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Markov chain Monte Carlo (MCMC) methods have existed for a long time and thefield is well-explored. The purpose of MCMC methods is to approximate adistribution through repeated sampling; most MCMC algorithms exhibitasymptotically optimal behavior in that they converge to the true distributionat the limit. However, what differentiates these algorithms are their practicalconvergence guarantees and efficiency. While a sampler may eventuallyapproximate a distribution well, because it is used in the real world it isnecessary that the point at which the sampler yields a good estimate of thedistribution is reachable in a reasonable amount of time. Similarly, if it iscomputationally difficult or intractable to produce good samples from adistribution for use in estimation, then there is no real-world utilityafforded by the sampler. Thus, most MCMC methods these days focus on improvingefficiency and speeding up convergence. However, many MCMC algorithms sufferfrom random walk behavior and often only mitigate such behavior as outrighterasing random walks is difficult. Hamiltonian Monte Carlo (HMC) is a class ofMCMC methods that theoretically exhibit no random walk behavior because ofproperties related to Hamiltonian dynamics. This paper introduces modificationsto a specific HMC algorithm known as the no-U-turn sampler (NUTS) that aims toexplore the sample space faster than NUTS, yielding a sampler that has fasterconvergence to the true distribution than NUTS.

SpreadNUTS -- Moderate Dynamic Extension of Paths for No-U-Turn Sampling & Partitioning Visited Regions