%cd ..
%load_ext autoreload
%autoreload 2
/home/runner/work/numpyro-doing-bayesian/numpyro-doing-bayesian
import arviz as az
import jax.numpy as jnp
import jax.random as random
import matplotlib.pyplot as plt
import numpy as np
import numpyro
from numpyro.infer.initialization import init_to_median
from numpyro.infer import NUTS, MCMC
import numpyro_glm.metric.models as glm_metric
import pandas as pd
import seaborn as sns
from scipy.stats import norm, t
numpyro.set_host_device_count(2)
salary_df = pd.read_csv('datasets/Salary.csv')
salary_df['Org'] = salary_df['Org'].astype('category')
salary_df['Pos'] = (salary_df['Pos']
.astype('category').cat
.set_categories(['FT3', 'FT2', 'FT1', 'NDW', 'DST']).cat
.rename_categories(['Assoc', 'Assis', 'Full', 'Endow', 'Disting']))
salary_df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 1080 entries, 0 to 1079 Data columns (total 6 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 Org 1080 non-null category 1 OrgName 1080 non-null object 2 Cla 1080 non-null object 3 Pos 1080 non-null category 4 ClaPos 1080 non-null object 5 Salary 1080 non-null int64 dtypes: category(2), int64(1), object(3) memory usage: 38.7+ KB
fig, axes = plt.subplots(
nrows=2, ncols=2,
figsize=(10, 6),
sharey=True)
departments = ['BFIN', 'CHEM', 'PSY', 'ENG']
for department, ax in zip(departments, axes.flatten()):
df = salary_df[salary_df['Org'] == department]
sns.stripplot(x='Pos', y='Salary', data=df, ax=ax)
ax.set_title(f'{department}\'s Salary')
fig.tight_layout()
kernel = NUTS(glm_metric.multi_nominal_predictors, target_accept_prob=0.99)
mcmc = MCMC(kernel, num_warmup=1000, num_samples=10000, num_chains=2)
mcmc.run(
random.PRNGKey(0),
y=jnp.array(salary_df['Salary'].values),
grp=jnp.concatenate([salary_df[c].cat.codes.values[..., None]
for c in ['Org', 'Pos']], axis=1),
nb_groups=(salary_df['Org'].cat.categories.size,
salary_df['Pos'].cat.categories.size),
)
mcmc.print_summary()
No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)
mean std median 5.0% 95.0% n_eff r_hat
a0_ 0.08 0.13 0.07 -0.12 0.27 4918.66 1.00
a1_[0] 2.65 0.34 2.65 2.10 3.20 4485.80 1.00
a1_[1] -0.49 0.33 -0.49 -1.01 0.07 7411.30 1.00
a1_[2] -0.54 0.33 -0.53 -1.11 -0.02 7904.97 1.00
a1_[3] -0.63 0.26 -0.62 -1.05 -0.18 5277.97 1.00
a1_[4] 0.10 0.26 0.10 -0.33 0.53 4836.83 1.00
a1_[5] 0.00 0.30 0.01 -0.49 0.49 7743.28 1.00
a1_[6] 1.58 0.32 1.57 1.05 2.09 5447.87 1.00
a1_[7] 3.53 0.40 3.52 2.90 4.20 4250.79 1.00
a1_[8] -0.11 0.22 -0.11 -0.47 0.24 4166.36 1.00
a1_[9] 0.59 0.30 0.58 0.09 1.08 7075.90 1.00
a1_[10] -0.53 0.26 -0.52 -0.94 -0.10 4634.74 1.00
a1_[11] -0.70 0.29 -0.69 -1.16 -0.23 5489.77 1.00
a1_[12] 0.62 0.22 0.62 0.24 0.97 4083.87 1.00
a1_[13] -0.52 0.28 -0.52 -0.99 -0.08 5456.79 1.00
a1_[14] -0.70 0.31 -0.70 -1.21 -0.21 6215.14 1.00
a1_[15] -0.73 0.25 -0.73 -1.14 -0.32 4448.00 1.00
a1_[16] 0.41 0.25 0.41 -0.00 0.81 4679.99 1.00
a1_[17] -0.58 0.27 -0.58 -1.03 -0.13 5476.42 1.00
a1_[18] 1.83 0.30 1.82 1.36 2.34 4504.80 1.00
a1_[19] -0.19 0.27 -0.19 -0.64 0.24 5941.37 1.00
a1_[20] -0.63 0.24 -0.63 -1.00 -0.23 3953.10 1.00
a1_[21] -0.71 0.30 -0.70 -1.21 -0.21 6747.73 1.00
a1_[22] -0.61 0.31 -0.61 -1.13 -0.11 7186.28 1.00
a1_[23] -0.72 0.28 -0.72 -1.19 -0.28 5777.34 1.00
a1_[24] -0.44 0.28 -0.44 -0.90 0.01 5443.91 1.00
a1_[25] -0.28 0.30 -0.28 -0.77 0.22 6567.86 1.00
a1_[26] -0.45 0.26 -0.45 -0.87 -0.03 4754.02 1.00
a1_[27] -0.99 0.33 -0.99 -1.53 -0.45 6754.73 1.00
a1_[28] -0.40 0.23 -0.40 -0.78 -0.02 4119.35 1.00
a1_[29] 0.30 0.25 0.30 -0.12 0.71 5276.44 1.00
a1_[30] -0.48 0.27 -0.47 -0.92 -0.03 6034.31 1.00
a1_[31] -0.23 0.27 -0.23 -0.67 0.20 5198.86 1.00
a1_[32] 1.30 0.27 1.30 0.85 1.72 4563.42 1.00
a1_[33] -0.65 0.30 -0.65 -1.14 -0.16 5455.98 1.00
a1_[34] -0.42 0.31 -0.42 -0.92 0.11 7462.68 1.00
a1_[35] -0.22 0.24 -0.22 -0.62 0.16 3855.26 1.00
a1_[36] 2.03 0.33 2.02 1.48 2.54 5790.52 1.00
a1_[37] 2.18 0.32 2.17 1.64 2.69 4722.05 1.00
a1_[38] -0.98 0.30 -0.98 -1.47 -0.50 6301.74 1.00
a1_[39] -0.75 0.24 -0.74 -1.13 -0.33 4353.24 1.00
a1_[40] -0.06 0.29 -0.06 -0.56 0.40 6349.85 1.00
a1_[41] -0.89 0.31 -0.88 -1.41 -0.37 6219.64 1.00
a1_[42] -0.91 0.31 -0.91 -1.43 -0.42 6321.85 1.00
a1_[43] 1.95 0.31 1.94 1.43 2.45 4750.73 1.00
a1_[44] -0.46 0.29 -0.46 -0.92 0.02 5909.34 1.00
a1_[45] -0.08 0.24 -0.08 -0.49 0.30 4572.47 1.00
a1_[46] -0.33 0.27 -0.33 -0.77 0.11 5320.05 1.00
a1_[47] 0.24 0.24 0.24 -0.16 0.63 4771.11 1.00
a1_[48] 0.22 0.21 0.22 -0.13 0.58 3884.71 1.00
a1_[49] -0.47 0.28 -0.47 -0.91 -0.01 6446.39 1.00
a1_[50] -0.13 0.29 -0.13 -0.59 0.36 6992.97 1.00
a1_[51] 0.17 0.27 0.17 -0.28 0.60 5092.82 1.00
a1_[52] -0.77 0.32 -0.77 -1.29 -0.24 7467.79 1.00
a1_[53] -0.20 0.24 -0.20 -0.58 0.19 4568.85 1.00
a1_[54] -0.57 0.26 -0.56 -1.00 -0.15 4635.71 1.00
a1_[55] 0.56 0.23 0.55 0.19 0.93 3706.01 1.00
a1_[56] 0.26 0.26 0.26 -0.17 0.68 5287.63 1.00
a1_[57] 0.11 0.31 0.11 -0.39 0.61 7584.69 1.00
a1_[58] -0.39 0.27 -0.39 -0.83 0.05 5774.71 1.00
a1_[59] -0.75 0.31 -0.75 -1.25 -0.22 5354.35 1.00
a1_sigma 30562.62 3024.11 30330.15 25729.09 35428.88 3703.91 1.00
a1a2_[0,0] 1.55 0.74 1.55 0.36 2.79 22253.99 1.00
a1a2_[0,1] 0.94 0.83 0.94 -0.40 2.30 25767.88 1.00
a1a2_[0,2] -1.28 0.74 -1.28 -2.49 -0.07 21186.15 1.00
a1a2_[0,3] -0.37 0.80 -0.37 -1.68 0.94 24257.82 1.00
a1a2_[0,4] -0.00 1.01 0.00 -1.62 1.70 30301.82 1.00
a1a2_[1,0] 0.00 1.01 -0.01 -1.69 1.60 31050.02 1.00
a1a2_[1,1] -0.02 0.84 -0.02 -1.40 1.37 21765.49 1.00
a1a2_[1,2] -0.14 0.84 -0.15 -1.58 1.22 20665.21 1.00
a1a2_[1,3] 0.00 0.99 0.00 -1.63 1.59 31671.10 1.00
a1a2_[1,4] 0.01 1.00 0.01 -1.66 1.64 31791.68 1.00
a1a2_[2,0] -0.08 0.86 -0.08 -1.50 1.31 22046.02 1.00
a1a2_[2,1] -0.11 0.85 -0.12 -1.47 1.30 18252.53 1.00
a1a2_[2,2] -0.00 1.00 0.00 -1.68 1.61 36207.60 1.00
a1a2_[2,3] -0.00 1.00 -0.01 -1.74 1.56 32338.17 1.00
a1a2_[2,4] 0.01 1.02 0.00 -1.63 1.72 31934.37 1.00
a1a2_[3,0] 0.25 0.90 0.26 -1.21 1.76 27243.09 1.00
a1a2_[3,1] 0.08 0.73 0.07 -1.14 1.27 15941.60 1.00
a1a2_[3,2] -0.09 0.73 -0.09 -1.29 1.11 15742.04 1.00
a1a2_[3,3] -0.42 0.90 -0.42 -1.91 1.07 27952.61 1.00
a1a2_[3,4] -0.00 1.01 -0.01 -1.63 1.72 31873.77 1.00
a1a2_[4,0] -0.57 0.77 -0.57 -1.80 0.73 18037.43 1.00
a1a2_[4,1] -0.36 0.74 -0.36 -1.56 0.88 15015.69 1.00
a1a2_[4,2] 0.95 0.79 0.95 -0.35 2.25 18968.89 1.00
a1a2_[4,3] 0.01 1.01 0.01 -1.63 1.67 34592.44 1.00
a1a2_[4,4] -0.00 0.99 0.01 -1.69 1.57 28937.15 1.00
a1a2_[5,0] -0.28 0.90 -0.28 -1.76 1.21 27667.29 1.00
a1a2_[5,1] -0.57 0.86 -0.57 -1.99 0.86 23249.96 1.00
a1a2_[5,2] -0.36 0.83 -0.36 -1.72 1.01 23939.08 1.00
a1a2_[5,3] 1.21 0.91 1.20 -0.29 2.69 24433.52 1.00
a1a2_[5,4] 0.00 1.00 0.00 -1.72 1.57 29349.64 1.00
a1a2_[6,0] -0.02 0.83 -0.02 -1.44 1.30 21731.21 1.00
a1a2_[6,1] 0.14 0.81 0.15 -1.17 1.50 21108.15 1.00
a1a2_[6,2] 0.00 0.99 -0.00 -1.68 1.57 34119.23 1.00
a1a2_[6,3] 0.39 0.86 0.39 -1.02 1.80 24056.79 1.00
a1a2_[6,4] 0.00 1.00 0.01 -1.65 1.62 27848.67 1.00
a1a2_[7,0] 0.63 0.75 0.63 -0.63 1.83 21490.27 1.00
a1a2_[7,1] 1.21 0.71 1.21 0.03 2.38 21532.67 1.00
a1a2_[7,2] 0.37 0.80 0.38 -0.95 1.69 26081.26 1.00
a1a2_[7,3] -1.05 0.80 -1.05 -2.35 0.29 26036.14 1.00
a1a2_[7,4] -0.00 1.00 0.00 -1.61 1.65 34054.19 1.00
a1a2_[8,0] -0.03 0.66 -0.03 -1.10 1.04 14868.23 1.00
a1a2_[8,1] -0.33 0.63 -0.32 -1.35 0.70 13248.74 1.00
a1a2_[8,2] 0.13 0.65 0.13 -0.92 1.21 13774.10 1.00
a1a2_[8,3] -0.36 0.90 -0.35 -1.92 1.05 28954.33 1.00
a1a2_[8,4] 0.54 0.73 0.54 -0.62 1.75 15688.75 1.00
a1a2_[9,0] 0.43 0.83 0.44 -0.93 1.82 22970.62 1.00
a1a2_[9,1] 0.12 0.86 0.12 -1.35 1.46 26984.00 1.00
a1a2_[9,2] 0.01 0.90 0.01 -1.55 1.43 24680.96 1.00
a1a2_[9,3] -0.37 0.91 -0.37 -1.92 1.06 27228.30 1.00
a1a2_[9,4] 0.01 1.00 0.01 -1.67 1.62 33623.17 1.00
a1a2_[10,0] 0.20 0.75 0.20 -0.99 1.46 17541.33 1.00
a1a2_[10,1] -0.14 0.73 -0.13 -1.31 1.08 14855.03 1.00
a1a2_[10,2] -0.24 0.74 -0.23 -1.44 0.98 14920.18 1.00
a1a2_[10,3] -0.00 0.99 -0.00 -1.62 1.64 30089.98 1.00
a1a2_[10,4] -0.01 0.99 -0.01 -1.60 1.67 31441.52 1.00
a1a2_[11,0] 0.11 0.89 0.11 -1.42 1.52 28604.96 1.00
a1a2_[11,1] 0.60 0.80 0.60 -0.69 1.92 21567.54 1.00
a1a2_[11,2] 0.32 0.80 0.31 -1.02 1.59 21205.74 1.00
a1a2_[11,3] -1.26 0.91 -1.26 -2.73 0.26 28477.65 1.00
a1a2_[11,4] 0.01 1.00 0.00 -1.67 1.61 28054.14 1.00
a1a2_[12,0] -1.30 0.67 -1.30 -2.41 -0.22 15175.95 1.00
a1a2_[12,1] -0.38 0.68 -0.39 -1.52 0.72 17030.67 1.00
a1a2_[12,2] 1.38 0.68 1.38 0.26 2.47 16708.05 1.00
a1a2_[12,3] 0.49 0.75 0.50 -0.75 1.71 22134.65 1.00
a1a2_[12,4] -0.01 0.78 -0.01 -1.28 1.28 22807.81 1.00
a1a2_[13,0] -0.27 0.82 -0.26 -1.66 1.03 21819.38 1.00
a1a2_[13,1] -0.17 0.75 -0.17 -1.43 1.05 16716.65 1.00
a1a2_[13,2] 0.27 0.80 0.27 -1.02 1.63 23751.42 1.00
a1a2_[13,3] 0.00 1.00 0.01 -1.71 1.59 32759.62 1.00
a1a2_[13,4] -0.00 1.02 -0.01 -1.67 1.67 31925.53 1.00
a1a2_[14,0] 0.12 0.85 0.12 -1.28 1.52 24259.89 1.00
a1a2_[14,1] -0.11 0.84 -0.12 -1.53 1.24 21497.92 1.00
a1a2_[14,2] -0.27 0.82 -0.26 -1.58 1.11 20567.60 1.00
a1a2_[14,3] -0.01 1.00 -0.01 -1.63 1.66 31284.49 1.00
a1a2_[14,4] 0.00 1.01 0.01 -1.69 1.62 31576.71 1.00
a1a2_[15,0] 0.39 0.74 0.38 -0.82 1.63 20209.33 1.00
a1a2_[15,1] 0.23 0.71 0.23 -0.94 1.39 18714.71 1.00
a1a2_[15,2] -0.36 0.72 -0.37 -1.55 0.84 18632.66 1.00
a1a2_[15,3] -0.53 0.83 -0.53 -1.87 0.84 26865.02 1.00
a1a2_[15,4] -0.01 1.00 -0.01 -1.65 1.67 29480.86 1.00
a1a2_[16,0] 0.09 0.74 0.09 -1.14 1.29 16023.27 1.00
a1a2_[16,1] 0.13 0.70 0.13 -0.99 1.28 13864.21 1.00
a1a2_[16,2] -0.08 0.72 -0.08 -1.28 1.08 15886.88 1.00
a1a2_[16,3] 0.00 0.99 0.01 -1.57 1.69 29224.80 1.00
a1a2_[16,4] -0.01 1.01 -0.01 -1.65 1.68 27421.75 1.00
a1a2_[17,0] 0.04 0.77 0.03 -1.21 1.31 18828.85 1.00
a1a2_[17,1] -0.17 0.79 -0.17 -1.43 1.16 18325.14 1.00
a1a2_[17,2] -0.05 0.80 -0.04 -1.33 1.30 21635.36 1.00
a1a2_[17,3] -0.01 0.99 -0.01 -1.64 1.60 29321.16 1.00
a1a2_[17,4] 0.00 1.00 -0.00 -1.71 1.58 29652.12 1.00
a1a2_[18,0] -1.69 0.74 -1.69 -2.90 -0.47 16732.54 1.00
a1a2_[18,1] 0.80 0.81 0.80 -0.56 2.09 20709.90 1.00
a1a2_[18,2] 0.57 0.74 0.57 -0.68 1.75 16417.67 1.00
a1a2_[18,3] 0.93 0.90 0.93 -0.59 2.38 31400.93 1.00
a1a2_[18,4] 0.00 1.01 -0.00 -1.58 1.72 33260.20 1.00
a1a2_[19,0] -0.34 0.81 -0.34 -1.66 1.02 24104.31 1.00
a1a2_[19,1] -0.34 0.75 -0.35 -1.58 0.88 15936.11 1.00
a1a2_[19,2] 0.62 0.79 0.62 -0.76 1.85 22221.18 1.00
a1a2_[19,3] 0.00 1.00 0.01 -1.65 1.63 36582.08 1.00
a1a2_[19,4] 0.00 1.01 0.01 -1.66 1.67 34162.26 1.00
a1a2_[20,0] 0.23 0.72 0.23 -0.98 1.38 17400.38 1.00
a1a2_[20,1] 0.38 0.66 0.37 -0.73 1.42 14139.09 1.00
a1a2_[20,2] 0.61 0.68 0.60 -0.49 1.73 14527.24 1.00
a1a2_[20,3] -1.41 0.80 -1.41 -2.70 -0.08 23200.06 1.00
a1a2_[20,4] 0.00 1.01 -0.00 -1.64 1.67 34251.44 1.00
a1a2_[21,0] 0.15 0.83 0.16 -1.20 1.50 21414.32 1.00
a1a2_[21,1] 0.05 0.82 0.05 -1.29 1.39 20477.38 1.00
a1a2_[21,2] -0.43 0.90 -0.44 -1.97 1.01 28295.01 1.00
a1a2_[21,3] -0.00 0.98 0.00 -1.59 1.65 31937.31 1.00
a1a2_[21,4] -0.01 1.00 -0.00 -1.66 1.63 32416.36 1.00
a1a2_[22,0] 0.01 0.89 0.01 -1.43 1.48 33733.91 1.00
a1a2_[22,1] -0.22 0.83 -0.23 -1.58 1.16 18149.98 1.00
a1a2_[22,2] -0.00 1.00 0.00 -1.69 1.59 33692.47 1.00
a1a2_[22,3] 0.01 0.89 0.02 -1.46 1.49 33507.27 1.00
a1a2_[22,4] -0.00 1.01 -0.00 -1.66 1.63 36003.86 1.00
a1a2_[23,0] 0.17 0.85 0.17 -1.20 1.59 27151.90 1.00
a1a2_[23,1] 0.17 0.79 0.17 -1.12 1.47 19952.59 1.00
a1a2_[23,2] -0.38 0.81 -0.38 -1.65 0.99 18641.77 1.00
a1a2_[23,3] -0.17 0.91 -0.18 -1.70 1.30 26294.89 1.00
a1a2_[23,4] 0.01 1.01 0.01 -1.57 1.75 31408.34 1.00
a1a2_[24,0] 0.11 0.83 0.12 -1.21 1.51 23131.42 1.00
a1a2_[24,1] -0.96 0.80 -0.97 -2.28 0.36 19874.47 1.00
a1a2_[24,2] 0.71 0.79 0.72 -0.60 1.99 18864.83 1.00
a1a2_[24,3] 0.00 1.00 0.00 -1.66 1.63 28871.62 1.00
a1a2_[24,4] 0.00 1.00 0.00 -1.57 1.70 24694.52 1.00
a1a2_[25,0] -0.12 0.82 -0.12 -1.48 1.21 20023.15 1.00
a1a2_[25,1] -0.16 0.89 -0.16 -1.63 1.29 32862.64 1.00
a1a2_[25,2] 0.20 0.85 0.20 -1.20 1.58 20806.15 1.00
a1a2_[25,3] 0.00 1.00 0.00 -1.73 1.59 34763.96 1.00
a1a2_[25,4] -0.01 1.01 -0.01 -1.64 1.66 26646.59 1.00
a1a2_[26,0] 0.21 0.78 0.22 -1.11 1.45 20548.15 1.00
a1a2_[26,1] -0.12 0.81 -0.12 -1.49 1.17 20941.65 1.00
a1a2_[26,2] 0.79 0.73 0.79 -0.38 2.02 16987.78 1.00
a1a2_[26,3] -1.04 0.89 -1.04 -2.49 0.42 26958.85 1.00
a1a2_[26,4] 0.00 1.00 -0.00 -1.61 1.66 27878.53 1.00
a1a2_[27,0] 0.00 1.00 0.00 -1.63 1.65 38243.85 1.00
a1a2_[27,1] 0.10 0.90 0.10 -1.47 1.51 27929.05 1.00
a1a2_[27,2] 0.44 0.84 0.45 -0.95 1.80 18896.71 1.00
a1a2_[27,3] -0.87 0.91 -0.86 -2.32 0.68 30985.71 1.00
a1a2_[27,4] 0.00 0.99 -0.01 -1.62 1.63 28663.54 1.00
a1a2_[28,0] -0.12 0.69 -0.12 -1.28 1.00 14701.78 1.00
a1a2_[28,1] 0.03 0.67 0.03 -1.06 1.14 14537.36 1.00
a1a2_[28,2] -0.03 0.69 -0.03 -1.24 1.03 15508.10 1.00
a1a2_[28,3] -0.03 0.80 -0.03 -1.31 1.32 22653.28 1.00
a1a2_[28,4] -0.00 1.00 -0.00 -1.64 1.62 33382.37 1.00
a1a2_[29,0] 0.11 0.81 0.11 -1.25 1.40 22401.34 1.00
a1a2_[29,1] -0.20 0.73 -0.21 -1.41 0.96 16236.16 1.00
a1a2_[29,2] 0.42 0.75 0.42 -0.81 1.64 17773.70 1.00
a1a2_[29,3] -0.21 0.90 -0.22 -1.72 1.23 32051.25 1.00
a1a2_[29,4] -0.01 1.00 -0.02 -1.69 1.60 32661.22 1.00
a1a2_[30,0] 0.20 0.80 0.20 -1.11 1.52 22646.58 1.00
a1a2_[30,1] 0.36 0.78 0.36 -0.96 1.60 21180.96 1.00
a1a2_[30,2] -0.71 0.78 -0.71 -1.97 0.60 18721.03 1.00
a1a2_[30,3] -0.01 1.02 -0.01 -1.71 1.67 32793.90 1.00
a1a2_[30,4] -0.01 1.03 -0.02 -1.63 1.71 28468.63 1.00
a1a2_[31,0] -0.20 0.77 -0.19 -1.49 1.05 18340.41 1.00
a1a2_[31,1] -0.12 0.79 -0.13 -1.36 1.23 20591.26 1.00
a1a2_[31,2] 0.24 0.77 0.23 -1.03 1.48 18607.35 1.00
a1a2_[31,3] 0.00 1.01 0.00 -1.63 1.68 30418.24 1.00
a1a2_[31,4] 0.00 1.00 -0.00 -1.61 1.63 31225.23 1.00
a1a2_[32,0] 0.00 1.00 -0.00 -1.65 1.63 32149.59 1.00
a1a2_[32,1] 1.11 0.71 1.11 -0.05 2.30 16461.67 1.00
a1a2_[32,2] -0.36 0.70 -0.36 -1.48 0.80 16002.35 1.00
a1a2_[32,3] 0.33 0.69 0.32 -0.79 1.47 15252.74 1.00
a1a2_[32,4] -0.66 0.90 -0.66 -2.20 0.75 29472.11 1.00
a1a2_[33,0] 0.11 0.84 0.10 -1.27 1.48 19128.37 1.00
a1a2_[33,1] 0.02 0.80 0.02 -1.31 1.30 16230.12 1.00
a1a2_[33,2] -0.31 0.90 -0.31 -1.75 1.20 27349.72 1.00
a1a2_[33,3] 0.00 1.00 0.01 -1.61 1.69 34208.75 1.00
a1a2_[33,4] 0.00 1.00 0.00 -1.68 1.62 36100.56 1.00
a1a2_[34,0] 0.05 0.90 0.04 -1.43 1.55 29731.17 1.00
a1a2_[34,1] -0.03 0.86 -0.03 -1.42 1.42 28606.41 1.00
a1a2_[34,2] -0.14 0.83 -0.14 -1.50 1.21 19600.99 1.00
a1a2_[34,3] 0.01 1.00 0.01 -1.67 1.59 34639.09 1.00
a1a2_[34,4] -0.01 0.99 -0.01 -1.68 1.57 36059.35 1.00
a1a2_[35,0] 0.50 0.74 0.50 -0.70 1.73 20970.25 1.00
a1a2_[35,1] -0.01 0.71 -0.01 -1.20 1.14 17114.41 1.00
a1a2_[35,2] -1.23 0.66 -1.23 -2.29 -0.14 14475.84 1.00
a1a2_[35,3] 1.34 0.91 1.35 -0.12 2.88 27121.13 1.00
a1a2_[35,4] -0.68 0.90 -0.68 -2.20 0.75 33438.06 1.00
a1a2_[36,0] -0.35 0.79 -0.34 -1.64 0.96 22977.33 1.00
a1a2_[36,1] 0.48 0.82 0.48 -0.87 1.83 24388.03 1.00
a1a2_[36,2] 0.00 0.98 0.00 -1.62 1.59 33991.05 1.00
a1a2_[36,3] 0.53 0.81 0.54 -0.76 1.89 26382.86 1.00
a1a2_[36,4] -0.00 1.02 0.00 -1.73 1.64 29866.08 1.00
a1a2_[37,0] 0.20 0.82 0.21 -1.09 1.62 22968.59 1.00
a1a2_[37,1] 0.91 0.77 0.92 -0.33 2.18 20317.46 1.00
a1a2_[37,2] -0.86 0.89 -0.87 -2.36 0.58 28599.05 1.00
a1a2_[37,3] 0.46 0.82 0.47 -0.86 1.85 24731.45 1.00
a1a2_[37,4] 0.00 1.00 0.01 -1.70 1.58 29929.62 1.00
a1a2_[38,0] 0.08 0.90 0.08 -1.40 1.56 31093.31 1.00
a1a2_[38,1] 0.17 0.81 0.18 -1.18 1.46 23629.62 1.00
a1a2_[38,2] 0.30 0.82 0.30 -1.01 1.66 25334.24 1.00
a1a2_[38,3] -0.00 1.01 0.00 -1.67 1.66 29871.89 1.00
a1a2_[38,4] -0.89 0.91 -0.89 -2.38 0.60 26696.28 1.00
a1a2_[39,0] -0.02 0.88 -0.02 -1.47 1.38 31078.65 1.00
a1a2_[39,1] 0.84 0.72 0.84 -0.34 2.02 18854.55 1.00
a1a2_[39,2] -0.23 0.65 -0.24 -1.32 0.82 14537.12 1.00
a1a2_[39,3] -0.35 0.79 -0.35 -1.70 0.93 25670.86 1.00
a1a2_[39,4] -0.46 0.84 -0.47 -1.84 0.93 29171.77 1.00
a1a2_[40,0] -0.00 1.00 -0.00 -1.66 1.62 28174.58 1.00
a1a2_[40,1] -0.47 0.90 -0.46 -1.95 1.04 26045.13 1.00
a1a2_[40,2] 0.54 0.80 0.54 -0.77 1.85 16785.45 1.00
a1a2_[40,3] -0.08 0.83 -0.08 -1.44 1.26 22737.61 1.00
a1a2_[40,4] 0.00 0.98 0.01 -1.63 1.59 31103.81 1.00
a1a2_[41,0] 0.05 0.90 0.05 -1.51 1.46 23945.61 1.00
a1a2_[41,1] -0.15 0.83 -0.15 -1.48 1.23 19734.42 1.00
a1a2_[41,2] -0.19 0.84 -0.19 -1.56 1.20 21113.12 1.00
a1a2_[41,3] -0.00 1.00 0.00 -1.69 1.60 32241.94 1.00
a1a2_[41,4] 0.01 1.00 0.01 -1.63 1.64 33215.43 1.00
a1a2_[42,0] 0.00 1.00 -0.01 -1.63 1.63 29800.82 1.00
a1a2_[42,1] 0.34 0.85 0.34 -1.06 1.73 25170.11 1.00
a1a2_[42,2] 0.35 0.82 0.35 -0.96 1.72 17945.18 1.00
a1a2_[42,3] 0.00 0.99 0.00 -1.55 1.67 33898.57 1.00
a1a2_[42,4] -0.97 0.90 -0.96 -2.42 0.56 24696.91 1.00
a1a2_[43,0] 0.50 0.75 0.50 -0.78 1.70 22108.47 1.00
a1a2_[43,1] 0.62 0.81 0.63 -0.67 1.97 24305.28 1.00
a1a2_[43,2] -0.63 0.84 -0.63 -2.02 0.75 27889.15 1.00
a1a2_[43,3] 0.14 0.85 0.15 -1.27 1.50 28423.97 1.00
a1a2_[43,4] 0.01 1.00 0.00 -1.58 1.73 33993.97 1.00
a1a2_[44,0] 0.46 0.83 0.46 -0.94 1.78 21062.17 1.00
a1a2_[44,1] 0.01 0.82 0.01 -1.32 1.37 22691.40 1.00
a1a2_[44,2] -0.66 0.80 -0.66 -1.94 0.68 18263.35 1.00
a1a2_[44,3] -0.00 0.99 -0.01 -1.59 1.68 28989.78 1.00
a1a2_[44,4] -0.00 1.00 -0.00 -1.67 1.62 32609.13 1.00
a1a2_[45,0] -0.01 0.72 -0.00 -1.18 1.18 15992.24 1.00
a1a2_[45,1] 0.21 0.75 0.21 -1.03 1.41 18888.50 1.00
a1a2_[45,2] 1.07 0.68 1.07 -0.03 2.19 13340.01 1.00
a1a2_[45,3] -0.00 1.00 0.00 -1.64 1.64 25820.96 1.00
a1a2_[45,4] -1.32 0.85 -1.32 -2.71 0.08 23952.61 1.00
a1a2_[46,0] -0.16 0.84 -0.17 -1.51 1.24 26967.82 1.00
a1a2_[46,1] -0.33 0.85 -0.33 -1.70 1.10 29254.95 1.00
a1a2_[46,2] 0.21 0.76 0.21 -1.07 1.44 18114.34 1.00
a1a2_[46,3] 0.17 0.81 0.17 -1.20 1.47 22904.29 1.00
a1a2_[46,4] -0.00 0.99 -0.01 -1.62 1.61 26794.19 1.00
a1a2_[47,0] -0.28 0.84 -0.28 -1.64 1.11 24090.21 1.00
a1a2_[47,1] -1.16 0.72 -1.16 -2.31 0.04 19646.34 1.00
a1a2_[47,2] 0.41 0.71 0.41 -0.80 1.54 20226.32 1.00
a1a2_[47,3] 0.98 0.83 0.99 -0.35 2.38 26221.21 1.00
a1a2_[47,4] 0.12 0.89 0.12 -1.38 1.57 27152.80 1.00
a1a2_[48,0] -0.33 0.70 -0.32 -1.47 0.82 19745.70 1.00
a1a2_[48,1] -1.26 0.67 -1.26 -2.38 -0.18 17561.09 1.00
a1a2_[48,2] -1.56 0.63 -1.55 -2.60 -0.51 14687.06 1.00
a1a2_[48,3] 2.13 0.72 2.13 0.94 3.29 20592.74 1.00
a1a2_[48,4] 1.07 0.76 1.07 -0.13 2.35 22379.82 1.00
a1a2_[49,0] -0.25 0.79 -0.25 -1.49 1.11 17539.34 1.00
a1a2_[49,1] -0.26 0.78 -0.26 -1.56 0.99 18264.19 1.00
a1a2_[49,2] 0.38 0.82 0.38 -1.03 1.67 21366.46 1.00
a1a2_[49,3] -0.01 1.00 -0.00 -1.65 1.61 30803.27 1.00
a1a2_[49,4] 0.01 1.01 0.01 -1.65 1.65 30011.10 1.00
a1a2_[50,0] -0.31 0.83 -0.31 -1.71 1.02 21795.71 1.00
a1a2_[50,1] 0.10 0.79 0.11 -1.21 1.38 19897.82 1.00
a1a2_[50,2] 0.14 0.84 0.14 -1.26 1.53 26904.61 1.00
a1a2_[50,3] -0.00 1.00 -0.01 -1.62 1.63 31188.63 1.00
a1a2_[50,4] -0.00 0.99 0.00 -1.65 1.60 28334.30 1.00
a1a2_[51,0] 0.13 0.82 0.13 -1.22 1.47 24110.72 1.00
a1a2_[51,1] -0.05 0.77 -0.06 -1.28 1.22 16665.47 1.00
a1a2_[51,2] -0.22 0.89 -0.22 -1.70 1.25 29703.07 1.00
a1a2_[51,3] 0.20 0.86 0.20 -1.22 1.59 24494.38 1.00
a1a2_[51,4] 0.00 1.00 -0.00 -1.59 1.66 29028.18 1.00
a1a2_[52,0] 0.12 0.84 0.13 -1.32 1.46 20621.44 1.00
a1a2_[52,1] -0.07 0.85 -0.07 -1.54 1.27 22097.63 1.00
a1a2_[52,2] -0.28 0.89 -0.28 -1.71 1.24 27547.94 1.00
a1a2_[52,3] -0.00 1.00 0.00 -1.64 1.62 32463.82 1.00
a1a2_[52,4] 0.00 1.01 0.00 -1.66 1.64 30573.32 1.00
a1a2_[53,0] 0.00 0.75 -0.01 -1.27 1.20 20814.88 1.00
a1a2_[53,1] -0.04 0.72 -0.04 -1.21 1.13 19796.46 1.00
a1a2_[53,2] -0.16 0.77 -0.16 -1.45 1.07 20973.22 1.00
a1a2_[53,3] 0.47 0.79 0.47 -0.80 1.80 22916.32 1.00
a1a2_[53,4] -0.32 0.90 -0.32 -1.78 1.20 29679.56 1.00
a1a2_[54,0] -0.06 0.77 -0.05 -1.31 1.20 17814.71 1.00
a1a2_[54,1] -0.24 0.74 -0.23 -1.45 0.97 14227.55 1.00
a1a2_[54,2] 0.11 0.75 0.12 -1.18 1.30 15766.87 1.00
a1a2_[54,3] 0.00 1.01 0.00 -1.65 1.64 37719.15 1.00
a1a2_[54,4] 0.01 1.00 0.00 -1.63 1.64 28963.58 1.00
a1a2_[55,0] -0.14 0.65 -0.14 -1.17 0.96 14436.76 1.00
a1a2_[55,1] -0.52 0.65 -0.52 -1.60 0.53 15119.86 1.00
a1a2_[55,2] 0.19 0.69 0.19 -0.91 1.34 17447.71 1.00
a1a2_[55,3] -1.54 0.80 -1.54 -2.89 -0.28 25234.79 1.00
a1a2_[55,4] 2.18 0.85 2.18 0.79 3.59 23029.76 1.00
a1a2_[56,0] -0.52 0.79 -0.53 -1.77 0.83 19906.87 1.00
a1a2_[56,1] -0.44 0.77 -0.44 -1.69 0.83 19889.83 1.00
a1a2_[56,2] -0.61 0.77 -0.61 -1.86 0.65 19924.45 1.00
a1a2_[56,3] -0.00 0.99 0.00 -1.62 1.62 33188.45 1.00
a1a2_[56,4] 1.65 0.91 1.65 0.13 3.13 28100.29 1.00
a1a2_[57,0] -0.08 0.83 -0.08 -1.39 1.33 20409.32 1.00
a1a2_[57,1] -0.24 0.89 -0.23 -1.71 1.21 27113.61 1.00
a1a2_[57,2] -0.00 0.99 -0.00 -1.65 1.60 29806.81 1.00
a1a2_[57,3] 0.39 0.91 0.39 -1.15 1.83 28661.05 1.00
a1a2_[57,4] -0.06 0.91 -0.06 -1.52 1.44 25378.39 1.00
a1a2_[58,0] -0.03 0.80 -0.03 -1.34 1.30 20829.20 1.00
a1a2_[58,1] -0.19 0.84 -0.19 -1.55 1.19 27764.50 1.00
a1a2_[58,2] 0.05 0.78 0.06 -1.17 1.39 20278.57 1.00
a1a2_[58,3] 0.01 1.00 0.01 -1.72 1.57 29840.12 1.00
a1a2_[58,4] 0.05 0.90 0.06 -1.42 1.51 29428.37 1.00
a1a2_[59,0] 0.06 0.83 0.07 -1.28 1.45 18150.51 1.00
a1a2_[59,1] -0.30 0.82 -0.30 -1.64 1.04 14759.47 1.00
a1a2_[59,2] -0.01 1.00 -0.01 -1.63 1.66 30147.56 1.00
a1a2_[59,3] -0.01 1.01 -0.00 -1.69 1.63 30415.83 1.00
a1a2_[59,4] -0.00 1.02 -0.01 -1.69 1.65 30174.17 1.00
a1a2_sigma 9702.75 1209.85 9678.15 7721.52 11684.98 5660.92 1.00
a2_[0] -0.96 0.57 -0.94 -1.90 -0.04 5923.37 1.00
a2_[1] -0.68 0.52 -0.67 -1.53 0.15 5781.52 1.00
a2_[2] -0.06 0.45 -0.05 -0.85 0.64 5585.19 1.00
a2_[3] 0.56 0.50 0.56 -0.30 1.34 5852.44 1.00
a2_[4] 1.15 0.62 1.13 0.15 2.16 6321.13 1.00
a2_sigma 56466.50 25969.65 50156.99 24958.66 90640.17 6365.23 1.00
y_sigma 17983.31 438.24 17974.32 17261.78 18697.42 16181.79 1.00
Number of divergences: 1
idata_hom = az.from_numpyro(
mcmc,
coords=dict(org=salary_df['Org'].cat.categories.values,
pos=salary_df['Pos'].cat.categories.values),
dims=dict(b1=['org'],
b2=['pos'],
b1b2=['org', 'pos']),
)
az.plot_trace(idata_hom)
plt.tight_layout()
fig, axes = plt.subplots(
nrows=2, ncols=2,
figsize=(10, 6),
sharey=True)
n_curves = 20
for org, ax in zip(departments, axes.flatten()):
# Plot data.
df = salary_df[salary_df['Org'] == org]
sns.stripplot(x='Pos', y='Salary', data=df, ax=ax)
ax.set_title(f'{org}\'s Salary with Pred. Post. Distrib.')
# Plot posterior distribution.
posterior = idata_hom.posterior
b0 = posterior['b0'].values.flatten()
b1 = posterior['b1'].sel(org=org).values.flatten()
y_sigma = posterior['y_sigma'].values.flatten()
curve_indices = np.random.choice(
posterior.draw.size * posterior.chain.size, n_curves, replace=False)
for pos_i, pos in enumerate(salary_df['Pos'].cat.categories):
b2 = posterior['b2'].sel(pos=pos).values.flatten()
b1b2 = posterior['b1b2'].sel(org=org, pos=pos).values.flatten()
mean = b0 + b1 + b2 + b1b2
for idx in curve_indices:
rv = norm(mean[idx], y_sigma[idx])
yrange = np.linspace(rv.ppf(0.01), rv.ppf(0.99), 1000)
xpdf = rv.pdf(yrange)
# Scale xpdf
xpdf = xpdf * 0.75 / np.max(xpdf)
# Plot pdf curve.
ax.plot(pos_i - xpdf, yrange, c='b', alpha=.1)
fig.tight_layout()
Contrasts¶
def plot_contrasts(
idata, coef: str,
left_sel: 'dict[str, list[str]]',
right_sel: 'dict[str, list[str]]',
comp_val: float = None,
rope: 'tuple[float, float]' = None,
ax: plt.Axes = None):
"""
Plot contrasts based on inference data from 2 nominal predictors
and homogeneous normal model.
Parameters
----------
idata: az.InferenceData
Inference Data converted from numpyro's MCMC object.
coef: str
Name of the coefficient to be used for contrasts comparison.
left_sel: dict[str, list[str]]
Selector that will be passed to .sel() function.
right_sel: dict[str, list[str]]
Selector that will be passed to .sel() function.
ax: plt.Axes
Axes to be used. If None, then new axes will be created.
"""
def average_last_dim_if_necessary(values):
if values.ndim == 2:
return values
values = np.reshape(values, (*values.shape[:2], -1))
return np.mean(values, axis=-1)
if ax is None:
_, ax = plt.subplots()
posterior = idata.posterior
left_values = average_last_dim_if_necessary(
posterior[coef].sel(left_sel).values)
right_values = average_last_dim_if_necessary(
posterior[coef].sel(right_sel).values)
diff = left_values - right_values
az.plot_posterior(
diff, point_estimate='median', hdi_prob=0.95, ref_val=comp_val, rope=rope, ax=ax)
ax.set_xlabel('Difference')
return ax
Main Effect Contrasts¶
pos_contrasts = [
dict(left='Full', right='Assoc', comp_val=0.0, rope=(-1000, 1000)),
dict(left='Assoc', right='Assis', comp_val=0.0, rope=(-1000, 1000)),
]
fig, axes = plt.subplots(ncols=2, figsize=(10, 4))
for contrast, ax in zip(pos_contrasts, axes):
plot_contrasts(
idata_hom, 'b2',
left_sel=dict(pos=contrast['left']),
right_sel=dict(pos=contrast['right']),
comp_val=contrast['comp_val'],
rope=contrast['rope'],
ax=ax)
ax.set_title(f'{contrast["left"]} vs {contrast["right"]}')
fig.tight_layout()
org_contrasts = [
dict(left='CHEM', right='ENG', comp_val=0.0, rope=(-1000, 1000)),
dict(left='CHEM', right='PSY', comp_val=0.0, rope=(-1000, 1000)),
dict(left='BFIN', right=['PSY', 'CHEM', 'ENG'],
comp_val=0.0, rope=(-1000, 1000)),
]
fig, axes = plt.subplots(ncols=3, figsize=(12, 4))
for contrast, ax in zip(org_contrasts, axes):
plot_contrasts(
idata_hom, 'b1',
left_sel=dict(org=contrast['left']),
right_sel=dict(org=contrast['right']),
comp_val=contrast['comp_val'],
rope=contrast['rope'],
ax=ax)
ax.set_title(f'{contrast["left"]} vs {contrast["right"]}')
fig.tight_layout()
Interaction Contrasts¶
TODO
Heterogeneous Variances and Robustness against Outliers¶
kernel = NUTS(
glm_metric.multi_nominal_predictors_het_var_robust,
init_strategy=init_to_median)
mcmc = MCMC(kernel, num_warmup=1000, num_samples=5000, num_chains=2)
mcmc.run(
random.PRNGKey(0),
y=jnp.array(salary_df['Salary'].values),
grp=jnp.concatenate([salary_df[c].cat.codes.values[..., None]
for c in ['Org', 'Pos']], axis=1),
y_sds=jnp.array(salary_df.groupby(['Org', 'Pos']).std().dropna().values),
nb_groups=(salary_df['Org'].cat.categories.size,
salary_df['Pos'].cat.categories.size),
)
mcmc.print_summary()
/tmp/ipykernel_4791/3016085570.py:10: FutureWarning: The default value of numeric_only in DataFrameGroupBy.std is deprecated. In a future version, numeric_only will default to False. Either specify numeric_only or select only columns which should be valid for the function. y_sds=jnp.array(salary_df.groupby(['Org', 'Pos']).std().dropna().values),
mean std median 5.0% 95.0% n_eff r_hat
a0_ 0.08 0.12 0.07 -0.09 0.28 1.25 3.31
a1_[0] 3.08 0.34 2.95 2.67 3.66 1.93 1.75
a1_[1] -0.44 0.23 -0.42 -0.83 -0.08 2.05 1.46
a1_[2] -0.54 0.12 -0.54 -0.75 -0.35 18.36 1.15
a1_[3] -0.63 0.15 -0.61 -0.85 -0.36 10.66 1.16
a1_[4] -0.15 0.12 -0.14 -0.32 0.06 13.80 1.22
a1_[5] -0.38 0.15 -0.37 -0.62 -0.13 14.64 1.08
a1_[6] 1.51 0.22 1.50 1.11 1.83 4.27 1.26
a1_[7] 3.71 0.43 3.64 3.06 4.36 2.50 1.53
a1_[8] -0.10 0.09 -0.11 -0.24 0.05 23.59 1.05
a1_[9] 0.64 0.15 0.63 0.43 0.90 16.16 1.08
a1_[10] -0.51 0.15 -0.49 -0.80 -0.31 7.06 1.33
a1_[11] -0.43 0.19 -0.44 -0.73 -0.10 7.32 1.26
a1_[12] 0.42 0.16 0.43 0.14 0.66 17.42 1.21
a1_[13] -0.55 0.18 -0.51 -0.84 -0.32 1.28 2.05
a1_[14] -0.69 0.19 -0.68 -1.03 -0.42 2.12 1.44
a1_[15] -0.61 0.13 -0.61 -0.82 -0.42 1.58 1.73
a1_[16] 0.46 0.14 0.47 0.23 0.68 15.80 1.17
a1_[17] -0.56 0.14 -0.58 -0.78 -0.35 3.50 1.31
a1_[18] 1.45 0.21 1.45 1.10 1.84 19.38 1.05
a1_[19] -0.36 0.18 -0.36 -0.63 -0.06 5.79 1.35
a1_[20] -0.53 0.09 -0.53 -0.66 -0.36 10.22 1.24
a1_[21] -0.72 0.20 -0.74 -1.09 -0.43 2.79 1.33
a1_[22] -0.53 0.12 -0.55 -0.73 -0.33 13.62 1.07
a1_[23] -0.65 0.13 -0.66 -0.84 -0.40 8.84 1.27
a1_[24] -0.63 0.16 -0.64 -0.88 -0.36 25.32 1.03
a1_[25] -0.31 0.18 -0.30 -0.60 -0.00 10.60 1.16
a1_[26] -0.31 0.16 -0.29 -0.61 -0.08 3.87 1.30
a1_[27] -0.77 0.27 -0.74 -1.12 -0.33 2.04 1.54
a1_[28] -0.35 0.15 -0.33 -0.61 -0.12 9.26 1.35
a1_[29] 0.43 0.14 0.43 0.17 0.65 14.27 1.09
a1_[30] -0.42 0.14 -0.40 -0.64 -0.20 2.51 1.48
a1_[31] -0.26 0.15 -0.24 -0.54 -0.06 23.86 1.02
a1_[32] 1.57 0.18 1.56 1.22 1.84 5.03 1.31
a1_[33] -0.65 0.13 -0.67 -0.89 -0.45 1.96 1.49
a1_[34] -0.43 0.17 -0.42 -0.71 -0.14 6.77 1.15
a1_[35] -0.25 0.14 -0.25 -0.49 -0.03 12.81 1.18
a1_[36] 2.05 0.32 1.97 1.61 2.63 2.31 1.56
a1_[37] 2.34 0.24 2.33 1.99 2.77 3.06 1.36
a1_[38] -0.82 0.20 -0.80 -1.12 -0.47 2.60 1.39
a1_[39] -0.53 0.16 -0.52 -0.80 -0.26 4.39 1.24
a1_[40] 0.03 0.24 0.03 -0.37 0.41 23.81 1.05
a1_[41] -0.80 0.18 -0.80 -1.09 -0.49 3.16 1.38
a1_[42] -0.69 0.21 -0.68 -1.03 -0.37 18.99 1.10
a1_[43] 2.08 0.21 2.06 1.73 2.42 4.41 1.27
a1_[44] -0.38 0.11 -0.37 -0.55 -0.20 10.13 1.27
a1_[45] 0.04 0.18 0.02 -0.25 0.33 5.56 1.55
a1_[46] -0.41 0.15 -0.41 -0.62 -0.17 9.40 1.31
a1_[47] 0.02 0.17 -0.01 -0.24 0.30 7.74 1.37
a1_[48] -0.10 0.15 -0.10 -0.35 0.15 4.25 1.30
a1_[49] -0.56 0.12 -0.55 -0.76 -0.36 19.75 1.14
a1_[50] -0.02 0.13 -0.02 -0.26 0.21 5.64 1.26
a1_[51] 0.16 0.11 0.15 -0.04 0.32 16.91 1.11
a1_[52] -0.74 0.12 -0.74 -0.93 -0.53 7.11 1.36
a1_[53] -0.15 0.11 -0.15 -0.33 0.00 16.03 1.15
a1_[54] -0.58 0.22 -0.56 -0.87 -0.29 1.07 3.89
a1_[55] 0.39 0.15 0.42 0.16 0.59 7.55 1.61
a1_[56] 0.00 0.13 0.00 -0.18 0.23 31.48 1.09
a1_[57] 0.23 0.19 0.25 -0.08 0.55 2.24 1.36
a1_[58] -0.36 0.21 -0.35 -0.68 -0.01 3.67 1.23
a1_[59] -0.76 0.18 -0.75 -1.05 -0.45 3.56 1.34
a1_sigma 31866.55 3371.29 32344.94 26064.87 37153.55 1.69 1.77
a1a2_[0,0] 0.76 0.81 0.70 -0.56 2.25 12.71 1.21
a1a2_[0,1] 1.12 0.81 1.13 -0.22 2.40 40.07 1.02
a1a2_[0,2] -0.81 1.01 -0.77 -2.63 0.67 49.79 1.02
a1a2_[0,3] -0.67 0.88 -0.68 -2.11 0.80 59.84 1.02
a1a2_[0,4] 0.17 1.12 0.20 -1.58 2.27 44.91 1.02
a1a2_[1,0] 0.05 0.92 0.05 -1.50 1.47 55.60 1.03
a1a2_[1,1] 0.03 0.95 0.09 -1.39 1.71 8.70 1.37
a1a2_[1,2] 0.25 0.90 0.29 -1.23 1.71 59.78 1.05
a1a2_[1,3] 0.05 0.97 0.03 -1.44 1.73 49.74 1.07
a1a2_[1,4] -0.02 0.94 0.06 -1.47 1.54 58.86 1.00
a1a2_[2,0] -0.01 0.68 0.01 -1.13 1.07 12.76 1.17
a1a2_[2,1] -0.02 0.66 0.00 -1.20 0.94 16.30 1.18
a1a2_[2,2] 0.08 1.08 0.16 -1.83 1.67 18.15 1.09
a1a2_[2,3] -0.13 1.01 -0.16 -1.75 1.57 19.00 1.12
a1a2_[2,4] 0.07 1.02 0.08 -1.56 1.86 81.69 1.01
a1a2_[3,0] 0.73 0.96 0.84 -0.87 2.28 15.70 1.25
a1a2_[3,1] 0.28 0.81 0.14 -0.88 1.71 12.69 1.20
a1a2_[3,2] -0.85 0.72 -0.87 -2.02 0.26 15.41 1.22
a1a2_[3,3] -0.65 0.87 -0.66 -2.10 0.74 61.04 1.06
a1a2_[3,4] -0.08 0.98 -0.07 -1.68 1.56 50.30 1.01
a1a2_[4,0] -0.37 0.64 -0.32 -1.53 0.52 12.88 1.16
a1a2_[4,1] 0.65 0.75 0.72 -0.57 1.76 9.95 1.23
a1a2_[4,2] 0.51 0.87 0.59 -0.81 2.02 84.43 1.03
a1a2_[4,3] -0.01 0.98 -0.01 -1.64 1.59 131.24 1.01
a1a2_[4,4] 0.32 1.08 0.35 -1.47 2.10 26.62 1.03
a1a2_[5,0] -0.20 0.86 -0.11 -1.50 1.24 18.22 1.00
a1a2_[5,1] -0.33 0.87 -0.33 -1.96 0.91 19.58 1.02
a1a2_[5,2] 0.07 0.99 0.09 -1.57 1.65 21.31 1.18
a1a2_[5,3] -0.28 1.20 -0.22 -2.30 1.51 3.68 1.58
a1a2_[5,4] -0.18 0.96 -0.17 -1.59 1.35 67.78 1.05
a1a2_[6,0] -0.05 0.88 -0.03 -1.41 1.54 32.21 1.02
a1a2_[6,1] 0.25 0.89 0.30 -1.12 1.73 26.28 1.05
a1a2_[6,2] 0.11 0.96 0.12 -1.50 1.71 106.78 1.02
a1a2_[6,3] -0.16 1.10 -0.21 -2.01 1.51 48.37 1.03
a1a2_[6,4] 0.21 0.94 0.20 -1.40 1.69 65.01 1.00
a1a2_[7,0] -0.05 0.81 -0.07 -1.34 1.32 34.74 1.03
a1a2_[7,1] 0.92 0.73 0.94 -0.27 2.11 65.17 1.03
a1a2_[7,2] 0.13 0.94 0.15 -1.38 1.71 55.25 1.03
a1a2_[7,3] -0.79 0.78 -0.80 -2.17 0.45 97.49 1.01
a1a2_[7,4] -0.04 0.92 0.04 -1.61 1.39 40.39 1.02
a1a2_[8,0] -0.15 0.57 -0.13 -0.97 0.91 13.39 1.10
a1a2_[8,1] -0.32 0.62 -0.35 -1.39 0.63 16.91 1.18
a1a2_[8,2] 0.29 0.72 0.25 -0.84 1.49 36.40 1.04
a1a2_[8,3] -0.35 0.84 -0.50 -1.66 1.08 22.42 1.14
a1a2_[8,4] 0.55 0.83 0.55 -0.92 1.79 89.51 1.03
a1a2_[9,0] 0.85 0.85 0.73 -0.42 2.37 24.93 1.07
a1a2_[9,1] 0.20 0.86 0.13 -1.04 1.82 29.70 1.06
a1a2_[9,2] 0.04 0.77 0.02 -1.22 1.24 30.38 1.04
a1a2_[9,3] -0.91 0.93 -0.96 -2.61 0.42 33.96 1.03
a1a2_[9,4] 0.07 0.88 0.04 -1.37 1.54 137.18 1.00
a1a2_[10,0] 0.40 0.71 0.41 -0.84 1.50 6.94 1.32
a1a2_[10,1] -0.32 0.67 -0.32 -1.46 0.77 29.96 1.08
a1a2_[10,2] 0.03 0.74 0.01 -1.11 1.36 49.82 1.00
a1a2_[10,3] -0.00 0.99 -0.01 -1.71 1.55 95.25 1.04
a1a2_[10,4] 0.06 1.08 0.06 -1.58 1.89 71.28 1.01
a1a2_[11,0] -0.22 0.60 -0.20 -1.12 0.76 29.77 1.11
a1a2_[11,1] 0.40 0.84 0.41 -0.99 1.74 35.26 1.07
a1a2_[11,2] 0.16 0.89 0.19 -1.34 1.62 52.53 1.03
a1a2_[11,3] -0.43 1.06 -0.39 -2.01 1.40 23.38 1.05
a1a2_[11,4] 0.05 1.04 -0.02 -1.55 1.81 16.65 1.09
a1a2_[12,0] -2.15 0.72 -2.16 -3.35 -1.02 29.30 1.02
a1a2_[12,1] -0.27 0.78 -0.26 -1.49 1.00 44.39 1.08
a1a2_[12,2] 0.90 0.90 0.94 -0.57 2.38 73.01 1.01
a1a2_[12,3] 0.52 0.97 0.49 -1.24 1.97 32.16 1.06
a1a2_[12,4] 0.13 1.04 0.20 -1.56 1.79 32.59 1.05
a1a2_[13,0] -0.63 0.75 -0.67 -1.77 0.77 2.91 1.32
a1a2_[13,1] 0.14 0.77 0.10 -1.06 1.52 3.68 1.26
a1a2_[13,2] 0.51 0.91 0.51 -0.97 2.02 59.82 1.02
a1a2_[13,3] -0.04 0.97 -0.10 -1.55 1.49 93.87 1.01
a1a2_[13,4] 0.19 1.23 0.16 -1.47 2.61 34.41 1.03
a1a2_[14,0] 0.47 0.81 0.46 -0.86 1.87 53.78 1.01
a1a2_[14,1] -0.21 0.80 -0.18 -1.46 1.16 12.62 1.11
a1a2_[14,2] -0.39 0.85 -0.35 -1.78 1.01 58.85 1.02
a1a2_[14,3] 0.12 0.89 0.07 -1.31 1.52 43.08 1.02
a1a2_[14,4] -0.04 0.97 -0.10 -1.59 1.58 62.12 1.04
a1a2_[15,0] 0.45 0.53 0.50 -0.48 1.23 19.56 1.06
a1a2_[15,1] 0.03 0.51 0.01 -0.89 0.85 21.65 1.09
a1a2_[15,2] -0.57 0.60 -0.56 -1.51 0.37 44.89 1.04
a1a2_[15,3] -0.69 0.80 -0.75 -1.96 0.68 52.30 1.03
a1a2_[15,4] -0.12 0.99 -0.13 -1.67 1.67 62.77 1.02
a1a2_[16,0] -0.24 0.74 -0.28 -1.34 0.93 19.14 1.09
a1a2_[16,1] 0.45 0.67 0.39 -0.52 1.64 24.00 1.04
a1a2_[16,2] -0.31 0.58 -0.33 -1.27 0.61 69.33 1.03
a1a2_[16,3] 0.05 0.99 0.02 -1.53 1.71 48.56 1.02
a1a2_[16,4] 0.28 1.01 0.27 -1.34 2.00 74.88 1.06
a1a2_[17,0] 0.07 0.63 0.03 -0.98 1.16 38.71 1.02
a1a2_[17,1] -0.36 0.67 -0.39 -1.41 0.80 49.26 1.00
a1a2_[17,2] -0.04 0.75 -0.04 -1.33 1.20 98.20 1.01
a1a2_[17,3] -0.12 0.94 -0.14 -1.54 1.46 65.27 1.03
a1a2_[17,4] -0.09 1.12 -0.07 -1.84 1.55 48.86 1.07
a1a2_[18,0] -1.95 0.98 -2.06 -3.45 -0.27 3.52 1.24
a1a2_[18,1] 1.11 1.04 1.23 -0.60 2.68 34.60 1.05
a1a2_[18,2] 0.47 0.98 0.52 -1.28 2.02 44.70 1.03
a1a2_[18,3] 0.12 1.00 0.13 -1.52 1.83 82.01 1.03
a1a2_[18,4] -0.14 0.95 -0.15 -1.64 1.43 38.64 1.06
a1a2_[19,0] -0.23 0.82 -0.19 -1.72 1.09 25.71 1.09
a1a2_[19,1] 0.04 0.83 0.07 -1.35 1.40 37.56 1.07
a1a2_[19,2] 0.32 0.90 0.33 -1.15 1.83 27.41 1.12
a1a2_[19,3] 0.03 0.84 0.01 -1.43 1.38 101.81 1.01
a1a2_[19,4] -0.27 0.95 -0.33 -1.95 1.12 81.96 1.03
a1a2_[20,0] -0.04 0.65 -0.04 -1.06 0.99 7.74 1.32
a1a2_[20,1] 0.22 0.58 0.19 -0.74 1.17 6.81 1.40
a1a2_[20,2] 0.77 0.71 0.78 -0.32 1.95 36.86 1.07
a1a2_[20,3] -0.87 0.93 -0.87 -2.46 0.55 92.80 1.03
a1a2_[20,4] 0.25 0.97 0.19 -1.38 1.89 29.01 1.11
a1a2_[21,0] 0.57 0.77 0.67 -0.88 1.72 27.13 1.05
a1a2_[21,1] 0.35 0.77 0.38 -0.85 1.70 37.39 1.03
a1a2_[21,2] -0.89 0.99 -0.96 -2.41 0.76 63.84 1.06
a1a2_[21,3] 0.01 0.99 0.02 -1.50 1.60 70.72 1.01
a1a2_[21,4] -0.06 0.83 -0.04 -1.55 1.16 49.94 1.01
a1a2_[22,0] -0.14 0.67 -0.13 -1.25 0.93 73.68 1.04
a1a2_[22,1] -0.69 0.79 -0.72 -1.91 0.78 7.18 1.21
a1a2_[22,2] 0.30 1.02 0.25 -1.34 1.96 48.25 1.03
a1a2_[22,3] 0.33 0.90 0.42 -1.13 1.85 39.90 1.06
a1a2_[22,4] 0.02 1.00 0.04 -1.52 1.72 42.96 1.00
a1a2_[23,0] 0.40 0.61 0.39 -0.50 1.44 17.46 1.07
a1a2_[23,1] -0.11 0.70 -0.10 -1.14 1.03 26.60 1.07
a1a2_[23,2] -0.16 0.96 -0.13 -1.71 1.30 52.81 1.01
a1a2_[23,3] 0.04 0.77 0.04 -1.19 1.26 32.91 1.09
a1a2_[23,4] -0.26 0.95 -0.24 -1.78 1.39 25.77 1.05
a1a2_[24,0] 1.19 0.96 1.20 -0.38 2.72 2.84 1.30
a1a2_[24,1] -0.98 0.95 -0.91 -2.52 0.47 7.54 1.16
a1a2_[24,2] 0.77 1.14 0.66 -0.96 2.71 14.22 1.11
a1a2_[24,3] 0.10 1.00 0.10 -1.45 1.83 38.74 1.02
a1a2_[24,4] -0.01 0.85 -0.03 -1.41 1.42 123.50 1.00
a1a2_[25,0] -0.14 0.93 -0.18 -1.97 1.24 26.88 1.01
a1a2_[25,1] -0.45 0.87 -0.39 -2.03 0.85 49.06 1.02
a1a2_[25,2] 0.44 0.91 0.44 -1.03 1.98 56.38 1.02
a1a2_[25,3] 0.09 1.00 0.10 -1.50 1.89 61.45 1.05
a1a2_[25,4] 0.24 0.99 0.20 -1.34 1.83 48.05 1.04
a1a2_[26,0] -0.10 0.67 -0.14 -1.24 1.00 17.31 1.08
a1a2_[26,1] -0.92 0.69 -1.01 -1.99 0.28 20.75 1.11
a1a2_[26,2] 0.43 0.80 0.44 -0.99 1.72 46.85 1.01
a1a2_[26,3] -0.53 1.01 -0.52 -2.09 1.27 53.37 1.05
a1a2_[26,4] 0.34 0.91 0.38 -1.19 1.77 79.52 1.02
a1a2_[27,0] -0.10 0.94 -0.12 -1.56 1.56 74.86 1.01
a1a2_[27,1] -0.22 0.89 -0.16 -1.82 1.10 32.11 1.09
a1a2_[27,2] 0.38 0.91 0.35 -1.16 1.81 7.18 1.15
a1a2_[27,3] -0.45 0.89 -0.40 -1.91 1.04 111.88 1.06
a1a2_[27,4] 0.04 0.95 0.06 -1.41 1.85 61.73 1.11
a1a2_[28,0] -0.49 0.71 -0.56 -1.58 0.78 6.36 1.35
a1a2_[28,1] -0.31 0.76 -0.41 -1.66 0.86 8.99 1.26
a1a2_[28,2] 0.10 0.78 0.04 -1.10 1.52 7.67 1.15
a1a2_[28,3] 0.57 0.82 0.57 -0.70 1.97 78.87 1.05
a1a2_[28,4] 0.08 1.01 0.08 -1.42 1.94 34.69 1.06
a1a2_[29,0] -0.01 0.84 -0.06 -1.35 1.45 47.69 1.03
a1a2_[29,1] -0.72 0.82 -0.76 -1.99 0.74 17.20 1.09
a1a2_[29,2] 0.68 0.62 0.64 -0.40 1.77 30.04 1.05
a1a2_[29,3] -0.60 0.79 -0.68 -1.75 0.74 28.34 1.03
a1a2_[29,4] 0.14 1.10 0.12 -1.86 1.74 17.53 1.10
a1a2_[30,0] 0.37 0.63 0.29 -0.66 1.40 19.46 1.06
a1a2_[30,1] 0.61 0.64 0.56 -0.44 1.63 29.88 1.04
a1a2_[30,2] -1.08 0.85 -1.14 -2.39 0.37 33.01 1.09
a1a2_[30,3] 0.04 1.06 -0.06 -1.60 1.78 53.98 1.04
a1a2_[30,4] -0.48 1.17 -0.53 -2.32 1.43 15.72 1.17
a1a2_[31,0] -0.25 0.82 -0.23 -1.65 1.02 22.62 1.09
a1a2_[31,1] 0.22 0.75 0.17 -0.90 1.62 23.52 1.07
a1a2_[31,2] 0.62 0.76 0.57 -0.62 1.87 23.49 1.08
a1a2_[31,3] -0.26 0.94 -0.27 -1.83 1.26 72.12 1.06
a1a2_[31,4] 0.31 0.98 0.31 -1.45 1.78 89.25 1.01
a1a2_[32,0] 0.07 1.00 0.06 -1.50 1.73 35.64 1.07
a1a2_[32,1] 1.08 0.73 1.09 -0.20 2.21 13.51 1.04
a1a2_[32,2] -0.85 0.71 -0.84 -2.09 0.25 53.05 1.01
a1a2_[32,3] 0.15 0.79 0.16 -1.10 1.39 69.13 1.02
a1a2_[32,4] -0.48 0.99 -0.48 -2.00 1.19 75.49 1.02
a1a2_[33,0] 0.51 0.59 0.55 -0.54 1.37 38.57 1.01
a1a2_[33,1] 0.30 0.54 0.27 -0.59 1.17 45.95 1.02
a1a2_[33,2] -0.79 0.87 -0.95 -2.26 0.59 35.03 1.05
a1a2_[33,3] 0.10 0.99 0.11 -1.65 1.71 95.66 1.01
a1a2_[33,4] -0.09 0.94 -0.15 -1.69 1.39 90.57 1.03
a1a2_[34,0] 0.38 0.84 0.40 -1.05 1.69 72.19 1.01
a1a2_[34,1] 0.06 0.79 0.08 -1.32 1.28 56.75 1.00
a1a2_[34,2] -0.15 0.91 -0.11 -1.59 1.37 63.34 1.05
a1a2_[34,3] 0.18 0.94 0.15 -1.38 1.72 72.43 1.01
a1a2_[34,4] -0.18 1.10 -0.11 -2.01 1.63 48.14 1.02
a1a2_[35,0] 1.50 0.73 1.47 0.16 2.55 11.09 1.20
a1a2_[35,1] 0.18 0.67 0.12 -0.94 1.20 41.86 1.05
a1a2_[35,2] -1.37 0.69 -1.37 -2.43 -0.15 16.94 1.15
a1a2_[35,3] 0.19 1.04 0.18 -1.45 1.94 58.08 1.04
a1a2_[35,4] -0.82 0.98 -0.82 -2.35 0.83 49.85 1.08
a1a2_[36,0] -1.21 0.77 -1.17 -2.45 0.10 7.33 1.14
a1a2_[36,1] 1.25 0.68 1.24 0.04 2.34 7.64 1.14
a1a2_[36,2] 0.11 1.00 0.18 -1.69 1.66 82.83 1.01
a1a2_[36,3] 0.66 0.92 0.66 -0.83 2.17 68.74 1.07
a1a2_[36,4] -0.16 1.01 -0.19 -1.75 1.66 43.77 1.03
a1a2_[37,0] -0.68 0.67 -0.62 -1.83 0.35 25.74 1.09
a1a2_[37,1] 1.01 0.70 1.06 -0.15 2.17 57.08 1.09
a1a2_[37,2] -0.30 1.05 -0.31 -2.05 1.39 68.69 1.02
a1a2_[37,3] 0.46 0.91 0.52 -1.21 1.81 96.80 1.03
a1a2_[37,4] -0.14 1.02 -0.15 -1.80 1.47 60.42 1.06
a1a2_[38,0] -0.10 0.90 -0.12 -1.71 1.13 28.08 1.01
a1a2_[38,1] 0.08 0.72 0.05 -1.00 1.40 42.13 1.04
a1a2_[38,2] 0.18 0.96 0.30 -1.23 1.89 16.17 1.24
a1a2_[38,3] 0.16 0.88 0.20 -1.31 1.59 64.33 1.01
a1a2_[38,4] -0.53 1.13 -0.60 -2.33 1.18 43.96 1.04
a1a2_[39,0] -0.80 0.77 -0.80 -2.00 0.49 27.52 1.03
a1a2_[39,1] 0.95 0.81 0.92 -0.48 2.17 74.75 1.01
a1a2_[39,2] -0.61 0.68 -0.60 -1.66 0.52 38.37 1.01
a1a2_[39,3] 0.11 0.90 0.11 -1.34 1.54 56.47 1.06
a1a2_[39,4] -0.13 0.93 -0.13 -1.63 1.49 76.37 1.01
a1a2_[40,0] -0.37 1.15 -0.42 -2.24 1.46 3.80 1.21
a1a2_[40,1] -0.73 1.10 -0.81 -2.44 1.21 23.27 1.09
a1a2_[40,2] 0.47 1.05 0.46 -1.15 2.23 30.16 1.02
a1a2_[40,3] 0.10 0.89 0.08 -1.32 1.59 42.70 1.02
a1a2_[40,4] 0.19 0.99 0.12 -1.40 1.77 52.62 1.00
a1a2_[41,0] 0.04 0.76 0.02 -1.21 1.30 24.47 1.15
a1a2_[41,1] -0.61 0.69 -0.66 -1.72 0.50 18.91 1.12
a1a2_[41,2] -0.31 0.83 -0.35 -1.62 1.17 51.56 1.02
a1a2_[41,3] -0.06 0.94 -0.03 -1.73 1.40 53.22 1.02
a1a2_[41,4] -0.01 1.02 -0.01 -1.57 1.66 57.29 1.01
a1a2_[42,0] 0.05 1.02 0.04 -1.62 1.73 58.57 1.03
a1a2_[42,1] 0.27 0.87 0.23 -1.08 1.86 16.18 1.15
a1a2_[42,2] -0.10 0.93 -0.09 -1.62 1.47 36.85 1.07
a1a2_[42,3] 0.01 0.84 -0.00 -1.34 1.36 27.18 1.01
a1a2_[42,4] -0.32 0.99 -0.28 -2.00 1.11 43.89 1.05
a1a2_[43,0] 0.31 0.66 0.32 -0.88 1.30 31.01 1.07
a1a2_[43,1] 1.00 0.64 0.98 -0.05 2.04 67.98 1.03
a1a2_[43,2] -0.76 1.02 -0.74 -2.57 0.81 68.25 1.09
a1a2_[43,3] -0.13 0.84 -0.14 -1.51 1.18 61.31 1.05
a1a2_[43,4] 0.11 0.84 0.26 -1.26 1.43 5.74 1.16
a1a2_[44,0] 1.31 0.54 1.34 0.51 2.19 8.72 1.23
a1a2_[44,1] -0.13 0.66 -0.13 -1.19 0.79 36.78 1.06
a1a2_[44,2] -1.43 0.59 -1.43 -2.43 -0.49 21.26 1.12
a1a2_[44,3] -0.14 0.89 -0.15 -1.64 1.26 68.15 1.04
a1a2_[44,4] -0.11 0.95 -0.07 -1.73 1.37 73.02 1.04
a1a2_[45,0] -0.77 0.80 -0.82 -1.86 0.75 9.80 1.27
a1a2_[45,1] 0.06 0.88 0.02 -1.27 1.53 11.75 1.20
a1a2_[45,2] 0.61 0.78 0.60 -0.60 1.91 25.57 1.07
a1a2_[45,3] 0.02 1.02 0.03 -1.60 1.72 49.31 1.02
a1a2_[45,4] -0.42 0.97 -0.52 -1.82 1.42 20.47 1.05
a1a2_[46,0] 0.02 0.79 0.01 -1.21 1.35 49.14 1.08
a1a2_[46,1] -0.52 0.72 -0.48 -1.79 0.63 15.05 1.19
a1a2_[46,2] 0.51 0.73 0.46 -0.54 1.90 67.70 1.04
a1a2_[46,3] -0.14 0.88 -0.19 -1.59 1.30 56.92 1.09
a1a2_[46,4] -0.02 1.06 -0.00 -1.73 1.71 16.81 1.15
a1a2_[47,0] -0.15 0.75 -0.07 -1.47 0.89 10.47 1.32
a1a2_[47,1] -1.02 0.70 -1.00 -2.19 0.11 35.08 1.11
a1a2_[47,2] 0.49 0.86 0.42 -0.96 1.89 36.68 1.09
a1a2_[47,3] 0.64 0.95 0.71 -1.00 2.14 76.87 1.02
a1a2_[47,4] 0.42 0.96 0.46 -1.24 1.89 42.97 1.06
a1a2_[48,0] 0.55 0.76 0.53 -0.61 1.84 36.60 1.06
a1a2_[48,1] -1.23 0.84 -1.14 -2.66 0.02 23.23 1.08
a1a2_[48,2] -0.63 1.00 -0.67 -2.12 1.22 43.27 1.01
a1a2_[48,3] 0.77 0.82 0.76 -0.47 2.20 57.38 1.05
a1a2_[48,4] 0.31 0.95 0.33 -1.32 1.79 69.91 1.06
a1a2_[49,0] -0.17 0.71 -0.17 -1.19 1.02 8.88 1.17
a1a2_[49,1] -0.05 0.68 -0.01 -1.09 1.11 8.82 1.15
a1a2_[49,2] 0.30 0.93 0.31 -1.23 1.90 79.88 1.03
a1a2_[49,3] -0.12 0.84 -0.20 -1.45 1.21 45.88 1.08
a1a2_[49,4] 0.17 1.14 0.17 -1.63 2.12 51.03 1.06
a1a2_[50,0] -1.15 0.81 -1.11 -2.62 0.12 27.91 1.03
a1a2_[50,1] 0.02 0.68 -0.01 -1.03 1.17 29.91 1.08
a1a2_[50,2] 0.70 0.65 0.71 -0.45 1.67 31.02 1.07
a1a2_[50,3] 0.06 0.91 0.04 -1.43 1.54 93.52 1.00
a1a2_[50,4] -0.07 1.02 -0.04 -1.74 1.58 71.03 1.02
a1a2_[51,0] 0.47 0.71 0.51 -0.72 1.60 21.48 1.14
a1a2_[51,1] 0.09 0.68 0.08 -1.21 1.08 7.25 1.22
a1a2_[51,2] -0.47 0.75 -0.49 -1.61 0.83 20.27 1.18
a1a2_[51,3] 0.33 0.99 0.27 -1.21 2.08 49.76 1.09
a1a2_[51,4] -0.04 0.90 -0.04 -1.55 1.40 60.56 1.06
a1a2_[52,0] 0.46 0.66 0.42 -0.64 1.48 8.62 1.27
a1a2_[52,1] -0.06 0.69 -0.12 -1.25 1.02 8.10 1.28
a1a2_[52,2] -0.67 0.88 -0.77 -2.17 0.71 36.22 1.07
a1a2_[52,3] 0.15 1.06 0.16 -1.56 1.84 32.79 1.03
a1a2_[52,4] -0.10 0.87 -0.12 -1.48 1.36 117.55 1.01
a1a2_[53,0] -0.23 0.54 -0.22 -1.04 0.62 33.94 1.01
a1a2_[53,1] -0.01 0.76 -0.05 -1.14 1.39 58.05 1.04
a1a2_[53,2] 0.02 0.76 0.01 -1.19 1.23 34.13 1.08
a1a2_[53,3] 0.37 0.82 0.41 -0.98 1.70 46.34 1.00
a1a2_[53,4] -0.18 0.98 -0.17 -1.81 1.35 41.95 1.04
a1a2_[54,0] -0.12 0.88 -0.09 -1.48 1.20 1.33 2.07
a1a2_[54,1] -0.42 0.94 -0.45 -2.04 1.01 1.33 2.13
a1a2_[54,2] 0.16 0.81 0.01 -1.12 1.54 3.26 1.31
a1a2_[54,3] -0.18 0.99 -0.21 -1.79 1.40 89.27 1.02
a1a2_[54,4] 0.19 0.98 0.17 -1.47 1.79 49.91 1.01
a1a2_[55,0] 0.51 0.72 0.42 -0.49 1.69 7.50 1.64
a1a2_[55,1] -0.28 0.73 -0.32 -1.44 1.01 26.34 1.16
a1a2_[55,2] 0.84 0.83 0.89 -0.53 2.19 20.67 1.09
a1a2_[55,3] -0.65 0.79 -0.69 -1.96 0.68 81.72 1.03
a1a2_[55,4] 0.48 0.98 0.52 -1.11 2.05 49.76 1.10
a1a2_[56,0] -0.30 0.74 -0.30 -1.50 0.81 43.39 1.04
a1a2_[56,1] 0.29 0.64 0.33 -0.81 1.40 55.18 1.03
a1a2_[56,2] 0.04 0.83 0.02 -1.48 1.22 33.17 1.04
a1a2_[56,3] 0.05 0.89 0.08 -1.49 1.50 146.60 1.00
a1a2_[56,4] 0.23 1.04 0.25 -1.43 1.96 22.31 1.07
a1a2_[57,0] -0.87 0.94 -0.90 -2.47 0.66 2.95 1.29
a1a2_[57,1] -0.71 0.97 -0.72 -2.24 0.91 34.02 1.05
a1a2_[57,2] 0.23 0.95 0.30 -1.33 1.67 33.99 1.09
a1a2_[57,3] 0.83 1.09 0.81 -0.96 2.54 5.93 1.17
a1a2_[57,4] 0.58 0.87 0.59 -0.81 2.10 32.81 1.07
a1a2_[58,0] -0.22 0.88 -0.18 -1.69 1.17 21.41 1.08
a1a2_[58,1] -0.24 0.74 -0.28 -1.43 0.96 31.93 1.08
a1a2_[58,2] 0.20 0.79 0.26 -1.32 1.29 20.94 1.09
a1a2_[58,3] 0.01 1.07 -0.04 -1.73 1.76 31.10 1.05
a1a2_[58,4] 0.51 1.09 0.55 -1.23 2.34 29.29 1.03
a1a2_[59,0] 0.37 0.80 0.40 -0.95 1.76 28.85 1.01
a1a2_[59,1] -0.42 0.79 -0.37 -1.80 0.88 28.50 1.01
a1a2_[59,2] -0.14 1.06 -0.15 -1.89 1.51 37.90 1.02
a1a2_[59,3] -0.00 1.04 -0.09 -1.65 1.75 57.79 1.01
a1a2_[59,4] 0.38 0.96 0.38 -1.20 1.88 42.58 1.00
a1a2_sigma 5663.52 706.92 5626.17 4528.59 6695.45 11.99 1.31
a2_[0] -0.82 0.42 -0.85 -1.43 -0.21 1.21 2.38
a2_[1] -0.58 0.42 -0.66 -1.21 -0.00 1.14 2.84
a2_[2] -0.05 0.48 -0.12 -0.74 0.56 1.15 2.79
a2_[3] 0.42 0.54 0.42 -0.37 1.13 1.34 2.15
a2_[4] 0.91 0.65 0.87 -0.20 1.86 1.63 1.90
a2_sigma 57755.30 21271.03 53637.01 28501.13 97354.90 7.48 1.30
nu 3.39 0.57 3.31 2.48 4.21 16.40 1.07
y_sigma_[0,0] 3692.11 1583.84 3431.64 1483.97 6057.65 26.92 1.06
y_sigma_[0,1] 5223.47 5426.80 3435.58 495.04 11204.78 17.56 1.11
y_sigma_[0,2] 27417.62 7001.44 27200.14 16378.19 39048.26 32.73 1.03
y_sigma_[0,3] 12720.17 6705.94 11684.63 3753.20 22565.98 56.50 1.02
y_sigma_[0,4] 9033.63 9125.06 6363.34 33.20 21258.13 61.89 1.06
y_sigma_[1,0] 9199.60 8821.19 6945.98 32.57 20541.87 77.56 1.04
y_sigma_[1,1] 9523.73 4845.89 8426.03 2696.91 16951.14 72.33 1.05
y_sigma_[1,2] 12230.08 5136.71 11135.62 4367.26 20273.10 61.58 1.03
y_sigma_[1,3] 8490.22 8388.87 5984.69 18.19 20139.77 62.46 1.01
y_sigma_[1,4] 12227.34 9866.03 9932.92 335.20 25578.79 20.32 1.14
y_sigma_[2,0] 5454.42 3621.64 4383.49 1140.33 11020.89 10.01 1.15
y_sigma_[2,1] 1774.14 1193.18 1416.63 431.03 3386.84 77.17 1.03
y_sigma_[2,2] 7812.79 7934.60 5569.17 39.36 18256.00 56.45 1.00
y_sigma_[2,3] 8585.89 8662.91 5678.24 56.97 20203.14 243.17 1.03
y_sigma_[2,4] 7978.25 7754.92 5616.59 109.24 17678.99 50.74 1.03
y_sigma_[3,0] 8987.66 7615.81 7049.71 87.47 19217.32 38.37 1.10
y_sigma_[3,1] 4185.83 1370.95 3932.98 2082.45 6239.28 38.25 1.04
y_sigma_[3,2] 13533.52 3720.42 13008.80 7563.39 19011.19 40.64 1.07
y_sigma_[3,3] 9440.96 7389.67 7452.79 412.87 19604.93 96.57 1.03
y_sigma_[3,4] 11947.06 11125.61 9163.99 68.01 24675.93 21.50 1.06
y_sigma_[4,0] 1862.02 1101.34 1590.43 509.31 3148.26 65.87 1.06
y_sigma_[4,1] 5339.08 1808.83 5061.04 2712.80 7780.35 140.14 1.02
y_sigma_[4,2] 23078.71 9393.26 21887.18 9027.61 36456.07 65.19 1.01
y_sigma_[4,3] 10525.46 9448.15 7729.52 84.53 23231.39 142.68 1.01
y_sigma_[4,4] 8656.81 8696.23 6014.74 3.66 20131.23 108.03 1.02
y_sigma_[5,0] 4667.66 5261.05 2860.87 1.46 11963.42 47.24 1.00
y_sigma_[5,1] 1501.62 2861.00 402.76 3.28 4070.04 113.36 1.02
y_sigma_[5,2] 18059.19 8312.07 16363.04 6216.74 29358.30 50.58 1.03
y_sigma_[5,3] 26671.06 12463.64 24402.69 8864.07 44736.02 77.73 1.02
y_sigma_[5,4] 9134.89 9138.17 6459.58 3.09 21270.10 180.29 1.00
y_sigma_[6,0] 20.70 43.89 9.06 0.02 41.03 44.97 1.07
y_sigma_[6,1] 9513.95 4328.21 8667.39 2952.22 14409.85 76.30 1.01
y_sigma_[6,2] 8148.21 8143.45 5514.25 31.71 18849.22 119.93 1.03
y_sigma_[6,3] 23110.04 10437.56 21250.04 7015.85 38711.52 53.83 1.11
y_sigma_[6,4] 8510.42 8478.66 5936.75 29.83 19150.23 290.69 1.00
y_sigma_[7,0] 6671.33 2970.74 6166.84 2425.78 10647.94 74.70 1.02
y_sigma_[7,1] 11597.56 4271.89 10592.45 5076.35 17812.64 73.38 1.01
y_sigma_[7,2] 27569.57 10419.41 25725.60 10511.29 42721.66 78.98 1.01
y_sigma_[7,3] 14666.28 8876.45 12569.28 2216.77 27260.39 39.35 1.08
y_sigma_[7,4] 8535.66 8487.82 5998.77 57.81 19861.79 99.39 1.04
y_sigma_[8,0] 367.70 156.15 341.28 148.14 561.80 17.91 1.11
y_sigma_[8,1] 10335.86 2744.34 9876.51 5825.22 14660.69 20.75 1.07
y_sigma_[8,2] 16636.66 4125.94 16044.70 10359.84 23071.43 104.02 1.06
y_sigma_[8,3] 8394.44 6963.08 6413.44 30.81 17478.76 52.98 1.03
y_sigma_[8,4] 24485.15 6461.99 23525.74 14381.31 34552.14 117.81 1.03
y_sigma_[9,0] 9233.31 5731.31 7715.19 2084.47 15949.00 66.55 1.01
y_sigma_[9,1] 4743.22 3132.90 3887.50 881.21 8867.78 88.98 1.01
y_sigma_[9,2] 5121.72 5318.55 3575.31 54.72 11267.86 99.12 1.03
y_sigma_[9,3] 7034.74 6725.84 5450.81 30.58 15270.97 103.09 1.01
y_sigma_[9,4] 9353.90 9259.91 6438.94 87.67 21470.84 117.86 1.02
y_sigma_[10,0] 6900.04 2467.01 6537.30 2958.27 10309.24 126.90 1.04
y_sigma_[10,1] 4628.23 1592.35 4374.34 2285.43 6958.71 75.67 1.01
y_sigma_[10,2] 12145.91 3552.67 11755.63 6630.56 17505.68 92.67 1.03
y_sigma_[10,3] 8017.86 8180.42 5326.21 23.91 18856.63 166.16 1.00
y_sigma_[10,4] 7055.41 7640.87 4523.39 4.06 17127.88 100.66 1.00
y_sigma_[11,0] 6761.35 6492.73 4622.27 118.65 15180.03 116.06 1.00
y_sigma_[11,1] 12152.82 5064.22 11189.73 4762.16 19532.65 72.96 1.02
y_sigma_[11,2] 16801.98 5666.51 15843.11 7722.44 25182.86 94.40 1.01
y_sigma_[11,3] 23492.92 11883.53 22028.32 5296.30 38790.19 34.59 1.04
y_sigma_[11,4] 10621.04 10103.74 7920.59 46.50 22787.56 103.09 1.02
y_sigma_[12,0] 3436.86 1581.79 3127.60 1299.28 5560.68 63.62 1.07
y_sigma_[12,1] 14674.91 4589.78 13945.35 7982.18 21456.14 62.30 1.03
y_sigma_[12,2] 23937.65 7373.57 23168.34 12149.77 34297.09 43.41 1.06
y_sigma_[12,3] 22230.12 9183.72 21060.21 7927.89 35438.21 43.79 1.02
y_sigma_[12,4] 33102.66 11086.83 31462.23 15017.11 49612.89 70.65 1.07
y_sigma_[13,0] 3164.32 2740.97 2282.85 385.53 6276.21 63.82 1.02
y_sigma_[13,1] 5697.82 1763.30 5451.78 3089.53 8307.85 19.26 1.08
y_sigma_[13,2] 18874.94 7332.88 17604.71 7317.73 29808.00 77.07 1.03
y_sigma_[13,3] 9393.79 8431.19 7075.82 74.83 20506.70 134.60 1.01
y_sigma_[13,4] 8486.23 7792.12 6366.92 59.80 18362.16 135.24 1.05
y_sigma_[14,0] 5788.02 4774.03 4434.20 730.56 11583.59 54.39 1.07
y_sigma_[14,1] 4669.26 4472.30 3250.30 498.08 9745.97 83.63 1.01
y_sigma_[14,2] 13332.02 6537.14 12067.92 4153.03 23367.36 55.75 1.04
y_sigma_[14,3] 8631.47 8677.78 5844.38 71.16 19967.65 171.15 1.01
y_sigma_[14,4] 11840.93 10226.58 9004.05 95.80 26004.90 30.47 1.10
y_sigma_[15,0] 2275.36 1527.92 1860.38 744.34 3824.19 52.66 1.08
y_sigma_[15,1] 3261.23 1235.55 3023.98 1406.73 5031.10 50.13 1.03
y_sigma_[15,2] 7036.78 2591.95 6711.56 2895.59 10391.11 81.79 1.03
y_sigma_[15,3] 7812.77 5467.14 6145.78 1468.75 15440.39 120.28 1.00
y_sigma_[15,4] 10558.36 9296.65 8098.75 0.93 22953.32 65.76 1.07
y_sigma_[16,0] 2431.08 958.44 2244.38 1020.21 3792.59 106.62 1.05
y_sigma_[16,1] 9618.52 2736.04 9393.28 5019.33 13651.47 58.30 1.01
y_sigma_[16,2] 13364.11 4101.55 12876.97 7030.85 19608.74 49.88 1.04
y_sigma_[16,3] 8484.27 8005.96 6031.80 187.62 18647.86 159.30 1.01
y_sigma_[16,4] 8416.87 8606.41 5917.16 5.05 19344.77 51.96 1.06
y_sigma_[17,0] 3840.70 1794.48 3446.44 1329.07 6244.46 64.46 1.05
y_sigma_[17,1] 3588.38 2140.44 3081.63 983.43 6177.57 80.35 1.02
y_sigma_[17,2] 11331.12 5339.84 9964.01 4446.63 18397.68 7.76 1.14
y_sigma_[17,3] 9692.24 9736.09 6361.80 20.96 21867.08 74.91 1.01
y_sigma_[17,4] 7735.70 8763.85 4866.55 0.46 18493.48 65.22 1.03
y_sigma_[18,0] 6861.66 2462.21 6338.95 3446.00 10876.36 54.45 1.04
y_sigma_[18,1] 19156.13 10063.08 16798.31 4208.46 33720.82 27.66 1.08
y_sigma_[18,2] 31049.89 7994.10 29610.16 18825.79 44959.96 50.00 1.04
y_sigma_[18,3] 24276.05 12006.89 22449.93 5672.40 41677.76 52.23 1.08
y_sigma_[18,4] 8409.55 8464.33 5863.87 196.43 18387.05 44.22 1.02
y_sigma_[19,0] 4815.08 2759.02 4138.77 1264.90 8800.88 92.88 1.01
y_sigma_[19,1] 12286.65 3709.74 11679.53 6395.91 17994.84 48.81 1.06
y_sigma_[19,2] 20497.02 8686.09 19165.80 7021.51 33632.89 37.07 1.14
y_sigma_[19,3] 9325.72 9419.97 6290.05 173.08 21453.07 93.56 1.01
y_sigma_[19,4] 8316.78 8019.20 5864.11 24.10 20030.00 78.36 1.03
y_sigma_[20,0] 3915.02 1658.79 3641.77 1385.48 6548.66 11.31 1.39
y_sigma_[20,1] 5839.48 1534.45 5656.78 3567.38 8306.89 97.62 1.01
y_sigma_[20,2] 13389.39 3574.33 13198.35 7151.04 18625.78 53.47 1.05
y_sigma_[20,3] 17836.17 6934.80 16768.68 6819.90 28287.61 102.38 1.01
y_sigma_[20,4] 10632.39 9202.39 8097.71 85.22 24644.18 57.64 1.09
y_sigma_[21,0] 3435.80 2463.68 2681.30 772.01 6319.09 55.89 1.04
y_sigma_[21,1] 6241.57 3459.24 5374.06 1796.46 11171.54 94.92 1.01
y_sigma_[21,2] 9737.48 7905.02 8131.77 48.26 19823.98 54.18 1.04
y_sigma_[21,3] 7767.24 8051.67 4960.56 9.92 18935.72 60.15 1.00
y_sigma_[21,4] 8955.18 8037.18 6687.01 299.56 19554.94 100.31 1.02
y_sigma_[22,0] 6902.86 6779.56 4598.22 137.09 16263.49 44.01 1.05
y_sigma_[22,1] 7205.06 2216.80 6825.62 4099.23 10688.62 30.44 1.12
y_sigma_[22,2] 8301.50 8812.56 5441.79 23.67 19310.13 162.33 1.00
y_sigma_[22,3] 8573.86 7422.92 6444.96 152.70 18539.14 108.15 1.03
y_sigma_[22,4] 8190.83 8253.02 5644.93 0.79 19735.53 66.41 1.01
y_sigma_[23,0] 3122.08 3566.93 1918.35 191.25 7097.54 54.74 1.03
y_sigma_[23,1] 9207.37 4401.71 8169.20 3037.42 15540.52 88.28 1.02
y_sigma_[23,2] 17718.13 7135.07 16497.71 6224.98 28148.51 75.05 1.03
y_sigma_[23,3] 4702.50 4718.70 3239.38 31.67 10193.10 40.13 1.08
y_sigma_[23,4] 9270.27 8731.11 6689.67 6.15 20486.74 81.96 1.00
y_sigma_[24,0] 6422.50 3854.59 5543.26 1683.70 11510.59 66.58 1.05
y_sigma_[24,1] 7880.37 3791.52 7026.28 3220.99 12742.11 63.34 1.00
y_sigma_[24,2] 23660.09 7130.23 22565.78 12223.50 34222.37 108.20 1.01
y_sigma_[24,3] 10011.60 9459.18 7421.83 180.36 22434.57 54.14 1.01
y_sigma_[24,4] 11067.25 10954.07 7367.56 224.00 27242.20 33.80 1.04
y_sigma_[25,0] 5752.77 3030.15 4961.39 1681.63 10425.42 32.42 1.03
y_sigma_[25,1] 6400.69 6172.76 4577.65 56.25 14627.93 89.21 1.00
y_sigma_[25,2] 12649.78 5034.34 11880.91 4811.31 19835.72 75.18 1.01
y_sigma_[25,3] 7618.69 7737.17 4932.62 114.25 17914.65 34.81 1.02
y_sigma_[25,4] 9288.70 7209.73 7468.76 88.96 19655.63 42.36 1.03
y_sigma_[26,0] 2454.96 1640.72 1957.37 479.81 4582.01 80.49 1.01
y_sigma_[26,1] 4037.50 3274.38 2961.37 680.27 8462.18 42.83 1.03
y_sigma_[26,2] 19458.49 4663.36 18725.62 11627.07 26424.62 82.01 1.04
y_sigma_[26,3] 20604.34 10779.27 18325.93 5372.62 35158.14 104.90 1.00
y_sigma_[26,4] 7500.60 7413.80 5302.02 227.12 16456.55 100.28 1.02
y_sigma_[27,0] 8562.87 8883.28 5630.95 14.40 19175.03 56.33 1.04
y_sigma_[27,1] 5620.58 6407.17 3326.03 18.79 13516.54 25.44 1.10
y_sigma_[27,2] 11494.27 4101.69 10778.84 5303.25 17712.81 66.80 1.01
y_sigma_[27,3] 18546.88 8496.39 17115.79 6039.72 31350.38 38.61 1.06
y_sigma_[27,4] 12135.45 10178.12 9942.24 82.53 25721.43 19.62 1.10
y_sigma_[28,0] 3215.47 1037.03 3042.95 1628.70 4952.58 74.28 1.03
y_sigma_[28,1] 11125.41 3058.72 10587.65 6770.57 16074.23 36.19 1.11
y_sigma_[28,2] 13903.02 3735.71 13278.36 7786.13 19381.39 71.84 1.02
y_sigma_[28,3] 10883.81 4537.60 10088.32 4550.36 17625.88 86.93 1.01
y_sigma_[28,4] 10481.38 8906.02 8147.99 17.49 22061.70 39.50 1.08
y_sigma_[29,0] 8997.95 5377.51 7935.66 1449.63 16000.96 56.00 1.02
y_sigma_[29,1] 10871.67 4186.85 9891.40 5143.26 16511.35 38.55 1.04
y_sigma_[29,2] 12871.23 4916.49 12104.03 5657.25 19747.03 102.85 1.00
y_sigma_[29,3] 4138.96 4771.83 2488.07 0.49 10165.85 54.01 1.03
y_sigma_[29,4] 9066.13 8567.90 6569.18 55.65 19742.66 116.83 1.00
y_sigma_[30,0] 1926.31 955.89 1741.78 442.00 3233.10 61.60 1.03
y_sigma_[30,1] 7402.24 3256.42 6772.19 2533.04 11864.12 97.48 1.01
y_sigma_[30,2] 9846.72 4164.14 8621.87 4478.63 16733.28 21.47 1.03
y_sigma_[30,3] 8862.33 8546.28 6358.46 85.22 20051.94 41.89 1.03
y_sigma_[30,4] 9360.61 8756.44 7341.23 26.04 20261.08 29.47 1.14
y_sigma_[31,0] 6477.90 2744.75 5991.45 2330.67 10183.54 85.13 1.01
y_sigma_[31,1] 6279.91 5059.87 5278.52 1813.03 10226.70 69.95 1.02
y_sigma_[31,2] 9620.06 4013.28 8703.62 3541.39 15427.73 45.56 1.05
y_sigma_[31,3] 7987.78 8748.00 4985.17 144.41 19229.44 121.70 1.03
y_sigma_[31,4] 7219.78 7951.57 4613.36 16.66 17017.02 56.88 1.04
y_sigma_[32,0] 7556.30 8376.37 5085.96 81.92 16958.29 63.25 1.02
y_sigma_[32,1] 1126.78 457.87 1016.46 507.30 1821.20 36.04 1.01
y_sigma_[32,2] 13116.91 3282.40 12844.95 7722.36 17903.67 66.84 1.00
y_sigma_[32,3] 22744.73 5502.56 21674.91 14977.23 31793.94 30.09 1.03
y_sigma_[32,4] 15510.77 9685.60 13530.78 1726.51 29230.54 20.45 1.04
y_sigma_[33,0] 1685.37 2154.60 1062.53 160.49 3424.43 85.11 1.02
y_sigma_[33,1] 3158.48 1141.76 2946.63 1434.72 4838.43 99.75 1.01
y_sigma_[33,2] 7194.25 7717.70 4636.85 4.55 17065.69 44.33 1.03
y_sigma_[33,3] 10061.82 9409.20 7346.58 22.55 22938.77 27.09 1.12
y_sigma_[33,4] 8457.78 10964.38 4192.14 15.59 21372.55 14.96 1.18
y_sigma_[34,0] 5443.30 6056.31 3691.11 4.49 13098.07 47.59 1.11
y_sigma_[34,1] 6260.72 5490.19 4491.77 912.15 12910.34 75.87 1.01
y_sigma_[34,2] 20148.04 7316.62 18980.41 8418.89 30992.38 47.61 1.03
y_sigma_[34,3] 8229.57 8101.86 5744.84 18.42 18982.42 102.44 1.00
y_sigma_[34,4] 8838.00 9113.49 5977.52 9.70 21047.79 51.19 1.02
y_sigma_[35,0] 3328.30 2842.26 2604.05 688.79 5568.86 49.36 1.02
y_sigma_[35,1] 11536.51 4181.55 10576.69 6098.22 18283.38 64.76 1.02
y_sigma_[35,2] 12812.10 2493.39 12683.71 8719.80 16667.23 26.85 1.05
y_sigma_[35,3] 24872.31 11823.53 22920.88 6963.28 42499.86 24.47 1.14
y_sigma_[35,4] 10182.51 7869.71 8224.34 254.99 21092.58 14.78 1.15
y_sigma_[36,0] 5680.84 2479.54 5197.25 2021.52 8766.09 35.61 1.05
y_sigma_[36,1] 2965.51 3849.36 1768.91 133.21 6219.82 46.15 1.04
y_sigma_[36,2] 7498.59 8045.47 4762.85 30.16 18214.39 42.83 1.09
y_sigma_[36,3] 18323.98 7008.38 17561.41 7550.80 29506.48 35.87 1.01
y_sigma_[36,4] 6766.81 6846.59 4299.24 232.03 15621.41 7.99 1.11
y_sigma_[37,0] 1098.60 1010.58 749.36 169.60 2274.54 104.08 1.01
y_sigma_[37,1] 10435.61 3496.21 9980.66 5242.65 16267.31 92.36 1.03
y_sigma_[37,2] 20700.96 10536.92 18699.03 5119.23 35774.14 74.28 1.01
y_sigma_[37,3] 15072.24 6528.02 13761.87 5162.79 24015.08 125.35 1.00
y_sigma_[37,4] 7353.66 8065.75 4687.77 37.09 16934.27 52.39 1.04
y_sigma_[38,0] 5609.31 5486.84 3643.96 184.01 12826.87 49.43 1.03
y_sigma_[38,1] 6374.89 3014.32 5777.02 1790.80 10239.29 62.80 1.00
y_sigma_[38,2] 9979.93 5082.81 9109.06 2506.06 16894.67 71.65 1.03
y_sigma_[38,3] 8290.39 7633.41 6284.33 97.01 17569.22 96.97 1.02
y_sigma_[38,4] 17668.17 9152.81 15714.73 5190.57 29924.15 99.27 1.01
y_sigma_[39,0] 6299.47 5540.42 4717.39 62.60 13456.99 97.40 1.00
y_sigma_[39,1] 10960.03 3696.01 10504.41 5259.62 17103.21 55.38 1.01
y_sigma_[39,2] 11039.37 1951.61 10754.49 7871.45 14007.72 80.71 1.01
y_sigma_[39,3] 14167.59 7017.93 12658.96 3939.81 23738.58 68.24 1.01
y_sigma_[39,4] 15921.33 7835.64 14137.22 4175.27 26542.35 31.61 1.12
y_sigma_[40,0] 8132.28 7973.97 4736.41 102.50 19521.64 26.36 1.08
y_sigma_[40,1] 12997.72 9538.37 11150.87 17.13 25170.04 38.54 1.04
y_sigma_[40,2] 15607.93 4373.52 14938.34 9263.62 22155.08 67.28 1.04
y_sigma_[40,3] 12186.43 6210.84 10805.78 3351.81 20680.25 52.63 1.04
y_sigma_[40,4] 8881.32 9259.26 5857.58 38.86 19923.94 70.00 1.01
y_sigma_[41,0] 6447.12 6990.87 4319.44 21.32 14478.31 73.46 1.04
y_sigma_[41,1] 5537.27 3026.71 4768.67 1807.90 9487.28 108.90 1.01
y_sigma_[41,2] 9065.17 4996.81 7906.42 2464.78 15913.68 83.80 1.02
y_sigma_[41,3] 8495.77 9232.75 5496.40 119.44 19064.64 63.92 1.01
y_sigma_[41,4] 8077.07 7417.05 5796.17 167.12 18372.45 77.65 1.01
y_sigma_[42,0] 8802.18 8737.43 6002.58 41.40 20587.37 24.84 1.07
y_sigma_[42,1] 6520.28 5772.23 4460.50 520.25 15230.41 20.32 1.09
y_sigma_[42,2] 13877.18 4950.22 13037.08 6058.23 21311.54 26.51 1.11
y_sigma_[42,3] 8504.50 9301.99 5873.18 4.65 20044.58 38.91 1.02
y_sigma_[42,4] 19353.99 10456.39 17575.91 4688.23 33736.94 43.67 1.01
y_sigma_[43,0] 4981.46 2406.61 4336.02 1810.46 8411.66 72.87 1.03
y_sigma_[43,1] 5676.79 3573.81 4598.22 1179.46 10972.59 73.22 1.07
y_sigma_[43,2] 15467.04 7524.53 14314.28 4848.92 25461.63 49.80 1.05
y_sigma_[43,3] 20647.56 8854.63 18922.52 7971.02 34621.84 49.76 1.03
y_sigma_[43,4] 9495.00 8459.40 6884.66 423.95 21610.96 48.50 1.05
y_sigma_[44,0] 1173.30 1228.31 744.68 93.73 2588.30 138.13 1.01
y_sigma_[44,1] 4939.18 3981.13 3866.67 648.23 9208.06 36.36 1.08
y_sigma_[44,2] 5229.02 2578.32 4625.66 1816.28 8824.67 64.06 1.01
y_sigma_[44,3] 9176.62 9080.60 6371.41 0.45 21844.30 150.08 1.00
y_sigma_[44,4] 8713.70 9187.78 5754.35 29.97 20929.41 66.56 1.09
y_sigma_[45,0] 1836.65 674.61 1709.58 808.02 2844.17 74.55 1.04
y_sigma_[45,1] 3636.61 1702.46 3221.67 1546.50 5683.14 90.65 1.04
y_sigma_[45,2] 22751.82 4764.29 22473.09 14799.45 30058.58 73.38 1.01
y_sigma_[45,3] 9074.09 8904.83 6640.86 7.01 20506.03 44.82 1.03
y_sigma_[45,4] 18939.57 9870.35 17324.71 3795.22 32363.13 32.59 1.05
y_sigma_[46,0] 9092.56 7662.83 7354.77 1692.80 15912.68 75.14 1.01
y_sigma_[46,1] 7308.38 4923.35 5851.79 1471.23 14413.70 90.43 1.00
y_sigma_[46,2] 20193.08 7110.17 18761.25 10060.92 31251.78 33.86 1.02
y_sigma_[46,3] 19159.85 9578.77 17496.89 5130.83 32226.94 51.74 1.06
y_sigma_[46,4] 9978.43 9344.00 7134.10 104.05 22992.89 45.72 1.02
y_sigma_[47,0] 2893.46 3449.63 1708.58 177.99 6553.23 77.26 1.02
y_sigma_[47,1] 8813.06 3124.52 8281.47 4156.45 13719.72 66.53 1.01
y_sigma_[47,2] 19390.01 7100.18 18664.52 5379.62 28416.99 51.01 1.01
y_sigma_[47,3] 24093.78 9341.58 22491.57 9578.09 38556.00 118.11 1.02
y_sigma_[47,4] 15244.72 10267.78 12678.25 1796.49 29054.56 64.34 1.05
y_sigma_[48,0] 5441.84 2949.67 4839.49 1481.94 9386.97 28.60 1.08
y_sigma_[48,1] 8257.44 3193.70 7706.88 3650.11 12732.91 67.76 1.01
y_sigma_[48,2] 22228.69 5227.82 21606.36 13885.03 30149.68 106.58 1.01
y_sigma_[48,3] 32641.35 10588.35 31059.29 17512.36 49846.23 79.25 1.03
y_sigma_[48,4] 30973.89 10488.36 29884.53 14480.19 46032.00 60.36 1.08
y_sigma_[49,0] 1363.17 1113.44 1046.84 294.53 2392.78 82.60 1.03
y_sigma_[49,1] 2902.18 1874.36 2526.94 814.52 4818.65 37.87 1.07
y_sigma_[49,2] 20912.73 8955.00 19123.34 8236.25 32991.40 83.59 1.04
y_sigma_[49,3] 9216.19 9929.89 6240.13 40.82 20172.66 42.20 1.05
y_sigma_[49,4] 7111.15 7414.21 4634.78 69.91 16964.63 64.27 1.01
y_sigma_[50,0] 6373.55 4360.30 5143.06 1308.02 11803.46 77.57 1.03
y_sigma_[50,1] 6597.82 3280.21 5805.11 2334.98 10618.40 40.64 1.02
y_sigma_[50,2] 2785.36 2793.30 1851.12 145.85 6168.72 81.17 1.03
y_sigma_[50,3] 10183.49 10256.76 6629.81 46.38 24008.62 57.26 1.05
y_sigma_[50,4] 9348.40 8986.48 6790.05 98.11 20324.91 166.78 1.01
y_sigma_[51,0] 7216.83 4292.32 6171.27 1471.57 13609.52 37.96 1.08
y_sigma_[51,1] 5380.84 1903.26 5011.71 2601.93 8222.73 95.40 1.03
y_sigma_[51,2] 4802.57 4937.65 3119.53 29.11 10812.22 4.46 1.18
y_sigma_[51,3] 16215.79 8474.13 14364.94 3437.05 28277.63 54.40 1.04
y_sigma_[51,4] 9847.80 8782.80 7370.19 53.33 21257.10 56.09 1.01
y_sigma_[52,0] 2767.06 3114.46 1796.53 320.43 5454.35 40.44 1.06
y_sigma_[52,1] 4559.30 2956.74 3752.02 912.94 8633.07 64.13 1.02
y_sigma_[52,2] 7247.59 6391.69 5646.92 75.63 15417.58 5.82 1.14
y_sigma_[52,3] 8449.63 9381.23 5121.59 31.98 20902.52 40.54 1.05
y_sigma_[52,4] 8246.31 7873.88 6239.58 38.54 17877.54 57.89 1.06
y_sigma_[53,0] 1217.02 688.51 1043.20 324.03 2181.89 47.06 1.00
y_sigma_[53,1] 10286.39 3722.67 9515.13 4730.41 15463.80 50.16 1.08
y_sigma_[53,2] 10401.27 4306.26 9806.89 3793.90 16935.61 46.12 1.03
y_sigma_[53,3] 14138.73 7752.16 12575.54 2943.00 25094.66 71.32 1.03
y_sigma_[53,4] 6596.79 6403.34 4757.77 11.22 14723.91 44.61 1.05
y_sigma_[54,0] 3294.77 2029.67 2764.02 927.00 5786.19 63.95 1.04
y_sigma_[54,1] 5131.13 2179.05 4599.31 2031.08 8446.49 70.80 1.01
y_sigma_[54,2] 11811.54 4863.37 10896.58 4943.99 19144.30 47.77 1.04
y_sigma_[54,3] 10341.78 8888.30 8036.14 19.00 22017.20 115.52 1.02
y_sigma_[54,4] 9326.64 9349.60 7034.74 9.18 20682.70 69.76 1.03
y_sigma_[55,0] 7409.25 2071.53 7119.12 4232.42 10605.27 67.00 1.02
y_sigma_[55,1] 11777.19 2829.69 11406.14 7384.88 16365.46 55.37 1.01
y_sigma_[55,2] 14713.70 4915.75 13887.86 7546.79 22115.10 75.99 1.04
y_sigma_[55,3] 15521.93 7344.11 14188.40 4974.69 26429.97 76.79 1.05
y_sigma_[55,4] 32537.72 11880.33 30671.22 15125.72 51151.27 91.09 1.00
y_sigma_[56,0] 3964.00 2465.55 3312.97 944.54 7527.71 33.85 1.12
y_sigma_[56,1] 6292.34 3191.67 5607.84 1625.49 10449.93 52.15 1.04
y_sigma_[56,2] 11964.05 4191.73 11202.61 5877.62 18610.50 85.90 1.00
y_sigma_[56,3] 11124.34 9373.77 8592.03 23.77 23328.39 69.30 1.03
y_sigma_[56,4] 30306.45 13702.30 28307.04 7191.21 48937.52 29.50 1.04
y_sigma_[57,0] 5462.17 2523.22 4926.23 1771.61 9071.98 100.08 1.00
y_sigma_[57,1] 10215.44 8143.76 8395.39 151.72 21370.68 7.89 1.15
y_sigma_[57,2] 9401.41 9528.09 6208.61 178.80 22028.50 145.70 1.01
y_sigma_[57,3] 12953.19 9680.29 11079.81 150.14 25983.76 4.73 1.18
y_sigma_[57,4] 6741.20 6785.67 4849.33 51.47 15231.93 86.99 1.04
y_sigma_[58,0] 3917.38 2276.93 3312.26 856.38 7057.98 50.11 1.05
y_sigma_[58,1] 8535.47 4995.27 7382.43 1620.75 15497.14 82.00 1.01
y_sigma_[58,2] 15152.24 5188.23 14269.95 6652.56 23139.57 139.60 1.02
y_sigma_[58,3] 8042.70 8178.67 5785.69 7.38 18905.61 47.50 1.05
y_sigma_[58,4] 11325.90 7752.78 10113.74 132.14 21903.02 46.20 1.01
y_sigma_[59,0] 2479.36 1914.81 1965.76 623.48 4503.26 94.23 1.02
y_sigma_[59,1] 3748.13 1139.36 3569.38 1976.74 5403.22 71.04 1.03
y_sigma_[59,2] 8627.24 8719.10 5966.94 18.21 19696.33 5.98 1.14
y_sigma_[59,3] 8564.31 8864.23 5843.12 25.91 19562.18 103.61 1.01
y_sigma_[59,4] 7048.13 7530.90 4240.22 120.05 15623.20 23.34 1.11
Number of divergences: 0
idata_het = az.from_numpyro(
mcmc,
coords=dict(org=salary_df['Org'].cat.categories.values,
pos=salary_df['Pos'].cat.categories.values),
dims=dict(b1=['org'],
b2=['pos'],
b1b2=['org', 'pos'],
y_sigma=['org', 'pos']),
)
az.plot_trace(idata_het, ['b1', 'b2', 'b1b2', 'y_sigma'])
plt.tight_layout()
fig, axes = plt.subplots(
nrows=2, ncols=2,
figsize=(10, 6),
sharey=True)
n_curves = 20
for org, ax in zip(departments, axes.flatten()):
# Plot data.
df = salary_df[salary_df['Org'] == org]
sns.stripplot(x='Pos', y='Salary', data=df, ax=ax)
ax.set_title(f'{org}\'s Salary with Pred. Post. Distrib.')
# Plot posterior distribution.
posterior = idata_het.posterior
b0 = posterior['b0'].values.flatten()
b1 = posterior['b1'].sel(org=org).values.flatten()
nu = posterior['nu'].values.flatten()
curve_indices = np.random.choice(
posterior.draw.size * posterior.chain.size, n_curves, replace=False)
for pos_i, pos in enumerate(salary_df['Pos'].cat.categories):
b2 = posterior['b2'].sel(pos=pos).values.flatten()
b1b2 = posterior['b1b2'].sel(org=org, pos=pos).values.flatten()
y_sigma = posterior['y_sigma'].sel(org=org, pos=pos).values.flatten()
mean = b0 + b1 + b2 + b1b2
for idx in curve_indices:
rv = t(nu[idx], mean[idx], y_sigma[idx])
yrange = np.linspace(rv.ppf(0.01), rv.ppf(0.99), 1000)
xpdf = rv.pdf(yrange)
# Scale xpdf
xpdf = xpdf * 0.75 / np.max(xpdf)
# Plot pdf curve.
ax.plot(pos_i - xpdf, yrange, c='b', alpha=.1)
ax.set_ylim(0, 400000)
fig.tight_layout()
az.plot_posterior(idata_het, ['nu', 'y_sigma'])
plt.tight_layout()
/opt/hostedtoolcache/Python/3.10.11/x64/lib/python3.10/site-packages/arviz/plots/plot_utils.py:271: UserWarning: rcParams['plot.max_subplots'] (40) is smaller than the number of variables to plot (301) in plot_posterior, generating only 40 plots warnings.warn(
Split-plot Design¶
agri_df = pd.read_csv('datasets/SplitPlotAgriData.csv')
agri_df['Field'] = agri_df['Field'].astype('category')
agri_df['Till'] = agri_df['Till'].astype('category')
agri_df['Fert'] = agri_df['Fert'].astype('category')
agri_df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 99 entries, 0 to 98 Data columns (total 4 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 Field 99 non-null category 1 Till 99 non-null category 2 Fert 99 non-null category 3 Yield 99 non-null int64 dtypes: category(3), int64(1) memory usage: 2.8 KB
fig, axes = plt.subplots(ncols=3, sharey=True)
for till, ax in zip(agri_df['Till'].cat.categories, axes):
df = agri_df[agri_df['Till'] == till]
for field in df['Field'].cat.categories:
df_ = df[df['Field'] == field]
sns.lineplot(x='Fert', y='Yield', data=df_, ax=ax)
ax.set_title(f'{till} Tilling')
ax.set_xlim(-0.5, 2.5)
fig.tight_layout()
