Update markov_chains_II.md #462
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This pull request update the lecture markov_chains_II.md based on #460 In particular, the changes include: - "We discussed uniqueness of stationary distributions our [earlier lecture on Markov chains](https://intro.quantecon.org/markov_chains_I.html)" -> We discussed uniqueness of stationary distributions in our [earlier lecture on Markov chains](https://intro.quantecon.org/markov_chains_I.html). - Unify`mathbb` for indicator function. - "an initial." -> "an initial". - Fix capitalization of the subtitle. - Discussed before -> discussed in [add doc link]. -`1 + np.arrange(ts_length)` -> `np.arrange(1, ts_length + 1)`. - Change the time length for the periodic chain. - Political institution mode -> political institution model. - Remove the `alpha` parameter for 33.3.4 graph and remove the `figsize`. - Add a seed for the `mc.simulate` (@longye-tian). - Delete https://intro.quantecon.org/markov_chains_II.html#expectations-of-geometric-sums. - Change the graph to the simple one in the exercise. - Change the number in the range to len(P)
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@longye-tian I just merged Humphrey's fixes for this lecture in #459. can you merge in the latest main when you're ready. Please let me know if you need any help with the conflict. |
Thank you @mmcky. I just merged the conflict! |
| @@ -196,16 +196,16 @@ This gives us another way to interpret the stationary distribution (provided irr | |||
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| Importantly, the result is valid for any choice of $\psi_0$. | |||
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| The theorem is related to {doc}`the Law of Large Numbers <lln_clt>`. | |||
| The theorem is related to {doc}`the law of large numbers <lln_clt>`. | |||
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@jstac re: style guide. Do we want to always use {doc} without replacing the title text (i.e. leaving the title text from the lecture it references) or have a more nuanced approach using replacement text in some cases where it makes sense. Just thinking of a "rule" we can have in the style guide.
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Good question @mmcky . I think we should default to the title text but replace it when clarity is enhanced. In this case it's enhanced.
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thanks @jstac I will add a section to our style guide.
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| for x0 in range(8): | ||
| for x0 in range(len(P)): |
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👏 for removing the magic numbers. Really nice work @longye-tian
lectures/markov_chains_II.md
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| * $\mathbb{1} \{X_t = x\} = 1$ if $X_t = x$ and zero otherwise. | ||
| * $\{X_t\}$ is a Markov chain with stochastic matrix $P$ and initial distribution $\psi_0$ | ||
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| * $\mathbf{1} \{X_t = x\} = 1$ if $X_t = x$ and zero otherwise. |
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@longye-tian , I think this should be mathbb. (We should make all of them \mathbb{1}.)
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Yes, thank you for pointing this out! I have just updated this issue.
lectures/markov_chains_II.md
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| It tells us that, in some settings, the law of large numbers sometimes holds even when the | ||
| sequence of random variables is [not IID](iid_violation). | ||
| sequence of random variables is {ref}`not IID <iid_violation>`. |
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@longye-tian , is this different? I have a feeling the html will be the same...
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It will be the same. I changed this line while I was doing troubleshooting. (I was a bit desperate hhaha :))
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I just changed them back
Best ❤️
Longye
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These are big improvements @longye-tian , many thanks! Please address the small comments above. |
Update related to #463
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Thanks @longye-tian , much appreciated. |
Dear @jstac ,
I have updated the lecture: markov_chains_II.md, based on #460.
In particular, the changes include:
mathbbfor indicator function.1 + np.arrange(ts_length)->np.arrange(1, ts_length + 1).alphaparameter for the 33.3.4 graph and remove thefigsize.mc. simulateIn addition, I have opened a new issue to discuss the way to add the definition of accessibility, as it may require altering the main text.
Thank you for reviewing the changes ❤️
Longye