Leverage existing ways in TuringLang (if they exist) / Julia ecosystem to approximate K in the case of Simulated Tempering

[HarrisonWilde]

When using Simulated Tempering, we require some normalising function K on the inverse temperatures, ideally we would have K(\beta) = [\int_x \pi(x)^\beta dx]^-1] to result in a uniform marginal distribution over the temperature component of the chain, the Wang-Landau algorithm can be used to learn K(\beta) but I think it has some issues, only done some preliminary reading per these papers:

• https://journals.aps.org/pre/abstract/10.1103/PhysRevE.64.056101
• https://dash.harvard.edu/bitstream/handle/1/14169382/58769082.pdf?sequence=1

Any other ideas on how to best calculate K?

[HarrisonWilde]

No plan for simulated tempering right now, we should focus on extensions to PT