docs: README 'Why use PyAETNA?' lists the advantages only, with the numbers of the paper

## Why Use PyAETNA?

> **Evidence-based model comparison and realistic noise models on a laptop.** On a consumer GPU, a joint fit of

> K2-140 with its Bayesian evidence takes under a minute (56 s), and one GPU-day holds about 1500 such fits.

- **One file, one command.** The data, priors, systematics, sampler and post-processing are set in a single readable

  configuration file, which an [online configurator](http://pyaetna-e92eeb.pages.ict.inaf.it/) can write for you; no

  scripting is needed.

- **Fast, on a laptop or a server.** The forward model and its derivatives are compiled with JAX and evaluated

  on many points at once, so the same configuration runs on a CPU or, faster, on a GPU. On the benchmark problems

  PyAETNA was much faster than allesfitter and faster than pyaneti with the same MCMC.

- **Trustworthy evidence.** On problems of known evidence, its nested sampler biases the Bayesian evidence several

  times less than dynesty, and the bias cancels in the Bayes factor between models.

- **Honest about its limits.** Its nested sampler needs more likelihood evaluations than juliet's or PyORBIT's, so it

  is slower than they are on a CPU, and it keeps only one of several separate peaks, which the peak search before

  sampling warns of. The numbers, with the cases where other codes are better, are in

  **[How PyAETNA compares with other codes](docs/benchmarks.md)**.

- **Agrees with the established codes.** On shared data sets, its posteriors match those of juliet, allesfitter,

  pyaneti and PyORBIT.

- **Transparent and robust.** Numerical precision is handled automatically where it matters (transit times), runs

  resume after a crash, and results are plain `.npz` and `.json` files that open with NumPy alone.

  scripting is needed, and a run ends with the reports ready to read.

- **Fast on a GPU, even a consumer one.** The forward model and its derivatives are compiled with JAX and evaluated

  on many points at once. On a laptop GPU, PyAETNA fits K2-140 2.1 times faster than juliet and 1.6 times faster than

  PyORBIT (each running on the CPUs of the same laptop), and 3.1 to 137 times faster than allesfitter. Sixteen pairs of

  runs of the two Pi Men models, with evidences, take 16 minutes against an estimated 35 hours for allesfitter. The

  same configuration also runs on CPUs: it is 1.7 to 50 times faster than allesfitter there, and 1.2 times faster than

  pyaneti with the same MCMC.

- **Evidences you can compare.** Its nested sampler returns the evidence together with the posterior, with a bias of

  0.1 to 0.2 nats on near-Gaussian posteriors, against 0.7 to 1.5 nats for dynesty, and within 0.5 nats of a

  reference nested sampler on the benchmark data. That makes it affordable to compute the evidence of every candidate

  model and to repeat it over seeds.

- **Realistic noise, at no extra setup.** Single, per-visit and multi-dimensional Gaussian processes, and

  errors-in-variables detrending, run inside the same compiled likelihood; the quasiseparable GP solver handles

  10⁵ points on a laptop GPU, and PLATO-length transit light curves are tractable on one.

- **Agrees with the established codes.** On the published data sets of juliet, allesfitter, pyaneti and PyORBIT,

  posterior medians agree within 0.7 sigma for almost all parameters, and injection-and-recovery tests give 68 % and

  95 % intervals that contain the true value in 69 % and 96 % of the cases.

- **Reproducible and robust.** Numerical precision is chosen automatically where it matters (transit times), runs

  resume after a crash, and results are plain `.npz` and `.json` files with their provenance, readable with NumPy

  alone.

For the cases where other codes are faster or better (CPU-only runs against juliet and PyORBIT, separate posterior

peaks) and for every number above, see **[How PyAETNA compares with other codes](docs/benchmarks.md)**.

## Quick Start