Accelerating Parallel Tempering: Quantile Tempering Algorithm (QuanTA)

Using MCMC to sample from a target distribution, $\pi(x)$ on a $d$-dimensional state space can be a difficult and computationally expensive problem. Particularly when the target exhibits multimodality, then the traditional methods can fail to explore the entire state space and this results in a bias sample output. Methods to overcome this issue include the parallel tempering algorithm which utilises an augmented state space approach to help the Markov chain traverse regions of low probability density and reach other modes. This method suffers from the curse of dimensionality which dramatically slows the transfer of mixing information from the auxiliary targets to the target of interest as $d \rightarrow \infty$. This paper introduces a novel prototype algorithm, QuanTA, that uses a Gaussian motivated transformation in an attempt to accelerate the mixing through the temperature schedule of a parallel tempering algorithm. This new algorithm is accompanied by a comprehensive theoretical analysis quantifying the improved efficiency and scalability of the approach; concluding that under weak regularity conditions the new approach gives accelerated mixing through the temperature schedule. Empirical evidence of the effectiveness of this new algorithm is illustrated on canonical examples

Parallel Tempering: Theory, Applications, and New Perspectives

We review the history of the parallel tempering simulation method. From its origins in data analysis, the parallel tempering method has become a standard workhorse of physiochemical simulations. We discuss the theory behind the method and its various generalizations. We mention a selected set of the many applications that have become possible with the introduction of parallel tempering and we suggest several promising avenues for future research.Comment: 21 pages, 4 figure

N-fold way simulated tempering for pairwise interaction point processes

Pairwise interaction point processes with strong interaction are usually difficult to sample. We discuss how Besag lattice processes can be used in a simulated tempering MCMC scheme to help with the simulation of such processes. We show how the N-fold way algorithm can be used to sample the lattice processes efficiently and introduce the N-fold way algorithm into our simulated tempering scheme. To calibrate the simulated tempering scheme we use the Wang-Landau algorithm

Weight-Preserving Simulated Tempering

Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for different inverse-temperature values, sometimes dramatically so. In this paper, we provide a fix to overcome this problem, by adjusting the mode weights to be preserved (i.e., constant) over different inverse-temperature settings. We then apply simulated tempering algorithms to multimodal targets using our mode weight correction. We present simulations in which our weight-preserving algorithm mixes between modes much more successfully than traditional tempering algorithms. We also prove a diffusion limit for an version of our algorithm, which shows that under appropriate assumptions, our algorithm mixes in time O(d [log d]^2)

Correlating fissure occurrence to rice quality for various drying and tempering treatments

When a rice kernel fissures, it can break in subsequent food processing operations and lose its commercial value. Head rice yield (HRY) is a measure of the percent of kernels that remain whole (at least three-fourths of original length) after rice has been milled. Our experiment was designed to test the effect of a rapid state transition during drying and tempering processes using cultivars Bengal and Cypress. ‘Bengal’ is a medium-size kernel and ‘Cypress’ is a longsize, thinner grained cultivar. Immediately after drying, the rice samples were separated into four sub-samples and tempered for 0, 80, 160, or 240 minutes at the temperature of the drying air. Tempering is a process to allow kernel moisture content gradients to decrease, thereby reducing the stress within the kernel. From each sample, 400 kernels were randomly selected, visually observed, and the percentage of fissured kernels determined. Results showed that the percentage of fissured kernels generally decreased with tempering. However, some samples still showed many fissures even after extended tempering, yet had a high HRY. While HRY is currently the primary index of rice quality, it is known that fissured kernels can severely and detrimentally affect end-use processing operations such as cooking or puffing. Thus, the tempering duration required for preventing kernel fissuring might be longer than the tempering duration required for maintaining a high HRY

Replica-Exchange Simulated Tempering Method for Simulations of Frustrated Systems

We propose a new method for the determination of the weight factor for the simulated tempering method. In this method a short replica-exchange simulation is performed and the simulated tempering weight factor is obtained by the multiple-histogram reweighting techniques. The new algorithm is particularly useful for studying frustrated systems with rough energy landscape where the determination of the simulated tempering weight factor by the usual iterative process becomes very difficult. The effectiveness of the method is illustrated by taking an example for protein folding.Comment: 8 pages, (ReVTeX), 5 figures, Chem. Phys. Lett., submitte