# Specific themes of interest

/Some specific themes we're interested in include:

- How can we best use samples once they've been collected?
- What estimators are more appropriate than the crude MC estimator for estimating expectations?
- How can such estimators be constructed, analyzed, and applied?

- How do we know when we've sampled enough?
- What MCMC convergence diagnostics are available, and when can we trust them?

- Which MCMC algorithm when?
- An extremely wide variety of sampling algorithms have been developed, often targeting a specific type of pathology (e.g. highly skewed distributions, local correlation structures, etc.). How can we systematically diagnose which sampling algorithm is most appropriate for a given sampling problem?

- Testing MCMC implementations
- Since MCMC is often the only feasible way to compute a given quantity and its output is stochastic, how can we test that our implementations are correct?

- Hybrid Monte Carlo and molecular dynamics
- Which methods are most efficient for sampling conformational distributions of large solvated systems?

- Nonequilibrium methods
- How can we use nonequilibrium fluctuation theorems to analyze and correct time-discretized SDEs?