Ch5 Exercises 1 through 5

[canyon289]

• Exercise 1 Approved
• Exercise 2 Approved
• Exercise 3 Approved
• Exercise 5 Approved

[aloctavodia]

It should be "Chapter 5 Exercises"

exercise 1 and 3

If you use original x_1s instead of linspace things look much more better. Or if you use linspace and then you normalize the new_data.

Something like this for i, (sd, trace) in enumerate(trace_1[:3]):

α_p_post = trace['α'].mean()
β_p_post = trace['β'].mean(axis=0)
x_1p = np.vstack([x_new**i for i in range(1, order_1+1)])
x_new_p = (x_1p - x_1p.mean(axis=1, keepdims=True)) / x_1p.std(axis=1, keepdims=True)

y_p_post = α_p_post + np.dot(β_p_post, x_new_p) 
plt.plot(x_new_p[0], y_p_post, f'C{i}',
         label=f'model order {order_1} sd-{sd}',
         alpha=.5)

plt.scatter(x_1s[0], y_1s, c='C0', marker='.')
plt.legend();

exercise 2

This is probably my mistake I guess at some point I had a block of code generating dummy_data
you can create more samples using a bootstraping + noise approach

idx = np.random.choice(range(len(dummy_data)), size=500)
dummy_data_500 = np.random.normal(dummy_data[idx], dummy_data.std(0) / 10)