notes.txt

POLYCHORD:
NLive is resolution of parameter space (theta)
what is the map Hypercube -> Theta? Why do we need it.
What if we have distinct classes of Theta e.g. (Field value, Triangulation configuration).
What is ndead, posteriors?

--- Scaling with dimension ---
Assume we have fast likelihood calls.
How does (Nlive, Nrepeats, phantoms, posteriors, equals) scale with dimension?
How does slice sampling scale with dimension? Do we have to sample all Theta_i each iteration?
How does clustering scale with dimension?
How well is topological freezing handled with increasing dimension, e.g. Ising model.
How does autocorrelation in the markov chain scale with dimension compared to HMC?


GPU ising - https://github.com/NVIDIA/ising-gpu

CDT (causal dynamical triangulations) - 1+1, 1+2,
EDT (euclidean dynamical triangulations) - Tim Budd
Lattice QCD sims do 96^3 X 96 sized lattices for g-2 factor (unknown number of fields generated)
Speak to Lattice QCD group at damtp

Things to explore:
Confinement in the Schwinger model
Non flat spacetime lattices
Fermion vs Boson fields

Phi to the four with Nested Sampling
CDT with nested sampling

Gradient sampling implementation for nested sampling (HMC)
Using nested sampling for coarse grained sampling.
Termination parameter.

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Plan:
Nested Sampling with Ising Model - then phi to the four - eventually gravity.

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Lots of potential changes to improve NS as an alternative to MCMC.

Schwinger model action is non local after we integrate out the fermion fields.
This means small MCMC steps (MH) have high rejection rates as change a field value has rippling effects throughout lattice.
Therefore large proposal changes to the field configuration with high acceptance rate is more efficient (HMC).
Not sure how well slice sampling will deal with non-local likelihood (hopefully well). Good direction to explore next with schwinger model.

Add an autocorrelation term to our likelihood to factor the transition variable (temperature) for phase transition.