[markov_chain_I] Animation of converging to stationary distribution

[longye-tian]

Dear John @jstac,

I’ve put together some code to animate the convergence to a stationary distribution in our Markov Chain lecture (markov_chain_I). I hope this will be helpful if we decide to include animations in the future. Here are some details.

It requires the following imports,

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation
from IPython.display import HTML

And putting the rest of the code in the Jupyter notebook after we define iterate_ψ()

ψ_0 = (0.0, 0.2, 0.8)

fig = plt.figure()
ax = fig.add_subplot(projection='3d')

def update(n):
    ψ_t = iterate_ψ(ψ_0, P, n+1)
    
    ax.clear()
    ax.set_xlim([0, 1])
    ax.set_ylim([0, 1])
    ax.set_zlim([0, 1])
    ax.view_init(30, 210)
    
    for i, point in enumerate(ψ_t):
        ax.scatter(point[0], point[1], point[2], color='r', s=60, alpha=(i+1)/len(ψ_t))
    
    mc = qe.MarkovChain(P)
    ψ_star = mc.stationary_distributions[0]
    ax.scatter(ψ_star[0], ψ_star[1], ψ_star[2], c='k', s=60)
    
    return fig,

anim = FuncAnimation(fig, update, frames=range(20), blit=False, repeat=False)
plt.close()
HTML(anim.to_jshtml())

It will render an interactive plot with a sliding bar and a play button and options as shown below:

animation.mov

Best ❤️
Longye

[jstac]

Very cool, thanks @longye-tian !

@mmcky , what do you think about including this in https://intro.quantecon.org/markov_chains_I.html ?

It would replace the existing figure in https://intro.quantecon.org/markov_chains_I.html#example-hamiltons-chain

[mmcky]

@longye-tian love your work here. This is really nice.

We will need to do some testing around jupyter-book and the object that is generated as the mov file. One option would be to serve the mov object from github as an asset and another is to generate it using code (if not time consuming to run) but we will need to confirm if the binary blob is supported. If it isn't will need to dive into jupyter-book to get it supported.

@longye-tian would you mind opening a PR (marked as DRAFT) and add this code as @jstac suggests. Then please tag me and I will dig into the PR and do some testing locally.

[longye-tian]

@longye-tian love your work here. This is really nice.

We will need to do some testing around jupyter-book and the object that is generated as the mov file. One option would be to serve the mov object from github as an asset and another is to generate it using code (if not time consuming to run) but we will need to confirm if the binary blob is supported. If it isn't will need to dive into jupyter-book to get it supported.

@longye-tian would you mind opening a PR (marked as DRAFT) and add this code as @jstac suggests. Then please tag me and I will dig into the PR and do some testing locally.

Hi Matt @mmcky ,

Thank you for the help with testing the animation :)) I have opened a PR for the animation code.

Best,
Longye