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

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)

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

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

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

Impact of Selected Infrared Wavelengths on Inactivation of Microbes on Rough Rice

Formation of harmful microbes and their associated mycotoxins on rough rice during storage presents negative socioeconomic impacts to producers and consumers. The objective for this study was to investigate the impact of treating rough rice with selected infrared (IR) wavelengths at different IR intensities and heating durations, followed by a tempering step for further inactivation of microbes (mold and bacteria) on the grain. Freshly-harvested long-grain, hybrid, rough rice (XL 745) with initial moisture content (IMC) of 18.4% wet basis (w.b.) was used. Two-hundred grams (200 g) samples of rice were treated at different IR wavelengths (λ), 3.2, 4.5, and 5.8 μm for 10, 20 and 30 seconds (s); at product-to-emitter gaps of 110, 275, and 440 mm. This was then followed by tempering the grain; putting samples in air-tight jars and holding at a constant temperature of 60 oC for 4 hours (h). Inoculated Petrifilm plates for mold and bacterial analyses were incubated at 25 oC for 120 h and 35 oC for 48 h respectively. Samples treated at wavelength 3.2 μm (product-to-emitter gap 110 mm) for 30 s showed the greatest reduction in mold and bacterial load; approximately 3.11 and 1.09 log reduction in the colony forming unit of mold and bacteria, respectively. Microbial analysis was performed on the rice prior to tempering, then all of the rice was tempered and microbial analysis was performed again to analyze the effectiveness of a tempering step. Tempering treatment further reduced the microbial load at each IR treatment condition. Molds showed more susceptibility to the IR decontamination than bacteria. This study provides useful information on the effectiveness of IR heating and tempering on microbial inactivation on rough rice