用不可逆吉布斯取样技术模拟回火
Simulated tempering with irreversible Gibbs sampling techniques
摘要：
本文提出了两种新的模拟回火算法，该算法打破了细致平衡条件（DBC），但满足倾斜的细致平衡，以保证目标分布的不变性。我们在这里提出的不可逆方法是基于吉布斯采样和关注打破DBC的温度交换的更新方案。我们利用三个系统作为我们的方法的测试床：MCMC模拟一个简单的系统所描述的一维双阱势，伊辛模型和MD模拟丙氨酸五肽（ALA 5）。伊辛模型的逆温度、磁化率和能量密度的弛豫时间表明，与传统的Gibbs采样技术和DBC相比，以及与传统使用的Metropolis-Hastings（MH）方案相比，采样效率明显提高。ALA 5与大量的温度的模拟表明，在混合时间的逆温度，从而系统的能量相比，传统的MH的明显收益。没有额外的计算开销，我们的方法被发现是更有效的替代传统使用的模拟回火方法与DBC。我们的算法应该是特别有利的，在模拟具有许多温度阶梯的大型系统，因为我们的算法显示了更有利的常数缩放伊辛自旋系统相比，可逆和不可逆MH算法。在未来的应用中，我们的不可逆方法也可以很容易地定制，以利用给定的动力学变量而不是温度来平整崎岖的自由能景观。
英文摘要：
We present here two novel algorithms for simulated tempering simulations, which break detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we present here are based on Gibbs sampling and concern breaking DBC at the update scheme of the temperature swaps. We utilise three systems as a test bed for our methods: an MCMC simulation on a simple system described by a 1D double well potential, the Ising model and MD simulations on Alanine pentapeptide (ALA5). The relaxation times of inverse temperature, magnetic susceptibility and energy density for the Ising model indicate clear gains in sampling efficiency over conventional Gibbs sampling techniques with DBC and also over the conventionally used simulated tempering with Metropolis-Hastings (MH) scheme. Simulations on ALA5 with large number of temperatures indicate distinct gains in mixing times for inverse temperature and consequently the energy of the system compared to conventional MH. With no additional computational overhead, our methods were found to be more efficient alternatives to conventionally used simulated tempering methods with DBC. Our algorithms should be particularly advantageous in simulations of large systems with many temperature ladders, as our algorithms showed a more favorable constant scaling in Ising spin systems as compared with both reversible and irreversible MH algorithms. In future applications, our irreversible methods can also be easily tailored to utilize a given dynamical variable other than temperature to flatten rugged free energy landscapes.
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