How is the true value of Tau in the Eight Schools model known?

Questions
1

I’m reading through Michael Betancourt’s writeup of the Eight Schools model and I’m wondering, how the true value of log(tau) is known to be 0.7657852. I’m also confused because if its known why even bother simulated draws from its distribution to try and estimate it?

Does anyone know what I’m missing?

Thanks in advance.

http://mc-stan.org/users/documentation/case-studies/divergences_and_bias.html
https://docs.pymc.io/notebooks/Diagnosing_biased_Inference_with_Divergences.html

2

From what I gather Gelman and the Stan team runs some very long chains using a carefully hand tuned HMC with many different validation to estimate it. Since then they are using those value as benchmark and validation on new sampling algorithm or modification of existing algorithms.