Update Jupyter style in lasso notebook (#279)

* update of jupyter style

* addressed oriol's comments

* run pre-commit

* rerun notebook

Co-authored-by: Oriol (ZBook) <[email protected]>

Author: ltoniazzi

examples/pymc3_howto/lasso_block_update.ipynb

@@ -6,74 +6,119 @@ jupytext:
     format_version: 0.13
     jupytext_version: 1.13.7
 kernelspec:
-  display_name: Python PyMC (Dev)
+  display_name: Python 3 (ipykernel)
   language: python
-  name: pymc-dev-py38
+  name: python3
 ---
 
+(lasso_block_update)=
 # Lasso regression with block updating
 
-Sometimes, it is very useful to update a set of parameters together. For example, variables that are highly correlated are often good to update together. In PyMC 3 block updating is simple, as example will demonstrate.
-
-Here we have a LASSO regression model where the two coefficients are strongly correlated. Normally, we would define the coefficient parameters as a single random variable, but here we define them separately to show how to do block updates.
-
-First we generate some fake data.
+:::{post} Feb 10, 2022
+:tags: pymc3.Exponential, pymc3.Laplace, pymc3.Metropolis, pymc3.Model, pymc3.Normal, pymc3.Slice, pymc3.Uniform, regression
+:category: beginner
+:author: Chris Fonnesbeck, Raul Maldonado, Michael Osthege, Thomas Wiecki, Lorenzo Toniazzi
+:::
 
 ```{code-cell} ipython3
-%matplotlib inline
+:tags: []
 
+%matplotlib inline
 import arviz as az
+import matplotlib.pyplot as plt
 import numpy as np
 import pymc as pm
 
-from matplotlib import pylab
+print(f"Running on PyMC v{pm.__version__}")
+```
+
+```{code-cell} ipython3
+RANDOM_SEED = 8927
+rng = np.random.default_rng(RANDOM_SEED)
+az.style.use("arviz-darkgrid")
+```
+
+Sometimes, it is very useful to update a set of parameters together. For example, variables that are highly correlated are often good to update together. In PyMC block updating is simple. This will be demonstrated using the parameter `step` of {class}`pymc.sample`.
+
+Here we have a [LASSO regression model](https://en.wikipedia.org/wiki/Lasso_(statistics)#Bayesian_interpretation) where the two coefficients are strongly correlated. Normally, we would define the coefficient parameters as a single random variable, but here we define them separately to show how to do block updates.
+
+First we generate some fake data.
 
-d = np.random.normal(size=(3, 30))
-d1 = d[0] + 4
-d2 = d[1] + 4
-yd = 0.2 * d1 + 0.3 * d2 + d[2]
+```{code-cell} ipython3
+x = rng.standard_normal(size=(3, 30))
+x1 = x[0] + 4
+x2 = x[1] + 4
+noise = x[2]
+y_obs = x1 * 0.2 + x2 * 0.3 + noise
 ```
 
 Then define the random variables.
 
 ```{code-cell} ipython3
-lam = 3
+:tags: []
+
+lam = 3000
 
 with pm.Model() as model:
-    s = pm.Exponential("s", 1)
-    tau = pm.Uniform("tau", 0, 1000)
+    sigma = pm.Exponential("sigma", 1)
+    tau = pm.Uniform("tau", 0, 1)
     b = lam * tau
-    m1 = pm.Laplace("m1", 0, b)
-    m2 = pm.Laplace("m2", 0, b)
+    beta1 = pm.Laplace("beta1", 0, b)
+    beta2 = pm.Laplace("beta2", 0, b)
 
-    p = d1 * m1 + d2 * m2
+    mu = x1 * beta1 + x2 * beta2
 
-    y = pm.Normal("y", mu=p, sigma=s, observed=yd)
+    y = pm.Normal("y", mu=mu, sigma=sigma, observed=y_obs)
 ```
 
-For most samplers, including Metropolis and HamiltonianMC, simply pass a list of variables to sample as a block. This works with both scalar and array parameters.
+For most samplers, including {class}`pymc.Metropolis` and {class}`pymc.HamiltonianMC`, simply pass a list of variables to sample as a block. This works with both scalar and array parameters.
 
 ```{code-cell} ipython3
 with model:
-    start = pm.find_MAP()
+    step1 = pm.Metropolis([beta1, beta2])
 
-    step1 = pm.Metropolis([m1, m2])
+    step2 = pm.Slice([sigma, tau])
 
-    step2 = pm.Slice([s, tau])
-
-    idata = pm.sample(10000, [step1, step2], start=start)
+    idata = pm.sample(draws=10000, step=[step1, step2])
 ```
 
+We conclude by plotting the sampled marginals and the joint distribution of `beta1` and `beta2`.
+
 ```{code-cell} ipython3
+:tags: []
+
 az.plot_trace(idata);
 ```
 
 ```{code-cell} ipython3
-pylab.hexbin(idata.posterior["m1"], idata.posterior["m2"], gridsize=50)
-pylab.axis("off");
+az.plot_pair(
+    idata,
+    var_names=["beta1", "beta2"],
+    kind="hexbin",
+    marginals=True,
+    figsize=(10, 10),
+    gridsize=50,
+)
 ```
 
+## Authors
+
+* Authored by [Chris Fonnesbeck](https://github.com/fonnesbeck) in Dec, 2020
+* Updated by [Raul Maldonado](https://github.com/CloudChaoszero) in Jan, 2021
+* Updated by Raul Maldonado in Mar, 2021
+* Reexecuted by [Thomas Wiecki](https://github.com/twiecki) and [Michael Osthege](https://github.com/michaelosthege) with PyMC v4 in Jan, 2022 ([pymc-examples#264](https://github.com/pymc-devs/pymc-examples/pull/264))
+* Updated by [Lorenzo Toniazzi](https://github.com/ltoniazzi) in Feb, 2022 ([pymc-examples#279](https://github.com/pymc-devs/pymc-examples/pull/279))
+
++++
+
+## Watermark
+
 ```{code-cell} ipython3
+:tags: []
+
 %load_ext watermark
-%watermark -n -u -v -iv -w
+%watermark -n -u -v -iv -w -p aesara,aeppl,xarray
 ```
+
+:::{include} ../page_footer.md
+:::