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fix readme headings

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NunoSempere 2023-07-23 23:29:57 +02:00
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@ -78,17 +78,18 @@ The first approach produces terser programs but might not scale. The second appr
Behaviour on error can be toggled by the `EXIT_ON_ERROR` variable. This library also provides a convenient macro, `PROCESS_ERROR`, to make error handling in either case much terser—see the usage in example 4 in the examples/ folder. Behaviour on error can be toggled by the `EXIT_ON_ERROR` variable. This library also provides a convenient macro, `PROCESS_ERROR`, to make error handling in either case much terser—see the usage in example 4 in the examples/ folder.
## Design choices ### Design choices
This code should be correct, then simple, then fast. This code should be correct, then simple, then fast.
- It should be correct. The user should be able to rely on it and not think about whether errors come from the library. - It should be correct. The user should be able to rely on it and not think about whether errors come from the library.
- Nonetheless, the user should understand the limitations of sampling-based methods. See the section on [Tests and the long tail of the lognormal](https://git.nunosempere.com/personal/squiggle.c#tests-and-the-long-tail-of-the-lognormal) for a discussion of how sampling is bad at capturing some aspects of distributions with long tails.
- It should be clear, conceptually simple. Simple for me to implement, simple for others to understand - It should be clear, conceptually simple. Simple for me to implement, simple for others to understand
- It should be fast. But when speed conflicts with simplicity, choose simplicity. For example, there might be several possible algorithms to sample a distribution, each of which is faster over part of the domain. In that case, it's conceptually simpler to just pick one algorithm, and pay the—normally small—performance penalty. In any case, though, the code should still be *way faster* than Python. - It should be fast. But when speed conflicts with simplicity, choose simplicity. For example, there might be several possible algorithms to sample a distribution, each of which is faster over part of the domain. In that case, it's conceptually simpler to just pick one algorithm, and pay the—normally small—performance penalty. In any case, though, the code should still be *way faster* than Python.
Note that being terse, or avoiding verbosity, is a non-goal. This is in part because of the constraints that C imposes. But it also aids with clarity and conceptual simplicity, as the issue of correlated samples illustrates in the next section. Note that being terse, or avoiding verbosity, is a non-goal. This is in part because of the constraints that C imposes. But it also aids with clarity and conceptual simplicity, as the issue of correlated samples illustrates in the next section.
## Correlated samples ### Correlated samples
In the original [squiggle](https://www.squiggle-language.com/) language, there is some ambiguity about what this code means: In the original [squiggle](https://www.squiggle-language.com/) language, there is some ambiguity about what this code means:
@ -243,15 +244,19 @@ Std of to(10.000000, 10000.000000): 23578.091775, vs expected std: 25836.381819
delta: -2258.290043, relative delta: -0.095779 delta: -2258.290043, relative delta: -0.095779
``` ```
Overall, I would caution that if you really care about the very far tails of distributions, you might want to instead use tools which can do some of the analytical manipulations for you, like the original Squiggle, Simple Squiggle (both linked below), or even doing lognormal multiplication by hand, relying on the fact that two lognormals multiplied together result in another lognormal with known shape.
## Related projects ## Related projects
- [Squiggle](https://www.squiggle-language.com/) - [Squiggle](https://www.squiggle-language.com/)
- [SquigglePy](https://github.com/rethinkpriorities/squigglepy) - [SquigglePy](https://github.com/rethinkpriorities/squigglepy)
- [Simple Squiggle](https://nunosempere.com/blog/2022/04/17/simple-squiggle/) - [Simple Squiggle](https://nunosempere.com/blog/2022/04/17/simple-squiggle/)
- [time to botec](https://github.com/NunoSempere/time-to-botec) - [time to botec](https://github.com/NunoSempere/time-to-botec)
- [beta]()
## To do list ## To do list
- [ ] Link to the examples in the examples section.
- [ ] Have some more complicated & realistic example - [ ] Have some more complicated & realistic example
- [ ] Add summarization functions: 90% ci (or all c.i.?) - [ ] Add summarization functions: 90% ci (or all c.i.?)
- [ ] Systematize references - [ ] Systematize references
@ -299,3 +304,5 @@ delta: -2258.290043, relative delta: -0.095779
- https://stats.stackexchange.com/questions/502146/how-does-numpy-generate-samples-from-a-beta-distribution - https://stats.stackexchange.com/questions/502146/how-does-numpy-generate-samples-from-a-beta-distribution
- https://github.com/numpy/numpy/blob/5cae51e794d69dd553104099305e9f92db237c53/numpy/random/src/distributions/distributions.c - https://github.com/numpy/numpy/blob/5cae51e794d69dd553104099305e9f92db237c53/numpy/random/src/distributions/distributions.c
- [x] Pontificate about lognormal tests - [x] Pontificate about lognormal tests
- [x] Give warning about sampling-based methods.
- [ ]