Update made to Markov Chains: Basic Concepts lecture

[Jiarui-ZH]

Update to Markov Chains: Basic Concepts lecture (#453 )

Content

• In “A stochastic matrix (or Markov matrix) is an 𝑛×𝑛 square matrix 𝑃 such that each row of 𝑃 is a probability mass function over 𝑛 outcomes.” delete “over 𝑛 outcomes”.
• Change titles “32.2.2.1. Example 1” and “32.2.2.2. Example 2” into titles that are intuitive of the respective examples. )
• For Example 3 (the example for democracy (D), autocracy (A), and an intermediate state called anocracy (N)), implement the following order: table; figure; matrix.
• Change date to time in section of “32.2.3. Defining Markov chains”
• Add “(probability mass function)” such that “𝑃(𝑥,⋅) is the conditional distribution (probability mass function) of 𝑋𝑡+1 given.”
• In “It can be shown that for a long series drawn from P, the fraction of the sample that takes value 0 will be about 0.25.”, change to “It can be proven that for a long series drawn from P, the fraction of the sample that takes value 0 will be about 0.25.”
• In the section “32.4. Distributions over time”, have subsections dividing into two parts: “One unit of time” and “m steps in the future”
• In 32.4.1, move the function above (after “m-th power of 𝑃”). After the function, add text “For one way to see it, consider again (32.6), but now with a 𝜓𝑡 that puts all probability on state 𝑥.
• Then 𝜓𝑡 is a vector with 1 in position 𝑥 and zero elsewhere.
• Inserting this into (32.6), we see that, conditional on 𝑋𝑡=𝑥, the distribution of 𝑋𝑡+𝑚 is the 𝑥-th row of 𝑃𝑚.”
• In 32.4.2, instead of the link “considered above”, include the section number (32.4.1) with a link.
• Search for “considered above” and replace it with section number and make sure the hyperlink works. (In pdf version, the “considered above” link does not work.)
• In 32.4.3, in (2), put a note to better explain “cross-sectional frequencies”.

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[mmcky]

Thanks @Jiarui-ZH just some minor comments below

[Jiarui-ZH]

@mmcky, Thank you for the review, please let me know if there is any thing else I need to change!

[mmcky]

thanks @Jiarui-ZH there are some undefined labels that need to be fixed. Once this is building I will do a full review.

• /home/runner/work/lecture-python-intro/lecture-python-intro/lectures/markov_chains_I.md: WARNING: label 'mc_eg2' not found.
• /home/runner/work/lecture-python-intro/lecture-python-intro/lectures/markov_chains_I.md:627: WARNING: prf:ref reference target not found: mc_eg2
• /home/runner/work/lecture-python-intro/lecture-python-intro/lectures/markov_chains_I.md: WARNING: label 'mc_eg1' not found.
• /home/runner/work/lecture-python-intro/lecture-python-intro/lectures/markov_chains_I.md:649: WARNING: prf:ref reference target not found: mc_eg1
• /home/runner/work/lecture-python-intro/lecture-python-intro/lectures/markov_chains_I.md: WARNING: label 'mc_eg1' not found.
• /home/runner/work/lecture-python-intro/lecture-python-intro/lectures/markov_chains_I.md:743: WARNING: prf:ref reference target not found: mc_eg1
• /home/runner/work/lecture-python-intro/lecture-python-intro/lectures/markov_chains_I.md: WARNING: label 'mc_eg2' not found.
• /home/runner/work/lecture-python-intro/lecture-python-intro/lectures/markov_chains_I.md:857: WARNING: prf:ref reference target not found: mc_eg2

[Jiarui-ZH]

Hi @mmcky , sorry for the trouble but can you give me a short rundown on the how prf:ref is used? I am still unclear with the referring of markdown

[mmcky]

Hi @mmcky , sorry for the trouble but can you give me a short rundown on the how prf:ref is used? I am still unclear with the referring of markdown

Hi @Jiarui-ZH here are the docs re: syntax

https://sphinx-proof.readthedocs.io/en/latest/syntax.html

you essentially use the label that is assigned to the directive item as a reference such as:

{prf:ref}`my-theorem`

[Jiarui-ZH]

Everything except for simplifying figures is mentioned in #453 is resolved

[mmcky]

@jstac this is ready for your review.

[mmcky]

thanks @Jiarui-ZH for opening #502. We can deal with that separately.

[Jiarui-ZH]

@mmcky I have tried to use the sphinix-proof for exampeles however the following warning pops up. I am not sure why this is happening it would be great if you can review this.

[mmcky]

Thanks for reaching out @Jiarui-ZH.

The main issues were:

1. The example directives were missing a closing gate using backticks.
2. When you have nested directives it is best practice to use different levels of backticks. So the main example directive would use 4 ticks while the nested directives use 3 ticks.

See 088d92b for fixes.

[Jiarui-ZH]

ahh I see, thank you for the fixes

[mmcky]

@Jiarui-ZH are there any other additions you are planning to make to this PR?

[Jiarui-ZH]

@mmcky Sorry for the late reply I have been swamped with deferred exams. I have made my final update to this lecture. Please let me know if there is anything else I should update

[Jiarui-ZH]

for Example 1: Economic states and Example 2: Unemployment which are the only two examples that were referred back to later in the lecture I left them as they are as I thought they are a bit long to be using prf:example and looks neat enough already