The leapfrog integrator is routinely used within the Hamiltonian Monte Carlo method and its variants. We give strong numerical evidence that alternative, easy to implement algorithms yield fewer rejections with a given computational effort. When the dimensionality of the target distribution is high, the number of accepted proposals may be multiplied by a factor of three or more. This increase in the number of accepted proposals is not achieved by impairing any positive features of the sampling. We also establish new non-asymptotic and asymptotic results on the monotonic relationship between the expected acceptance rate and the expected energy error. These results further validate the derivation of one of the integrators we consider and are of independent interest.

跨跃积分器通常在汉密尔顿蒙特卡罗方法及其变体中使用。我们提供了强有力的数值证据，表明在给定的计算工作量下，易于实现的替代算法产生的拒绝次数更少。当目标分布的维数较高时，可以将接受的投标数量乘以三倍或更多倍。不能通过削弱采样的任何积极特征来实现接受提案数量的增加。我们还根据预期接受率和预期能量误差之间的单调关系建立了新的非渐近和渐近结果。这些结果进一步验证了我们考虑的且具有独立利益的集成商之一的推导。