Synthetic control with pymc models#
import arviz as az
import causalpy as cp
%load_ext autoreload
%autoreload 2
%config InlineBackend.figure_format = 'retina'
seed = 42
Load data#
df = cp.load_data("sc")
treatment_time = 70
Considerations#
Donor pool selection#
Before fitting, it is good practice to inspect pairwise correlations among units in the pre-treatment period. Negatively correlated donors should be excluded to avoid interpolation bias [Abadie et al., 2010, Abadie, 2021].
pre = df.loc[:treatment_time]
corr, ax = cp.plot_correlations(pre, columns=["a", "b", "c", "d", "e", "f", "g"])
ax.set(title="Pre-treatment correlations")
[Text(0.5, 1.0, 'Pre-treatment correlations')]
All control units are positively correlated with the treated unit (actual), so no donor pool curation is needed for this dataset. In practice, you would exclude any controls with negative or near-zero correlations.
Convex Hull Assumption#
The synthetic control method uses non-negative weights that sum to one. This means the synthetic control is a convex combination of the control units—it can only produce values within the range spanned by the controls at each time point.
Note
For the method to work well, the treated unit’s pre-intervention trajectory should lie within the “envelope” of the control units. If all controls are consistently above or below the treated unit, the method cannot construct an accurate counterfactual.
CausalPy automatically checks this assumption when you create a SyntheticControl object and will issue a warning if violated. See the Convex hull condition glossary entry and Abadie et al. [2010] for more details. The Augmented Synthetic Control Method [Ben-Michael et al., 2021] can handle cases where this assumption is violated.
Observation noise prior#
The default WeightedSumFitter places a \(\mathrm{HalfNormal}(1)\) prior on the observation noise \(\sigma\). This prior assumes the data is approximately on unit scale. If your outcome variable has values much larger than 1 (e.g., daily revenue in the thousands), the prior will likely severely constrain \(\sigma\), producing confidence intervals that are much too narrow.
By default, SyntheticControl automatically rescales this prior to match the scale of the treated-unit data (auto_scale_sigma=True). If you need the original HalfNormal(1) default, pass auto_scale_sigma=False. You can also specify a fully custom prior via the WeightedSumFitter priors parameter.
Run the analysis#
Note
The random_seed keyword argument for the PyMC sampler is not necessary. We use it here so that the results are reproducible.
df.head()
| a | b | c | d | e | f | g | counterfactual | causal effect | actual | |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.806091 | -0.271100 | 0.664254 | 1.705922 | -1.449230 | 0.785439 | -1.234083 | -0.232966 | -0.0 | -0.076404 |
| 1 | 1.442677 | 0.462594 | 0.559940 | 1.862041 | -1.615366 | 0.386238 | -1.798470 | -0.069413 | -0.0 | -0.063946 |
| 2 | 1.916486 | 0.845719 | 0.894046 | 2.061073 | -1.978696 | 0.971803 | -0.490287 | 0.095440 | -0.0 | 0.392813 |
| 3 | 2.001511 | 1.067162 | 0.288606 | 1.934534 | -2.093951 | 1.889334 | -0.478545 | 0.261716 | -0.0 | 0.133106 |
| 4 | 2.662849 | 1.243252 | 0.966345 | 2.482698 | -1.407598 | 2.184504 | -0.434592 | 0.429432 | -0.0 | 0.293294 |
result = cp.SyntheticControl(
df,
treatment_time,
control_units=["a", "b", "c", "d", "e", "f", "g"],
treated_units=["actual"],
model=cp.pymc_models.WeightedSumFitter(
sample_kwargs={"target_accept": 0.95, "random_seed": seed}
),
)
Show code cell output
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [beta, y_hat_sigma]
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Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 453 0 0.018 127 124.53 0:00:03 0:00:13
draws/s
━╸━━━━━ 517 0 0.014 63 142.09 0:00:03 0:00:11
draws/s
━╸━━━━━ 479 0 0.020 31 131.82 0:00:03 0:00:12
draws/s
━╸━━━━━ 518 0 0.021 31 142.78 0:00:03 0:00:11
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 472 0 0.017 63 125.91 0:00:03 0:00:13
draws/s
━╸━━━━━ 530 0 0.017 255 141.37 0:00:03 0:00:11
draws/s
━╸━━━━━ 491 0 0.021 159 131.10 0:00:03 0:00:12
draws/s
━╸━━━━━ 531 0 0.023 63 142.11 0:00:03 0:00:11
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 485 0 0.017 119 125.56 0:00:03 0:00:13
draws/s
━╸━━━━━ 544 0 0.019 191 140.86 0:00:03 0:00:11
draws/s
━╸━━━━━ 505 0 0.026 255 130.94 0:00:03 0:00:12
draws/s
━╸━━━━━ 542 0 0.018 31 141.04 0:00:03 0:00:11
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 500 0 0.019 127 126.18 0:00:03 0:00:12
draws/s
━╸━━━━━ 563 0 0.016 127 141.76 0:00:03 0:00:11
draws/s
━╸━━━━━ 515 0 0.019 127 129.85 0:00:03 0:00:12
draws/s
━╸━━━━━ 553 0 0.017 255 139.52 0:00:03 0:00:11
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 514 0 0.026 63 125.85 0:00:04 0:00:12
draws/s
━━╺━━━━ 576 0 0.020 71 141.20 0:00:04 0:00:11
draws/s
━╸━━━━━ 528 0 0.021 127 129.41 0:00:04 0:00:12
draws/s
━╸━━━━━ 567 0 0.015 127 139.27 0:00:04 0:00:11
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 523 0 0.024 319 124.89 0:00:04 0:00:12
draws/s
━━╺━━━━ 593 0 0.020 127 141.51 0:00:04 0:00:10
draws/s
━╸━━━━━ 539 0 0.024 191 128.89 0:00:04 0:00:12
draws/s
━━╺━━━━ 581 0 0.016 127 138.68 0:00:04 0:00:11
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 538 0 0.032 159 125.08 0:00:04 0:00:12
draws/s
━━╺━━━━ 609 0 0.022 31 141.35 0:00:04 0:00:10
draws/s
━╸━━━━━ 552 0 0.019 159 128.26 0:00:04 0:00:12
draws/s
━━╺━━━━ 597 0 0.017 255 138.76 0:00:04 0:00:11
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 557 0 0.024 31 126.40 0:00:04 0:00:12
draws/s
━━╺━━━━ 626 0 0.025 127 141.79 0:00:04 0:00:10
draws/s
━╸━━━━━ 566 0 0.021 127 128.34 0:00:04 0:00:12
draws/s
━━╺━━━━ 607 0 0.015 255 137.66 0:00:04 0:00:11
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━╸━━━━━ 571 0 0.025 127 126.19 0:00:04 0:00:12
draws/s
━━╺━━━━ 639 0 0.025 191 141.21 0:00:04 0:00:10
draws/s
━━╺━━━━ 582 0 0.024 127 128.74 0:00:04 0:00:12
draws/s
━━╺━━━━ 624 0 0.013 31 138.06 0:00:04 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 585 0 0.024 127 126.10 0:00:04 0:00:12
draws/s
━━╺━━━━ 655 0 0.026 31 141.14 0:00:04 0:00:10
draws/s
━━╺━━━━ 593 0 0.024 319 128.05 0:00:04 0:00:11
draws/s
━━╺━━━━ 634 0 0.017 255 136.97 0:00:04 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 598 0 0.027 127 125.68 0:00:04 0:00:12
draws/s
━━╺━━━━ 670 0 0.030 63 140.87 0:00:04 0:00:10
draws/s
━━╺━━━━ 608 0 0.022 63 128.00 0:00:04 0:00:11
draws/s
━━╺━━━━ 648 0 0.016 255 136.57 0:00:04 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 610 0 0.023 127 125.40 0:00:04 0:00:12
draws/s
━━╺━━━━ 688 0 0.021 63 141.53 0:00:04 0:00:10
draws/s
━━╺━━━━ 623 0 0.017 83 128.27 0:00:04 0:00:11
draws/s
━━╺━━━━ 663 0 0.020 95 136.66 0:00:04 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 623 0 0.016 511 125.50 0:00:04 0:00:11
draws/s
━━╺━━━━ 704 0 0.020 255 141.63 0:00:04 0:00:10
draws/s
━━╺━━━━ 636 0 0.018 159 127.96 0:00:04 0:00:11
draws/s
━━╺━━━━ 673 0 0.019 127 135.73 0:00:04 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 636 0 0.022 255 125.05 0:00:05 0:00:11
draws/s
━━╸━━━━ 722 0 0.022 255 142.32 0:00:05 0:00:09
draws/s
━━╺━━━━ 647 0 0.019 151 127.31 0:00:05 0:00:11
draws/s
━━╺━━━━ 688 0 0.017 127 135.55 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 652 0 0.024 31 125.41 0:00:05 0:00:11
draws/s
━━╸━━━━ 735 0 0.021 255 141.50 0:00:05 0:00:09
draws/s
━━╺━━━━ 664 0 0.021 127 127.78 0:00:05 0:00:11
draws/s
━━╺━━━━ 699 0 0.020 127 134.60 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 666 0 0.025 255 125.34 0:00:05 0:00:11
draws/s
━━╸━━━━ 749 0 0.019 255 141.07 0:00:05 0:00:09
draws/s
━━╺━━━━ 679 0 0.023 127 128.03 0:00:05 0:00:11
draws/s
━━╺━━━━ 711 0 0.019 255 134.01 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 683 0 0.025 63 125.99 0:00:05 0:00:11
draws/s
━━╸━━━━ 758 0 0.017 23 140.20 0:00:05 0:00:09
draws/s
━━╺━━━━ 699 0 0.020 127 128.94 0:00:05 0:00:11
draws/s
━━╸━━━━ 723 0 0.016 255 133.37 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 697 0 0.020 255 125.90 0:00:05 0:00:11
draws/s
━━╸━━━━ 770 0 0.014 255 139.15 0:00:05 0:00:09
draws/s
━━╺━━━━ 709 0 0.020 255 128.17 0:00:05 0:00:11
draws/s
━━╸━━━━ 735 0 0.017 255 132.93 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╺━━━━ 706 0 0.022 127 125.19 0:00:05 0:00:11
draws/s
━━╸━━━━ 779 0 0.018 255 138.09 0:00:05 0:00:09
draws/s
━━╸━━━━ 720 0 0.017 255 127.66 0:00:05 0:00:11
draws/s
━━╸━━━━ 747 0 0.017 255 132.46 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 721 0 0.024 127 125.09 0:00:05 0:00:11
draws/s
━━╸━━━━ 794 0 0.015 127 137.93 0:00:05 0:00:09
draws/s
━━╸━━━━ 734 0 0.021 255 127.63 0:00:05 0:00:10
draws/s
━━╸━━━━ 760 0 0.016 47 132.18 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 736 0 0.020 175 125.40 0:00:05 0:00:11
draws/s
━━╸━━━━ 803 0 0.017 511 136.99 0:00:05 0:00:09
draws/s
━━╸━━━━ 749 0 0.016 255 127.63 0:00:05 0:00:10
draws/s
━━╸━━━━ 769 0 0.016 255 131.01 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 754 0 0.021 79 125.97 0:00:05 0:00:10
draws/s
━━╸━━━━ 810 0 0.019 255 135.48 0:00:05 0:00:09
draws/s
━━╸━━━━ 761 0 0.020 63 127.31 0:00:05 0:00:10
draws/s
━━╸━━━━ 778 0 0.021 95 130.35 0:00:05 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 769 0 0.023 127 126.29 0:00:06 0:00:10
draws/s
━━╸━━━━ 824 0 0.023 127 135.40 0:00:06 0:00:09
draws/s
━━╸━━━━ 776 0 0.021 127 127.42 0:00:06 0:00:10
draws/s
━━╸━━━━ 787 0 0.022 191 129.26 0:00:06 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 785 0 0.019 31 126.48 0:00:06 0:00:10
draws/s
━━╸━━━━ 839 0 0.024 255 135.28 0:00:06 0:00:09
draws/s
━━╸━━━━ 786 0 0.014 255 126.71 0:00:06 0:00:10
draws/s
━━╸━━━━ 799 0 0.024 127 129.05 0:00:06 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 800 0 0.023 63 126.60 0:00:06 0:00:10
draws/s
━━╸━━━━ 855 0 0.027 127 135.34 0:00:06 0:00:09
draws/s
━━╸━━━━ 794 0 0.017 511 125.69 0:00:06 0:00:10
draws/s
━━╸━━━━ 814 0 0.027 127 128.95 0:00:06 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 813 0 0.024 127 126.41 0:00:06 0:00:10
draws/s
━━━╺━━━ 869 0 0.027 255 135.26 0:00:06 0:00:09
draws/s
━━╸━━━━ 806 0 0.018 63 125.41 0:00:06 0:00:10
draws/s
━━╸━━━━ 826 0 0.025 63 128.56 0:00:06 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 827 0 0.016 255 126.69 0:00:06 0:00:10
draws/s
━━━╺━━━ 881 0 0.021 63 134.94 0:00:06 0:00:09
draws/s
━━╸━━━━ 815 0 0.021 255 124.86 0:00:06 0:00:10
draws/s
━━╸━━━━ 840 0 0.018 255 128.55 0:00:06 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 837 0 0.017 127 125.88 0:00:06 0:00:10
draws/s
━━━╺━━━ 896 0 0.021 255 134.76 0:00:06 0:00:09
draws/s
━━╸━━━━ 826 0 0.022 143 124.33 0:00:06 0:00:10
draws/s
━━╸━━━━ 848 0 0.020 255 127.64 0:00:06 0:00:10
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━╸━━━━ 848 0 0.017 167 125.70 0:00:06 0:00:10
draws/s
━━━╺━━━ 907 0 0.024 223 134.20 0:00:06 0:00:09
draws/s
━━╸━━━━ 840 0 0.021 127 124.39 0:00:06 0:00:10
draws/s
━━━╺━━━ 862 0 0.019 255 127.73 0:00:06 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 858 0 0.019 83 124.84 0:00:06 0:00:10
draws/s
━━━╺━━━ 914 0 0.022 31 133.11 0:00:06 0:00:09
draws/s
━━╸━━━━ 848 0 0.020 255 123.45 0:00:06 0:00:10
draws/s
━━━╺━━━ 870 0 0.013 127 126.72 0:00:06 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 871 0 0.016 255 124.72 0:00:06 0:00:10
draws/s
━━━╺━━━ 926 0 0.024 127 132.67 0:00:06 0:00:09
draws/s
━━╸━━━━ 857 0 0.023 255 122.71 0:00:06 0:00:10
draws/s
━━━╺━━━ 878 0 0.015 127 125.75 0:00:06 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 885 0 0.017 127 124.68 0:00:07 0:00:09
draws/s
━━━╺━━━ 939 0 0.026 255 132.32 0:00:07 0:00:09
draws/s
━━━╺━━━ 874 0 0.021 255 123.33 0:00:07 0:00:10
draws/s
━━━╺━━━ 884 0 0.015 383 124.68 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 898 0 0.019 63 124.71 0:00:07 0:00:09
draws/s
━━━╺━━━ 957 0 0.024 127 132.80 0:00:07 0:00:08
draws/s
━━━╺━━━ 889 0 0.021 127 123.36 0:00:07 0:00:10
draws/s
━━━╺━━━ 893 0 0.019 319 124.07 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 909 0 0.018 255 124.21 0:00:07 0:00:09
draws/s
━━━╺━━━ 970 0 0.025 127 132.55 0:00:07 0:00:08
draws/s
━━━╺━━━ 902 0 0.025 255 123.29 0:00:07 0:00:09
draws/s
━━━╺━━━ 903 0 0.019 255 123.54 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 919 0 0.015 63 123.76 0:00:07 0:00:09
draws/s
━━━╺━━━ 984 0 0.023 127 132.49 0:00:07 0:00:08
draws/s
━━━╺━━━ 917 0 0.028 31 123.53 0:00:07 0:00:09
draws/s
━━━╺━━━ 914 0 0.019 63 123.19 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 935 0 0.019 255 123.90 0:00:07 0:00:09
draws/s
━━━╺━━━ 993 0 0.025 255 131.76 0:00:07 0:00:08
draws/s
━━━╺━━━ 937 0 0.026 127 124.23 0:00:07 0:00:09
draws/s
━━━╺━━━ 931 0 0.023 127 123.60 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 946 0 0.020 255 123.66 0:00:07 0:00:09
draws/s
━━━╸━━━ 1004 0 0.027 255 131.31 0:00:07 0:00:08
draws/s
━━━╺━━━ 955 0 0.028 63 124.91 0:00:07 0:00:09
draws/s
━━━╺━━━ 943 0 0.020 255 123.36 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 960 0 0.021 191 123.75 0:00:07 0:00:09
draws/s
━━━╸━━━ 1015 0 0.027 255 130.89 0:00:07 0:00:08
draws/s
━━━╺━━━ 969 0 0.026 63 125.12 0:00:07 0:00:09
draws/s
━━━╺━━━ 955 0 0.024 255 123.29 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 973 0 0.020 127 123.73 0:00:07 0:00:09
draws/s
━━━╸━━━ 1027 0 0.027 191 130.68 0:00:07 0:00:08
draws/s
━━━╺━━━ 989 0 0.029 31 125.84 0:00:07 0:00:09
draws/s
━━━╺━━━ 968 0 0.020 255 123.22 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 984 0 0.014 271 123.47 0:00:07 0:00:09
draws/s
━━━╸━━━ 1041 0 0.027 15 130.65 0:00:07 0:00:08
draws/s
━━━╸━━━ 1002 0 0.024 511 125.90 0:00:07 0:00:08
draws/s
━━━╺━━━ 977 0 0.024 63 122.66 0:00:07 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╺━━━ 995 0 0.018 511 123.09 0:00:08 0:00:09
draws/s
━━━╸━━━ 1054 0 0.027 63 130.38 0:00:08 0:00:08
draws/s
━━━╸━━━ 1013 0 0.024 255 125.49 0:00:08 0:00:08
draws/s
━━━╺━━━ 994 0 0.027 255 123.02 0:00:08 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1012 0 0.021 31 123.53 0:00:08 0:00:09
draws/s
━━━╸━━━ 1067 0 0.027 255 130.30 0:00:08 0:00:08
draws/s
━━━╸━━━ 1024 0 0.024 127 125.14 0:00:08 0:00:08
draws/s
━━━╸━━━ 1008 0 0.025 319 123.18 0:00:08 0:00:09
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1025 0 0.021 95 123.52 0:00:08 0:00:08
draws/s
━━━╸━━━ 1080 0 0.027 127 130.12 0:00:08 0:00:08
draws/s
━━━╸━━━ 1040 0 0.024 63 125.29 0:00:08 0:00:08
draws/s
━━━╸━━━ 1023 0 0.025 31 123.33 0:00:08 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1039 0 0.021 255 123.43 0:00:08 0:00:08
draws/s
━━━╸━━━ 1094 0 0.027 159 130.12 0:00:08 0:00:08
draws/s
━━━╸━━━ 1056 0 0.024 63 125.62 0:00:08 0:00:08
draws/s
━━━╸━━━ 1039 0 0.025 255 123.59 0:00:08 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1051 0 0.021 191 123.35 0:00:08 0:00:08
draws/s
━━━╸━━━ 1112 0 0.027 31 130.57 0:00:08 0:00:07
draws/s
━━━╸━━━ 1071 0 0.024 255 125.79 0:00:08 0:00:08
draws/s
━━━╸━━━ 1053 0 0.025 255 123.63 0:00:08 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1062 0 0.021 255 122.98 0:00:08 0:00:08
draws/s
━━━╸━━━ 1125 0 0.027 255 130.26 0:00:08 0:00:07
draws/s
━━━╸━━━ 1084 0 0.024 255 125.56 0:00:08 0:00:08
draws/s
━━━╸━━━ 1067 0 0.025 255 123.63 0:00:08 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1079 0 0.021 63 123.26 0:00:08 0:00:08
draws/s
━━━━╺━━ 1143 0 0.027 255 130.63 0:00:08 0:00:07
draws/s
━━━╸━━━ 1096 0 0.024 127 125.37 0:00:08 0:00:08
draws/s
━━━╸━━━ 1081 0 0.025 63 123.59 0:00:08 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1088 0 0.021 31 122.75 0:00:08 0:00:08
draws/s
━━━━╺━━ 1153 0 0.027 63 130.08 0:00:08 0:00:07
draws/s
━━━╸━━━ 1106 0 0.024 127 124.76 0:00:08 0:00:08
draws/s
━━━╸━━━ 1088 0 0.025 255 122.89 0:00:08 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1106 0 0.021 95 123.22 0:00:08 0:00:08
draws/s
━━━━╺━━ 1168 0 0.027 127 130.41 0:00:08 0:00:07
draws/s
━━━╸━━━ 1120 0 0.024 191 124.84 0:00:08 0:00:08
draws/s
━━━╸━━━ 1100 0 0.025 255 122.67 0:00:08 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1118 0 0.021 127 123.16 0:00:09 0:00:08
draws/s
━━━━╺━━ 1184 0 0.027 127 130.44 0:00:09 0:00:07
draws/s
━━━╸━━━ 1134 0 0.024 127 125.05 0:00:09 0:00:08
draws/s
━━━╸━━━ 1111 0 0.025 255 122.44 0:00:09 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━╸━━━ 1129 0 0.021 255 122.90 0:00:09 0:00:08
draws/s
━━━━╺━━ 1197 0 0.027 255 130.27 0:00:09 0:00:07
draws/s
━━━━╺━━ 1149 0 0.024 7 125.05 0:00:09 0:00:07
draws/s
━━━╸━━━ 1123 0 0.025 255 122.32 0:00:09 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1143 0 0.021 159 122.90 0:00:09 0:00:08
draws/s
━━━━╺━━ 1211 0 0.027 255 130.26 0:00:09 0:00:07
draws/s
━━━━╺━━ 1159 0 0.024 63 124.71 0:00:09 0:00:07
draws/s
━━━╸━━━ 1137 0 0.025 63 122.34 0:00:09 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1157 0 0.021 127 122.88 0:00:09 0:00:07
draws/s
━━━━╺━━ 1223 0 0.027 191 129.89 0:00:09 0:00:07
draws/s
━━━━╺━━ 1177 0 0.024 31 125.11 0:00:09 0:00:07
draws/s
━━━━╺━━ 1154 0 0.025 63 122.68 0:00:09 0:00:08
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1166 0 0.021 511 122.43 0:00:09 0:00:07
draws/s
━━━━╺━━ 1243 0 0.027 127 130.47 0:00:09 0:00:07
draws/s
━━━━╺━━ 1191 0 0.024 63 125.08 0:00:09 0:00:07
draws/s
━━━━╺━━ 1165 0 0.025 127 122.43 0:00:09 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1176 0 0.021 255 122.03 0:00:09 0:00:07
draws/s
━━━━╺━━ 1257 0 0.027 127 130.46 0:00:09 0:00:06
draws/s
━━━━╺━━ 1206 0 0.024 95 125.19 0:00:09 0:00:07
draws/s
━━━━╺━━ 1175 0 0.025 255 121.99 0:00:09 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1188 0 0.021 255 121.92 0:00:09 0:00:07
draws/s
━━━━╺━━ 1267 0 0.027 191 129.98 0:00:09 0:00:06
draws/s
━━━━╺━━ 1220 0 0.024 255 125.24 0:00:09 0:00:07
draws/s
━━━━╺━━ 1193 0 0.025 127 122.40 0:00:09 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1206 0 0.021 15 122.28 0:00:09 0:00:07
draws/s
━━━━╺━━ 1278 0 0.027 255 129.67 0:00:09 0:00:06
draws/s
━━━━╺━━ 1235 0 0.024 95 125.27 0:00:09 0:00:07
draws/s
━━━━╺━━ 1204 0 0.025 255 122.15 0:00:09 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1218 0 0.021 255 122.10 0:00:09 0:00:07
draws/s
━━━━╸━━ 1290 0 0.027 159 129.35 0:00:09 0:00:06
draws/s
━━━━╺━━ 1248 0 0.024 127 125.15 0:00:09 0:00:07
draws/s
━━━━╺━━ 1218 0 0.025 127 122.18 0:00:09 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1229 0 0.021 255 121.92 0:00:10 0:00:07
draws/s
━━━━╸━━ 1303 0 0.027 127 129.26 0:00:10 0:00:06
draws/s
━━━━╺━━ 1265 0 0.024 27 125.52 0:00:10 0:00:06
draws/s
━━━━╺━━ 1229 0 0.025 127 121.98 0:00:10 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1241 0 0.021 63 121.73 0:00:10 0:00:07
draws/s
━━━━╸━━ 1318 0 0.027 127 129.29 0:00:10 0:00:06
draws/s
━━━━╺━━ 1277 0 0.024 239 125.24 0:00:10 0:00:06
draws/s
━━━━╺━━ 1243 0 0.025 127 121.96 0:00:10 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1253 0 0.021 255 121.53 0:00:10 0:00:07
draws/s
━━━━╸━━ 1331 0 0.027 239 129.19 0:00:10 0:00:06
draws/s
━━━━╸━━ 1291 0 0.024 31 125.23 0:00:10 0:00:06
draws/s
━━━━╺━━ 1259 0 0.025 127 122.21 0:00:10 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1263 0 0.021 255 121.21 0:00:10 0:00:07
draws/s
━━━━╸━━ 1344 0 0.027 127 128.99 0:00:10 0:00:06
draws/s
━━━━╸━━ 1303 0 0.024 127 125.05 0:00:10 0:00:06
draws/s
━━━━╺━━ 1274 0 0.025 127 122.25 0:00:10 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1275 0 0.021 31 121.05 0:00:10 0:00:07
draws/s
━━━━╸━━ 1359 0 0.027 127 129.01 0:00:10 0:00:06
draws/s
━━━━╸━━ 1315 0 0.024 191 124.83 0:00:10 0:00:06
draws/s
━━━━╺━━ 1285 0 0.025 159 122.14 0:00:10 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╺━━ 1284 0 0.021 127 120.60 0:00:10 0:00:07
draws/s
━━━━╸━━ 1367 0 0.027 127 128.49 0:00:10 0:00:06
draws/s
━━━━╸━━ 1325 0 0.024 95 124.52 0:00:10 0:00:06
draws/s
━━━━╸━━ 1294 0 0.025 255 121.61 0:00:10 0:00:07
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1298 0 0.021 255 120.74 0:00:10 0:00:06
draws/s
━━━━╸━━ 1377 0 0.027 255 128.12 0:00:10 0:00:06
draws/s
━━━━╸━━ 1338 0 0.024 383 124.49 0:00:10 0:00:06
draws/s
━━━━╸━━ 1311 0 0.025 215 121.93 0:00:10 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1320 0 0.021 159 121.45 0:00:10 0:00:06
draws/s
━━━━╸━━ 1386 0 0.027 383 127.56 0:00:10 0:00:06
draws/s
━━━━╸━━ 1354 0 0.024 127 124.62 0:00:10 0:00:06
draws/s
━━━━╸━━ 1322 0 0.025 255 121.73 0:00:10 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1334 0 0.021 95 121.63 0:00:10 0:00:06
draws/s
━━━━╸━━ 1400 0 0.027 255 127.59 0:00:10 0:00:05
draws/s
━━━━╸━━ 1364 0 0.024 191 124.38 0:00:10 0:00:06
draws/s
━━━━╸━━ 1335 0 0.025 63 121.70 0:00:10 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1346 0 0.021 127 121.45 0:00:11 0:00:06
draws/s
━━━━╸━━ 1409 0 0.027 255 127.20 0:00:11 0:00:05
draws/s
━━━━╸━━ 1376 0 0.024 191 124.36 0:00:11 0:00:06
draws/s
━━━━╸━━ 1344 0 0.025 127 121.46 0:00:11 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1359 0 0.021 63 121.44 0:00:11 0:00:06
draws/s
━━━━╸━━ 1418 0 0.027 255 126.76 0:00:11 0:00:05
draws/s
━━━━╸━━ 1389 0 0.024 15 124.25 0:00:11 0:00:06
draws/s
━━━━╸━━ 1358 0 0.025 255 121.39 0:00:11 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1373 0 0.021 127 121.43 0:00:11 0:00:06
draws/s
━━━━━╺━ 1431 0 0.027 127 126.68 0:00:11 0:00:05
draws/s
━━━━╸━━ 1399 0 0.024 127 123.82 0:00:11 0:00:05
draws/s
━━━━╸━━ 1374 0 0.025 63 121.58 0:00:11 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1388 0 0.021 127 121.51 0:00:11 0:00:06
draws/s
━━━━━╺━ 1446 0 0.027 255 126.66 0:00:11 0:00:05
draws/s
━━━━╸━━ 1413 0 0.024 255 123.77 0:00:11 0:00:05
draws/s
━━━━╸━━ 1388 0 0.025 127 121.58 0:00:11 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1400 0 0.021 127 121.40 0:00:11 0:00:06
draws/s
━━━━━╺━ 1460 0 0.027 127 126.59 0:00:11 0:00:05
draws/s
━━━━╸━━ 1424 0 0.024 127 123.58 0:00:11 0:00:05
draws/s
━━━━╸━━ 1399 0 0.025 511 121.34 0:00:11 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1414 0 0.021 127 121.54 0:00:11 0:00:05
draws/s
━━━━━╺━ 1473 0 0.027 255 126.49 0:00:11 0:00:05
draws/s
━━━━━╺━ 1436 0 0.024 255 123.41 0:00:11 0:00:05
draws/s
━━━━╸━━ 1408 0 0.025 127 120.99 0:00:11 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━╸━━ 1427 0 0.021 63 121.35 0:00:11 0:00:05
draws/s
━━━━━╺━ 1482 0 0.027 231 126.11 0:00:11 0:00:05
draws/s
━━━━━╺━ 1447 0 0.024 255 123.17 0:00:11 0:00:05
draws/s
━━━━╸━━ 1420 0 0.025 191 120.85 0:00:11 0:00:06
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1441 0 0.021 127 121.43 0:00:11 0:00:05
draws/s
━━━━━╺━ 1497 0 0.027 191 126.19 0:00:11 0:00:05
draws/s
━━━━━╺━ 1466 0 0.024 63 123.55 0:00:11 0:00:05
draws/s
━━━━━╺━ 1436 0 0.025 159 121.10 0:00:11 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1450 0 0.021 127 121.13 0:00:11 0:00:05
draws/s
━━━━━╺━ 1510 0 0.027 255 126.07 0:00:11 0:00:05
draws/s
━━━━━╺━ 1482 0 0.024 31 123.76 0:00:11 0:00:05
draws/s
━━━━━╺━ 1448 0 0.025 255 121.04 0:00:11 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1460 0 0.021 223 120.81 0:00:12 0:00:05
draws/s
━━━━━╺━ 1517 0 0.027 127 125.59 0:00:12 0:00:05
draws/s
━━━━━╺━ 1491 0 0.024 127 123.51 0:00:12 0:00:05
draws/s
━━━━━╺━ 1454 0 0.025 63 120.38 0:00:12 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1471 0 0.021 255 120.68 0:00:12 0:00:05
draws/s
━━━━━╺━ 1530 0 0.027 191 125.47 0:00:12 0:00:04
draws/s
━━━━━╺━ 1506 0 0.024 63 123.52 0:00:12 0:00:05
draws/s
━━━━━╺━ 1468 0 0.025 63 120.44 0:00:12 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1481 0 0.021 255 120.41 0:00:12 0:00:05
draws/s
━━━━━╺━ 1551 0 0.027 95 126.08 0:00:12 0:00:04
draws/s
━━━━━╺━ 1516 0 0.024 95 123.24 0:00:12 0:00:05
draws/s
━━━━━╺━ 1480 0 0.025 71 120.39 0:00:12 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1491 0 0.021 127 120.14 0:00:12 0:00:05
draws/s
━━━━━╺━ 1561 0 0.027 63 125.76 0:00:12 0:00:04
draws/s
━━━━━╺━ 1532 0 0.024 71 123.44 0:00:12 0:00:04
draws/s
━━━━━╺━ 1489 0 0.025 31 120.09 0:00:12 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1502 0 0.021 127 119.98 0:00:12 0:00:05
draws/s
━━━━━╸━ 1577 0 0.027 63 125.91 0:00:12 0:00:04
draws/s
━━━━━╺━ 1546 0 0.024 63 123.49 0:00:12 0:00:04
draws/s
━━━━━╺━ 1502 0 0.025 127 120.06 0:00:12 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1518 0 0.021 255 120.13 0:00:12 0:00:05
draws/s
━━━━━╸━ 1588 0 0.027 255 125.72 0:00:12 0:00:04
draws/s
━━━━━╺━ 1560 0 0.024 255 123.54 0:00:12 0:00:04
draws/s
━━━━━╺━ 1516 0 0.025 143 120.05 0:00:12 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1530 0 0.021 159 120.08 0:00:12 0:00:04
draws/s
━━━━━╸━ 1596 0 0.027 255 125.33 0:00:12 0:00:04
draws/s
━━━━━╸━ 1574 0 0.024 159 123.55 0:00:12 0:00:04
draws/s
━━━━━╺━ 1528 0 0.025 127 119.93 0:00:12 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1544 0 0.021 31 120.10 0:00:12 0:00:04
draws/s
━━━━━╸━ 1613 0 0.027 31 125.50 0:00:12 0:00:04
draws/s
━━━━━╸━ 1587 0 0.024 255 123.48 0:00:12 0:00:04
draws/s
━━━━━╺━ 1542 0 0.025 127 120.01 0:00:12 0:00:05
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1555 0 0.021 63 119.95 0:00:12 0:00:04
draws/s
━━━━━╸━ 1626 0 0.027 127 125.44 0:00:12 0:00:04
draws/s
━━━━━╸━ 1599 0 0.024 111 123.37 0:00:12 0:00:04
draws/s
━━━━━╺━ 1556 0 0.025 255 120.09 0:00:12 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╺━ 1568 0 0.021 191 119.99 0:00:13 0:00:04
draws/s
━━━━━╸━ 1638 0 0.027 119 125.37 0:00:13 0:00:04
draws/s
━━━━━╸━ 1612 0 0.024 127 123.43 0:00:13 0:00:04
draws/s
━━━━━╺━ 1568 0 0.025 95 120.01 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1575 0 0.021 255 119.70 0:00:13 0:00:04
draws/s
━━━━━╸━ 1653 0 0.027 31 125.52 0:00:13 0:00:03
draws/s
━━━━━╸━ 1626 0 0.024 191 123.46 0:00:13 0:00:04
draws/s
━━━━━╸━ 1577 0 0.025 255 119.80 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1586 0 0.021 127 119.35 0:00:13 0:00:04
draws/s
━━━━━╸━ 1664 0 0.027 511 125.26 0:00:13 0:00:03
draws/s
━━━━━╸━ 1644 0 0.024 63 123.76 0:00:13 0:00:03
draws/s
━━━━━╸━ 1592 0 0.025 255 119.96 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1595 0 0.021 127 119.16 0:00:13 0:00:04
draws/s
━━━━━╸━ 1673 0 0.027 255 124.92 0:00:13 0:00:03
draws/s
━━━━━╸━ 1659 0 0.024 75 123.88 0:00:13 0:00:03
draws/s
━━━━━╸━ 1601 0 0.025 63 119.60 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1601 0 0.021 31 118.65 0:00:13 0:00:04
draws/s
━━━━━╸━ 1682 0 0.027 63 124.55 0:00:13 0:00:03
draws/s
━━━━━╸━ 1665 0 0.024 127 123.35 0:00:13 0:00:03
draws/s
━━━━━╸━ 1607 0 0.025 63 119.06 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1611 0 0.021 63 118.39 0:00:13 0:00:04
draws/s
━━━━━╸━ 1695 0 0.027 127 124.59 0:00:13 0:00:03
draws/s
━━━━━╸━ 1679 0 0.024 255 123.38 0:00:13 0:00:03
draws/s
━━━━━╸━ 1619 0 0.025 127 118.99 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1625 0 0.021 127 118.41 0:00:13 0:00:04
draws/s
━━━━━╸━ 1709 0 0.027 95 124.53 0:00:13 0:00:03
draws/s
━━━━━╸━ 1686 0 0.024 127 122.97 0:00:13 0:00:03
draws/s
━━━━━╸━ 1632 0 0.025 127 118.94 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1633 0 0.021 23 118.10 0:00:13 0:00:04
draws/s
━━━━━━╺ 1719 0 0.027 383 124.30 0:00:13 0:00:03
draws/s
━━━━━╸━ 1694 0 0.024 255 122.55 0:00:13 0:00:03
draws/s
━━━━━╸━ 1641 0 0.025 127 118.64 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1642 0 0.021 255 117.78 0:00:13 0:00:04
draws/s
━━━━━━╺ 1730 0 0.027 191 124.13 0:00:13 0:00:03
draws/s
━━━━━╸━ 1700 0 0.024 63 122.04 0:00:13 0:00:03
draws/s
━━━━━╸━ 1649 0 0.025 255 118.37 0:00:13 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1650 0 0.021 127 117.50 0:00:14 0:00:04
draws/s
━━━━━━╺ 1740 0 0.027 223 123.82 0:00:14 0:00:03
draws/s
━━━━━╸━ 1709 0 0.024 143 121.68 0:00:14 0:00:03
draws/s
━━━━━╸━ 1659 0 0.025 63 118.15 0:00:14 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1660 0 0.021 127 117.26 0:00:14 0:00:04
draws/s
━━━━━━╺ 1748 0 0.027 255 123.51 0:00:14 0:00:03
draws/s
━━━━━━╺ 1722 0 0.024 127 121.63 0:00:14 0:00:03
draws/s
━━━━━╸━ 1672 0 0.025 111 118.14 0:00:14 0:00:04
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1671 0 0.021 255 117.09 0:00:14 0:00:03
draws/s
━━━━━━╺ 1763 0 0.027 191 123.56 0:00:14 0:00:03
draws/s
━━━━━━╺ 1733 0 0.024 63 121.46 0:00:14 0:00:03
draws/s
━━━━━╸━ 1684 0 0.025 255 118.10 0:00:14 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1678 0 0.021 383 116.77 0:00:14 0:00:03
draws/s
━━━━━━╺ 1771 0 0.027 319 123.17 0:00:14 0:00:03
draws/s
━━━━━━╺ 1741 0 0.024 127 121.29 0:00:14 0:00:03
draws/s
━━━━━╸━ 1690 0 0.025 511 117.62 0:00:14 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1686 0 0.021 255 116.35 0:00:14 0:00:03
draws/s
━━━━━━╺ 1782 0 0.027 127 122.99 0:00:14 0:00:02
draws/s
━━━━━━╺ 1749 0 0.024 127 120.73 0:00:14 0:00:03
draws/s
━━━━━╸━ 1700 0 0.025 71 117.48 0:00:14 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1696 0 0.021 191 116.16 0:00:14 0:00:03
draws/s
━━━━━━╺ 1794 0 0.027 255 122.81 0:00:14 0:00:02
draws/s
━━━━━━╺ 1762 0 0.024 255 120.65 0:00:14 0:00:03
draws/s
━━━━━╸━ 1712 0 0.025 191 117.32 0:00:14 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1702 0 0.021 191 115.93 0:00:14 0:00:03
draws/s
━━━━━━╺ 1801 0 0.027 127 122.73 0:00:14 0:00:02
draws/s
━━━━━━╺ 1768 0 0.024 255 120.45 0:00:14 0:00:03
draws/s
━━━━━━╺ 1718 0 0.025 239 116.76 0:00:14 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━╸━ 1712 0 0.021 255 115.36 0:00:14 0:00:03
draws/s
━━━━━━╺ 1815 0 0.027 255 122.32 0:00:14 0:00:02
draws/s
━━━━━━╺ 1779 0 0.024 127 120.04 0:00:14 0:00:02
draws/s
━━━━━━╺ 1729 0 0.025 255 116.53 0:00:14 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1723 0 0.021 127 115.25 0:00:14 0:00:03
draws/s
━━━━━━╺ 1827 0 0.027 31 122.21 0:00:14 0:00:02
draws/s
━━━━━━╺ 1790 0 0.024 255 119.78 0:00:14 0:00:02
draws/s
━━━━━━╺ 1741 0 0.025 63 116.56 0:00:14 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1734 0 0.021 31 115.13 0:00:15 0:00:03
draws/s
━━━━━━╺ 1840 0 0.027 127 122.18 0:00:15 0:00:02
draws/s
━━━━━━╺ 1805 0 0.024 191 119.86 0:00:15 0:00:02
draws/s
━━━━━━╺ 1758 0 0.025 63 116.81 0:00:15 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1745 0 0.021 63 115.02 0:00:15 0:00:03
draws/s
━━━━━━╺ 1850 0 0.027 351 121.96 0:00:15 0:00:02
draws/s
━━━━━━╺ 1816 0 0.024 127 119.81 0:00:15 0:00:02
draws/s
━━━━━━╺ 1768 0 0.025 63 116.57 0:00:15 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1758 0 0.021 31 115.04 0:00:15 0:00:03
draws/s
━━━━━━╸ 1861 0 0.027 127 121.87 0:00:15 0:00:02
draws/s
━━━━━━╺ 1828 0 0.024 95 119.65 0:00:15 0:00:02
draws/s
━━━━━━╺ 1775 0 0.025 255 116.22 0:00:15 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1771 0 0.021 95 115.08 0:00:15 0:00:03
draws/s
━━━━━━╸ 1873 0 0.027 255 121.79 0:00:15 0:00:02
draws/s
━━━━━━╺ 1842 0 0.024 255 119.71 0:00:15 0:00:02
draws/s
━━━━━━╺ 1781 0 0.025 511 115.82 0:00:15 0:00:03
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1783 0 0.021 255 115.10 0:00:15 0:00:03
draws/s
━━━━━━╸ 1883 0 0.027 255 121.47 0:00:15 0:00:02
draws/s
━━━━━━╺ 1854 0 0.024 255 119.64 0:00:15 0:00:02
draws/s
━━━━━━╺ 1788 0 0.025 215 115.38 0:00:15 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1796 0 0.021 255 115.08 0:00:15 0:00:02
draws/s
━━━━━━╸ 1895 0 0.027 95 121.49 0:00:15 0:00:01
draws/s
━━━━━━╸ 1863 0 0.024 255 119.40 0:00:15 0:00:02
draws/s
━━━━━━╺ 1796 0 0.025 127 115.06 0:00:15 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1809 0 0.021 31 115.09 0:00:15 0:00:02
draws/s
━━━━━━╸ 1905 0 0.027 255 121.21 0:00:15 0:00:01
draws/s
━━━━━━╸ 1872 0 0.024 63 119.18 0:00:15 0:00:02
draws/s
━━━━━━╺ 1807 0 0.025 255 114.99 0:00:15 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1819 0 0.021 127 114.88 0:00:15 0:00:02
draws/s
━━━━━━╸ 1913 0 0.027 255 121.13 0:00:15 0:00:01
draws/s
━━━━━━╸ 1877 0 0.024 255 118.86 0:00:15 0:00:02
draws/s
━━━━━━╺ 1814 0 0.025 127 114.94 0:00:15 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1831 0 0.021 127 114.76 0:00:15 0:00:02
draws/s
━━━━━━╸ 1927 0 0.027 127 120.79 0:00:15 0:00:01
draws/s
━━━━━━╸ 1893 0 0.024 63 118.69 0:00:15 0:00:01
draws/s
━━━━━━╺ 1828 0 0.025 255 114.59 0:00:15 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1842 0 0.021 255 114.67 0:00:16 0:00:02
draws/s
━━━━━━╸ 1938 0 0.027 127 120.68 0:00:16 0:00:01
draws/s
━━━━━━╸ 1910 0 0.024 63 118.96 0:00:16 0:00:01
draws/s
━━━━━━╺ 1837 0 0.025 127 114.42 0:00:16 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╺ 1852 0 0.021 63 114.46 0:00:16 0:00:02
draws/s
━━━━━━╸ 1947 0 0.027 191 120.46 0:00:16 0:00:01
draws/s
━━━━━━╸ 1926 0 0.024 63 119.07 0:00:16 0:00:01
draws/s
━━━━━━╺ 1848 0 0.025 255 114.25 0:00:16 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1863 0 0.021 319 114.42 0:00:16 0:00:02
draws/s
━━━━━━╸ 1959 0 0.027 127 120.27 0:00:16 0:00:01
draws/s
━━━━━━╸ 1940 0 0.024 127 119.11 0:00:16 0:00:01
draws/s
━━━━━━╸ 1859 0 0.025 127 114.15 0:00:16 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1873 0 0.021 255 114.19 0:00:16 0:00:02
draws/s
━━━━━━╸ 1970 0 0.027 255 120.13 0:00:16 0:00:01
draws/s
━━━━━━╸ 1952 0 0.024 63 119.04 0:00:16 0:00:01
draws/s
━━━━━━╸ 1871 0 0.025 31 114.11 0:00:16 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1882 0 0.021 255 114.05 0:00:16 0:00:02
draws/s
━━━━━━╸ 1985 0 0.027 127 120.24 0:00:16 0:00:01
draws/s
━━━━━━╸ 1965 0 0.024 127 119.05 0:00:16 0:00:01
draws/s
━━━━━━╸ 1880 0 0.025 63 114.01 0:00:16 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1897 0 0.021 95 114.16 0:00:16 0:00:01
draws/s
━━━━━━╸ 1997 0 0.027 255 120.19 0:00:16 0:00:01
draws/s
━━━━━━╸ 1977 0 0.024 95 118.96 0:00:16 0:00:01
draws/s
━━━━━━╸ 1892 0 0.025 127 113.93 0:00:16 0:00:02
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1904 0 0.021 31 114.32 0:00:16 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━╸ 1979 0 0.024 255 118.92 0:00:16 0:00:01
draws/s
━━━━━━╸ 1896 0 0.025 23 113.87 0:00:16 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1912 0 0.021 255 114.25 0:00:16 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━╸ 1988 0 0.024 255 118.86 0:00:16 0:00:01
draws/s
━━━━━━╸ 1907 0 0.025 63 113.99 0:00:16 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1921 0 0.021 127 114.27 0:00:16 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━╸ 1994 0 0.024 223 118.63 0:00:16 0:00:01
draws/s
━━━━━━╸ 1917 0 0.025 207 113.82 0:00:16 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1927 0 0.021 127 114.12 0:00:16 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━╸ 1923 0 0.025 127 113.93 0:00:16 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1936 0 0.021 255 114.11 0:00:16 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━╸ 1935 0 0.025 127 114.08 0:00:16 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1949 0 0.021 127 114.14 0:00:17 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━╸ 1951 0 0.025 63 114.36 0:00:17 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1967 0 0.021 127 114.47 0:00:17 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━╸ 1966 0 0.025 255 114.47 0:00:17 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1985 0 0.021 75 114.80 0:00:17 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━╸ 1978 0 0.025 79 114.43 0:00:17 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━╸ 1996 0 0.021 255 114.77 0:00:17 0:00:01
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━╸ 1993 0 0.025 127 114.58 0:00:17 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━━ 2000 0 0.021 63 114.78 0:00:17 0:00:00
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━╸ 1995 0 0.025 255 114.58 0:00:17 0:00:01
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━━ 2000 0 0.021 63 114.78 0:00:17 0:00:00
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.025 31 114.65 0:00:17 0:00:00
draws/s
Step Grad
Progre… Draw Diverg… size evals Speed Elapsed Remaini…
──────────────────────────────────────────────────────────────────────────────
━━━━━━━ 2000 0 0.021 63 114.78 0:00:17 0:00:00
draws/s
━━━━━━━ 2000 0 0.027 127 120.07 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.024 63 118.40 0:00:16 0:00:00
draws/s
━━━━━━━ 2000 0 0.025 31 114.65 0:00:17 0:00:00
draws/s
?25hSampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 18 seconds.
Sampling: [beta, y_hat, y_hat_sigma]
Sampling: [y_hat]
Sampling: [y_hat]
Sampling: [y_hat]
Sampling: [y_hat]
fig, ax = result.plot(plot_predictors=True)
result.summary()
================================SyntheticControl================================
Control units: ['a', 'b', 'c', 'd', 'e', 'f', 'g']
Treated unit: actual
Model coefficients:
a 0.054, 94% HDI [0.0021, 0.13]
b 0.2, 94% HDI [0.14, 0.25]
c 0.21, 94% HDI [0.12, 0.29]
d 0.061, 94% HDI [0.0072, 0.13]
e 0.26, 94% HDI [0.22, 0.29]
f 0.11, 94% HDI [0.071, 0.15]
g 0.11, 94% HDI [0.075, 0.15]
y_hat_sigma 0.25, 94% HDI [0.21, 0.3]
Pre-treatment correlation (actual): 0.9992
We can get nicely formatted tables from our integration with the maketables package.
from maketables import ETable
result.set_maketables_options(hdi_prob=0.95)
ETable(result, coef_fmt="b:.3f \n [ci95l:.3f, ci95u:.3f]")
| y | |
|---|---|
| (1) | |
| coef | |
| a | 0.054 [0.000, 0.121] |
| b | 0.196 [0.144, 0.253] |
| c | 0.209 [0.126, 0.295] |
| d | 0.061 [0.000, 0.120] |
| e | 0.256 [0.224, 0.290] |
| f | 0.112 [0.071, 0.153] |
| g | 0.113 [0.073, 0.151] |
| stats | |
| N | 100 |
| Bayesian R2 | 0.998 |
| Format of coefficient cell: Coefficient [95% CI Lower, 95% CI Upper] | |
As well as the model coefficients, we might be interested in the average causal impact and average cumulative causal impact.
az.summary(result.post_impact.mean("obs_ind"))
| mean | sd | hdi_3% | hdi_97% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| x[actual] | -1.239 | 0.363 | -1.906 | -0.585 | 0.012 | 0.006 | 946.0 | 1492.0 | 1.0 |
Warning
Care must be taken with the mean impact statistic. It only makes sense to use this statistic if it looks like the intervention had a lasting (and roughly constant) effect on the outcome variable. If the effect is transient, then clearly there will be a lot of post-intervention period where the impact of the intervention has ‘worn off’. If so, then it will be hard to interpret the mean impacts real meaning.
We can also ask for the summary statistics of the cumulative causal impact.
# get index of the final time point
index = result.post_impact_cumulative.obs_ind.max()
# grab the posterior distribution of the cumulative impact at this final time point
last_cumulative_estimate = result.post_impact_cumulative.sel({"obs_ind": index})
# get summary stats
az.summary(last_cumulative_estimate)
| mean | sd | hdi_3% | hdi_97% | mcse_mean | mcse_sd | ess_bulk | ess_tail | r_hat | |
|---|---|---|---|---|---|---|---|---|---|
| x[actual] | -37.181 | 10.888 | -57.189 | -17.546 | 0.352 | 0.182 | 946.0 | 1492.0 | 1.0 |
Effect Summary Reporting#
For decision-making, you often need a concise summary of the causal effect with key statistics. The effect_summary() method provides a decision-ready report with average and cumulative effects, HDI intervals, tail probabilities, and relative effects.
# Generate effect summary for the full post-period
stats = result.effect_summary(treated_unit="actual")
stats.table
| mean | median | hdi_lower | hdi_upper | p_gt_0 | relative_mean | relative_hdi_lower | relative_hdi_upper | |
|---|---|---|---|---|---|---|---|---|
| average | -1.239357 | -1.241476 | -1.913526 | -0.545315 | 0.0 | -5.049057 | -7.617849 | -2.295991 |
| cumulative | -37.180701 | -37.244276 | -57.405766 | -16.359464 | 0.0 | -5.049057 | -7.617849 | -2.295991 |
print(stats.text)
During the Post-period (70 to 99), the response variable had an average value of approx. 23.21. By contrast, in the absence of an intervention, we would have expected an average response of 24.44. The 95% interval of this counterfactual prediction is [23.75, 25.12]. Subtracting this prediction from the observed response yields an estimate of the causal effect the intervention had on the response variable. This effect is -1.24 with a 95% interval of [-1.91, -0.55].
Summing up the individual data points during the Post-period, the response variable had an overall value of 696.16. By contrast, had the intervention not taken place, we would have expected a sum of 733.34. The 95% interval of this prediction is [712.52, 753.57].
The 95% HDI of the effect [-1.91, -0.55] does not include zero. The posterior probability of a decrease is 1.000. Relative to the counterfactual, the effect represents a -5.05% change (95% HDI [-7.62%, -2.30%]).
This analysis assumes that the control units used to construct the synthetic counterfactual were not themselves affected by the intervention, and that the pre-treatment relationship between control and treated units remains stable throughout the post-treatment period. We recommend inspecting model fit, examining pre-intervention trends, and conducting sensitivity analyses (e.g., placebo tests) to support any causal conclusions drawn from this analysis.
You can customize the summary in several ways:
Window: Analyze a specific time period instead of the full post-period
Direction: Specify whether you’re testing for an increase, decrease, or two-sided effect
Options: Include/exclude cumulative or relative effects
# Example: Analyze first half of post-period
post_indices = result.datapost.index
window_start = post_indices[0]
window_end = post_indices[len(post_indices) // 2]
stats_windowed = result.effect_summary(
window=(window_start, window_end),
treated_unit="actual",
direction="two-sided",
cumulative=True,
relative=True,
)
stats_windowed.table
| mean | median | hdi_lower | hdi_upper | p_two_sided | prob_of_effect | relative_mean | relative_hdi_lower | relative_hdi_upper | |
|---|---|---|---|---|---|---|---|---|---|
| average | -2.655351 | -2.641739 | -3.146364 | -2.144796 | 0.0 | 1.0 | -11.823094 | -13.782409 | -9.845488 |
| cumulative | -42.485612 | -42.267822 | -50.341832 | -34.316743 | 0.0 | 1.0 | -11.823094 | -13.782409 | -9.845488 |
print(stats_windowed.text)
During the Post-period (70 to 85), the response variable had an average value of approx. 19.78. By contrast, in the absence of an intervention, we would have expected an average response of 22.44. The 95% interval of this counterfactual prediction is [21.93, 22.93]. Subtracting this prediction from the observed response yields an estimate of the causal effect the intervention had on the response variable. This effect is -2.66 with a 95% interval of [-3.15, -2.14].
Summing up the individual data points during the Post-period, the response variable had an overall value of 316.49. By contrast, had the intervention not taken place, we would have expected a sum of 358.98. The 95% interval of this prediction is [350.81, 366.84].
The 95% HDI of the effect [-3.15, -2.14] does not include zero. The posterior probability of an effect is 1.000. Relative to the counterfactual, the effect represents a -11.82% change (95% HDI [-13.78%, -9.85%]).
This analysis assumes that the control units used to construct the synthetic counterfactual were not themselves affected by the intervention, and that the pre-treatment relationship between control and treated units remains stable throughout the post-treatment period. We recommend inspecting model fit, examining pre-intervention trends, and conducting sensitivity analyses (e.g., placebo tests) to support any causal conclusions drawn from this analysis.