New chapter "Metropolis" with Python Implementation #929
Conversation
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I feel like this would make more sense grouped together with monte carlo under "Monte Carlo Methods", and rename monte carlo to "Approximating Areas" |
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I dislike using numpy. It's specialised enough that not everyone will know it, and it has no counterpart in many languages. It could be replaced here with |
I agree - they belong in a similar category. |
I'm not sure I agree, but I see where you're coming from, with |
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Overall, I think the quality here is good. I a few lingering remarks that I didn't mention yet:
- I think random walk should not be capitalized in the text body
- It would be nice to talk briefly about how this is used in practice. I know it's used a lot in various physical applications, so maybe pointing to those with citations would be nice. I like that the code is for a general PDF, but maybe mentioning Mawell--Boltzmann or something would make the physics folk happy
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For numpy, I think it's fine in this case. As someone coming from an HPC background, I genuinely thought the first thing everyone did when using python was to import numpy. I think we should be cognizant of the fact that this is not true for everyone and maybe remove numpy from less numerical methods. |
Co-authored-by: James Schloss <jrs.schloss@gmail.com>
Mostly typos, spelling, punctuation, and grammar. Co-authored-by: James Schloss <jrs.schloss@gmail.com>
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I need to tell you two things @shudipto-amin. First we receive a notification on the discord server after every single commit. Second, I have a few problems with your notation, since I come from a mathematical background, the main thing being that I have never seen the [2..12] notation used anywhere. I have already seen "double brackets" (something that looks like I[2, 12]I, I can't reproduce it better right now) and $ [2, 12] \cap \mathbb{N}$ for the integer interval [2, 12]. |
I'm sorry about that, I was adding from conversations where that seems to be the only option. Later, I did discover that option in the files tab, and started batching about half-way through.
I personally only discovered this notation recently - I normally see something like your example with |
No problem, but keep that in mind for the future.
Yeah, that just tells me we need a mathematical notation chapter. I personally would prefer the ⟦a, b⟧ notation, but that's not a native latex symbol if I remember correctly. |
Mostly punctuation and grammar. Co-authored-by: James Schloss <jrs.schloss@gmail.com>
Yeah, it looks good :) |
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| ## The Algorithm for a One Dimensional Example | ||
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There should be a comment here introducing the upcoming sections
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Couldn't come up with anything other than the line (147) below. Feel free to throw in some suggestions.
| {% endmethod %} | ||
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| However, $$g$$ can be any function symmetric about $$0$$ for the above algorithm to work. | ||
| For example, it can be a number chosen randomly from a discrete list, such as $$[ -3, -1, -1, +1, +1, +3]$$. |
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To be clear: this was meant to have multiple 1's, right?
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Yes, just to illustrate that g doesn't have to be uniform, only symmetric.
Mostly grammar and sentence structure. Co-authored-by: James Schloss <jrs.schloss@gmail.com>
| {% endmethod %} | ||
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| However, $$g$$ can be any function symmetric about $$0$$ for the above algorithm to work. | ||
| For example, it can be a number chosen randomly from a discrete list, such as $$[ -3, -1, -1, +1, +1, +3]$$. |
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Yes, just to illustrate that g doesn't have to be uniform, only symmetric.
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| ## The Algorithm for a One Dimensional Example | ||
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Couldn't come up with anything other than the line (147) below. Feel free to throw in some suggestions.
…ithm-archive into metropolis_in_python
contents/metropolis/metropolis.md
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| On the other hand, a walker with a large step size may not sample nearby regions accurately – and actually has a higher chance of being rejected if the walker is already in a high probability region, since the acceptance ratio is more drastic for large steps. | ||
| The effect of step-size on the walker's efficiency is far from obvious! | ||
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| How to choose $$g$$ is in itself a research field and depends on what the goal of the sampling is. |
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| How to choose $$g$$ is in itself a research field and depends on what the goal of the sampling is. | |
| How to choose $$g$$ is in itself a research field and depends on what the goal of the sampling is. |
| How to choose $$g$$ is in itself a research field and depends on what the goal of the sampling is. | |
| How to choose $$g$$ is, itself, a research field and depends on what the goal of the sampling is. |
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| if __name__ == "__main__": | ||
| xmin, xmax = -7, 7 |
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Didn't we say in the chapter that our domain was from -10 to 10?
* Minor edits for grammar and clarity. * Applies to both metropolis and probablity chapters. Co-authored-by: James Schloss <jrs.schloss@gmail.com>
Co-authored-by: Shudipto <32040453+shudipto-amin@users.noreply.github.com>
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