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Update LKJ nb to avoid crashing at model seeding #583

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Merged
merged 1 commit into from
Oct 12, 2023
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Update LKJ nb to avoid crashing at model seeding #583

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278 changes: 78 additions & 200 deletions examples/case_studies/LKJ.ipynb
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7 changes: 3 additions & 4 deletions examples/case_studies/LKJ.myst.md
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Original file line number Diff line number Diff line change
Expand Up @@ -27,11 +27,9 @@ colab:
id: 17Thh2DHr2Pa
outputId: 90631275-86c9-4f4a-f81a-22465d0c8b8c
---
%env MKL_THREADING_LAYER=GNU
import arviz as az
import numpy as np
import pymc as pm
import seaborn as sns

from matplotlib import pyplot as plt
from matplotlib.lines import Line2D
Expand Down Expand Up @@ -156,7 +154,7 @@ Often however, you'll be interested in the posterior distribution of the correla
:id: ac3eQeMJr2Pf

coords = {"axis": ["y", "z"], "axis_bis": ["y", "z"], "obs_id": np.arange(N)}
with pm.Model(coords=coords, rng_seeder=RANDOM_SEED) as model:
with pm.Model(coords=coords) as model:
chol, corr, stds = pm.LKJCholeskyCov(
"chol", n=2, eta=2.0, sd_dist=pm.Exponential.dist(1.0, shape=2)
)
Expand Down Expand Up @@ -189,6 +187,7 @@ outputId: f039bfb8-1acf-42cb-b054-bc2c97697f96
---
with model:
trace = pm.sample(
random_seed=rng,
idata_kwargs={"dims": {"chol_stds": ["axis"], "chol_corr": ["axis", "axis_bis"]}},
)
az.summary(trace, var_names="~chol", round_to=2)
Expand Down Expand Up @@ -264,7 +263,7 @@ Sigma_post = trace.posterior["cov"].mean(("chain", "draw")).values

+++ {"id": "DMDwKtp0r2Pj"}

So the posterior means are within 3% of the true values of $\mu$ and $\Sigma$.
So the posterior means are within 1% of the true values of $\mu$ and $\Sigma$.

Now let's replicate the plot we did at the beginning, but let's overlay the posterior distribution on top of the true distribution -- you'll see there is excellent visual agreement between both:

Expand Down