8 problems

Longer-chain improvement conjecture. Running these chains longer is likely to result in improved estimation.

Let $g$ be the function used to impose oscillatory dynamics in the point-process sampler, and let mixing time and asymptotic variance be efficiency metrics. Oscillatory-dynamics ef…

Consider the point-process sampler and the birth-death sampler for a target distribution on a discrete state space, and let $\textsc{ess}$ denote the effective sample size. Point-p…

Dimension-dependence conjecture. Replacing the random-walk Metropolis--Hastings sampler in each local chain $M_i$ by a proximal sampler or a Metropolis-adjusted Langevin algorithm…

Consider a diagram formed by vertical and horizontal cuts, where a diagram corresponds to a tree when it can be represented by the recursive subdivision associated with a decision…

Consider an MCMC-based annealing algorithm, such as simulated annealing or rapid simulated annealing, applied to a planted inference problem. Let $T_\text{\tiny KS}$ be the critica…

The paper considers rough target densities and the anomalous scaling behavior of Metropolis–Hastings chains exhibited by its examples. Typicality conjecture. Despite the examples b…

Let $P$ be a reversible transition matrix with stationary distribution $\pi$, and let its corresponding graph have vertices given by the states and an edge between distinct states…