Use cases for DAGResults analysis scenarios for various Protocol types

As requested, here are some potential use cases for retrieving and using sets of DAGResults for a Transformation for various Protocol types we may want to implement. They are roughly sorted from near-term to long-term. I will keep adding use cases to this as I am able.

Nonequilibrium cycling (`NonequilibriumCyclingProtocol`)

Simple BAR analysis

The simplest kind of analysis involves retrieving all results (where each result is a pair of forward/reverse work values) to estimate the free energy for the transformation and its uncertainty using BAR.

Simple BAR with bootstrapping

Current practice is to retrieve all results and estimate a distribution of free energies via bootstrapping over clones to estimate the uncertainty.

Filtering to discard data to equilibration

We have also discarded the first generation of cycles and retrieved the rest to allow the first generation to be used to "equilibrate" the pose within the binding site.

Replica exchange

MBAR analysis

If each DAGResult represents one iteration of one replica, storing energies computed at all alchemical stats for the final snapshot of that replica and the alchemical state sampled during the iteration, we will need to retrieve all results and organize these into state index and energy trajectories by each replica to perform correlation analysis and subsampling prior to constructing the input data to feed to MBAR.

xTRAM analysis

To perform xTRAM analysis, we will need to also retrieve configuration trajectories from all iterations and replicas to build a Markov state model. Generally, we build a different model for each alchemical state, so could retrieve results generated for each thermodynamic state index in a different process, with each process building an MSM in parallel.

OpenFreeEnergy / alchemiscale