Add fit_discrete_mc

[Smit-create]

#678

[coveralls]

Coverage: 92.815% (+0.03%) from 92.782% when pulling 55b6c9e on Smit-create:i-678 into 147d862 on QuantEcon:main.

[oyamad]

Thanks @Smit-create

• This part is missing:

  QuantEcon.py/quantecon/markov/approximation.py

  Lines 371 to 373 in 745c0d4

  	# Assign the visited states in the cartesian product as the state values
  	prod = cartesian(V, order=order)
  	mc.state_values = prod[mc.state_values]

• Add tests
• Examples section will be helpful

There are a few points open for discussion:

• What shape should X be of?
• Is the name S of the second argument appropriate?
• Is this for approximation or estimation (which of approximation.py or estimate.py to include this code in)?

[jstac]

Thanks for the review @oyamad .

I think this should be in estimate.py because there is no specified model to approximate. I suggest a better name for S is grids.

I am away from my computer so I won't give further feedback. @Smit-create , it would be great if you could coordinate with @oyamad to finish this PR.

[Smit-create]

There are a few points open for discussion:

• What shape should X be of?
• Is the name S of the second argument appropriate?
• Is this for approximation or estimation (which of approximation.py or estimate.py to include this code in)?

Thanks, @oyamad. I have addressed these questions and added the missing part. If the current diff looks good, I can start working on Examples and tests.

[oyamad]

• Regarding the shape of X, I would prefer to follow the convention in estimate_mc(X) and cartesian_nearest_index(X, ...) where X is supposed to be a T x n array with X[t] containing the t-th observation. What do you think?
• For the second argument, I would follow the suggestion from @jstac (plural grids).

[Smit-create]

• where X is supposed to be a T x n array

I kept it as n x T because the output of simulate_linear_model is n x T, moreover, one can easily think of this as horizontally stacked individual vectors of shape n x 1.

I would follow the suggestion from

Sure will change that.

[jstac]

I kept it as n x T because the output of simulate_linear_model is n x T

Both @oyamad and @Smit-create 's opinions are sensible on this point.

Another option --- combining these opinions but with a breaking change --- is to convert linear_state_space so that its output is $T \times n$.

This is more work but I personally prefer it, so that we have consistency across all of these functions.

[oyamad]

When n=1, it is supposed to pass for example X = [[0.1], [0.6], [1.2], [0.2]] and grids = ([0., 0.5, 1.],). Is there any clever way to detect this case and allow passing X = [0.1, 0.6, 1.2, 0.2] and grids = [0., 0.5, 1.]?

[Smit-create]

Is there any clever way to detect this case

Thanks for the review. I am not sure if we should support this as we are clearly expecting the input shape of T X n which is independent of n. IMHO, it is good to keep it unchanged regarding this.

[oyamad]

@Smit-create Thanks!

[jstac]

Many thanks @Smit-create and @oyamad