.54558566],
             [-34413.06825876, -34413.06825876, -33480.26252096, ...,
              -33232.41037504, -33233.17626208, -33233.17626208],
             [-38026.5045024 , -38026.5045024 , -36028.36860329, ...,
              -33233.46780578, -33233.39815729, -33234.84656638]])

    • maxdepth_reached
      (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]])

    • mean_tree_accept
      (chain, draw)
      float64
      0.0 0.0 0.0 ... 0.479 0.9126 0.867

      array([[0.00000000e+000, 0.00000000e+000, 0.00000000e+000, ...,
              7.30907190e-001, 9.54723315e-001, 1.00000000e+000],
             [0.00000000e+000, 4.69302497e-292, 0.00000000e+000, ...,
              8.70746379e-001, 6.03980118e-001, 8.90695554e-001],
             [0.00000000e+000, 0.00000000e+000, 0.00000000e+000, ...,
              9.65682999e-001, 9.98729417e-001, 7.97136414e-001],
             [0.00000000e+000, 0.00000000e+000, 0.00000000e+000, ...,
              4.79023997e-001, 9.12640964e-001, 8.67024506e-001]])

    • mean_tree_accept_sym
      (chain, draw)
      float64
      0.0 0.0 0.0 ... 0.5329 0.9539 0.918

      array([[0.00000000e+000, 0.00000000e+000, 0.00000000e+000, ...,
              8.04181743e-001, 7.01565958e-001, 6.20854112e-001],
             [0.00000000e+000, 9.38604994e-292, 0.00000000e+000, ...,
              9.10675356e-001, 6.73580716e-001, 9.31439815e-001],
             [0.00000000e+000, 0.00000000e+000, 0.00000000e+000, ...,
              9.13141458e-001, 8.96811790e-001, 8.77418415e-001],
             [0.00000000e+000, 0.00000000e+000, 0.00000000e+000, ...,
              5.32922868e-001, 9.53882120e-001, 9.17997356e-001]])

    • n_steps
      (chain, draw)
      uint64
      0 1 1 3 1 1 1 ... 11 15 7 11 3 15

      array([[ 0,  1,  1, ...,  7,  3,  3],
             [ 0,  2,  1, ..., 11,  7,  7],
             [ 0,  1,  1, ...,  7, 15, 15],
             [ 0,  1,  1, ..., 11,  3, 15]], dtype=uint64)

    • step_size
      (chain, draw)
      float64
      3.2 7.472 0.7368 ... 0.6007 0.6479

      array([[3.2       , 7.47220733, 0.73675471, ..., 0.67593927, 0.6366274 ,
              0.57001259],
             [0.8       , 1.86805183, 0.18418868, ..., 0.7324825 , 0.67737268,
              0.7365279 ],
             [1.6       , 3.73610367, 0.36837736, ..., 0.63593743, 0.67711044,
              0.71218091],
             [3.2       , 7.47220733, 0.73675471, ..., 0.54442185, 0.60066422,
              0.64789197]])

    • step_size_bar
      (chain, draw)
      float64
      3.2 7.472 1.885 ... 0.6418 0.6418

      array([[3.2       , 7.47220733, 1.88452898, ..., 0.68490389, 0.68462115,
              0.68391353],
             [0.8       , 1.86805183, 0.47113224, ..., 0.68880352, 0.68873841,
              0.68899926],
             [1.6       , 3.73610367, 0.94226449, ..., 0.6607446 , 0.66083593,
              0.6611151 ],
             [3.2       , 7.47220733, 1.88452898, ..., 0.64201947, 0.64177805,
              0.6418124 ]])

  • Indexes: (2)
    • chain
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='chain'))

    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             990, 991, 992, 993, 994, 995, 996, 997, 998, 999],
            dtype='int64', name='draw', length=1000))

  • Attributes: (2)

    created_at :

    2024-09-12T21:27:00.663215+00:00

    arviz_version :

    0.18.0