++Tutorial: "Mathematical Transformations of Spatially Balanced Samples"

[falkmielke]

Description

A brief writeup of some useful tweaks I first implemented here for the MNM project.
I found this of general relevance, and spiced it up with references to spatially balanced sampling and basic application of functional programming.

Task list

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[bserrien]

Hi Falk, this is a very interesting tutorial! I am not an expert in spatial sampling (but I'm trying to learn it on my own), but everything is conceptually clear to me (I'll have to deal with the mathematics of Halton sequences another time). As a non-expert, I would mainly benefit from having more examples in the tutorial, maybe in the form of references to specific applications. Some examples:

• (3) Choose Your Distribution Pattern: And in many applications, it is a valid strategy to give points closer to the center a higher chance of being chosen [?? EXAMPLE ??], or to have a sampling pattern that reduces likelihood with distance from center, or just the opposite (i.e. bias towards the rim) [?? EXAMPLE ??].
• Spatial Balance - in a Weird Way: Close to the center, it is high, but it reduces towards the edges of our circle. Logical, if you think about it: the orbits close to the center are much shorter, yet they house equally many points as the distant orbits. This outcome might be fine in some situations [?? EXAMPLE ??], but undesired in others [?? EXAMPLE ??].
• If you would have real-life examples for the special variants (line 508 and further) that would be cool, but the tutorial is fine without.

On line 339 there is a typo: it refers to apply_transform but it was coded as apply_trafo.

Thanks for writing this nice tutorial!

[falkmielke]

Hi Falk, this is a very interesting tutorial! I am not an expert in spatial sampling (but I'm trying to learn it on my own), but everything is conceptually clear to me (I'll have to deal with the mathematics of Halton sequences another time). As a non-expert, I would mainly benefit from having more examples in the tutorial, maybe in the form of references to specific applications. Some examples:

• (3) Choose Your Distribution Pattern: And in many applications, it is a valid strategy to give points closer to the center a higher chance of being chosen [?? EXAMPLE ??], or to have a sampling pattern that reduces likelihood with distance from center, or just the opposite (i.e. bias towards the rim) [?? EXAMPLE ??].
• Spatial Balance - in a Weird Way: Close to the center, it is high, but it reduces towards the edges of our circle. Logical, if you think about it: the orbits close to the center are much shorter, yet they house equally many points as the distant orbits. This outcome might be fine in some situations [?? EXAMPLE ??], but undesired in others [?? EXAMPLE ??].
• If you would have real-life examples for the special variants (line 508 and further) that would be cool, but the tutorial is fine without.

On line 339 there is a typo: it refers to apply_transform but it was coded as apply_trafo.

Thanks for writing this nice tutorial!

Great suggestions, thank you for reviewing, @bserrien !

I have added (fully made-up) examples; and although I would prefer actual applications, I hope they serve the purpose of illustration.

Note: I have also moved the figures to /static, which is "good practice" for hugo but seems not common practice on this website. I have tested and it should work on the website, but please double check.

[bserrien]

Hello Falk, thank you for adding some real-life examples for the spatial patterns of sampling more towards the center or more towards the edge. I found them very helpful to understand the rationale for the tutorial. Nice work!