Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs

A computational approach to determine the equilibrium structures of nanoclusters in the whole temperature range from 0 K to melting is developed. Our approach relies on Parallel Tempering Molecular Dynamics...

Comparison of Bayesian Methods for Recovering Sinusoids

In this paper, we study a problem of estimating parameters of sinusoids from noisy data within Bayesian inferential framework. In this context, three different computational schemes such as, Bretthorst’s integral method (BRETTHORST), Gibbs sampling (GIBBS) and parallel tempering (PT) are studied and modifications of their algorithms were tested on data generated from synthetic signals. In addition, our emphasis is given to a comparison of their performances with respect to Cramér-Rao lower bound (CRLB).

Algorithmic Parameter Estimation and Uncertainty Quantification for Hodgkin-Huxley Neuron Models

Experimental data-based parameter search for Hodgkin-Huxley-style (HH) neuron models is a major challenge for neuroscientists and neuroengineers. Current search strategies are often computationally expensive, are slow to converge, have difficulty handling nonlinearities or multimodalities in the objective function, or require good initial parameter guesses. Most important, many existing approaches lack quantification of uncertainties in parameter estimates even though such uncertainties are of immense biological significance. We propose a novel method for parameter inference and uncertainty quantification in a Bayesian framework using the Markov chain Monte Carlo (MCMC) approach. This approach incorporates prior knowledge about model parameters (as probability distributions) and aims to map the prior to a posterior distribution of parameters informed by both the model and the data. Furthermore, using the adaptive parallel tempering strategy for MCMC, we tackle the highly nonlinear, noisy, and multimodal loss function, which depends on the HH neuron model. We tested the robustness of our approach using the voltage trace data generated from a 9-parameter HH model using five levels of injected currents (0.0, 0.1, 0.2, 0.3, and 0.4 nA). Each test consisted of running the ground truth with its respective currents to estimate the model parameters. To simulate the condition for fitting a frequency-current (F-I) curve, we also introduced an aggregate objective that runs MCMC against all five levels simultaneously. We found that MCMC was able to produce many solutions with acceptable loss values (e.g., for 0.0 nA, 889 solutions were within 0.5% of the best solution and 1,595 solutions within 1% of the best solution). Thus, an adaptive parallel tempering MCMC search provides a "landscape" of the possible parameter sets with acceptable loss values in a tractable manner. Our approach is able to obtain an intelligently sampled global view of the solution distributions within a search range in a single computation. Additionally, the advantage of uncertainty quantification allows for exploration of further solution spaces, which can serve to better inform future experiments.

Evidence for Influenza and RSV interaction from 10 years of enhanced surveillance in Nha Trang, Vietnam, a modelling study.

Influenza and Respiratory Syncytial Virus (RSV) interact within their host posing the concern for heterologous ecological changes following vaccination. We aimed to estimate the population level impact of their interaction. We developed a dynamic age-stratified two-pathogen mathematical model that includes pathogen interaction through competition for infection and enhanced severity of dual infections. We used parallel tempering to fit it's parameters to 11 years of enhanced hospital-based surveillance for acute respiratory illnesses (ARI) in children under 5 years old in Nha Trang, Vietnam. The data supported either a 41% (95%CrI: 36 - 54) reduction in heterologous acquisition during infection and for 10.0 days (95%CrI 7.1 -12.8) thereafter, or no cross protection. We estimate that co-infection increased the probability for an infection in <2y old children to be reported 7.2 fold (95%CrI 5.0 - 11.4); or 16.6 fold (95%CrI 14.5 - 18.4) in the respective scenarios. Absence of either pathogen was not to the detriment of the other. We find stronger evidence for severity enhancing than for acquisition limiting interaction. In this setting vaccination against either pathogen is unlikely to have a major detrimental effect on the burden of disease caused by the other.

Anytime parallel tempering

Developing efficient MCMC algorithms is indispensable in Bayesian inference. In parallel tempering, multiple interacting MCMC chains run to more efficiently explore the state space and improve performance. The multiple chains advance independently through local moves, and the performance enhancement steps are exchange moves, where the chains pause to exchange their current sample amongst each other. To accelerate the independent local moves, they may be performed simultaneously on multiple processors. Another problem is then encountered: depending on the MCMC implementation and inference problem, local moves can take a varying and random amount of time to complete. There may also be infrastructure-induced variations, such as competing jobs on the same processors, which arises in cloud computing. Before exchanges can occur, all chains must complete the local moves they are engaged in to avoid introducing a potentially substantial bias (Proposition 1). To solve this issue of randomly varying local move completion times in multi-processor parallel tempering, we adopt the Anytime Monte Carlo framework of (Murray, L. M., Singh, S., Jacob, P. E., and Lee, A.: Anytime Monte Carlo. arXiv preprintarXiv:1612.03319, (2016): we impose real-time deadlines on the parallel local moves and perform exchanges at these deadlines without any processor idling. We show our methodology for exchanges at real-time deadlines does not introduce a bias and leads to significant performance enhancements over the naïve approach of idling until every processor’s local moves complete. The methodology is then applied in an ABC setting, where an Anytime ABC parallel tempering algorithm is derived for the difficult task of estimating the parameters of a Lotka–Volterra predator-prey model, and similar efficiency enhancements are observed.

Generalized parallel tempering on Bayesian inverse problems

In the current work we present two generalizations of the Parallel Tempering algorithm in the context of discrete-time Markov chain Monte Carlo methods for Bayesian inverse problems. These generalizations use state-dependent swapping rates, inspired by the so-called continuous time Infinite Swapping algorithm presented in Plattner et al. (J Chem Phys 135(13):134111, 2011). We analyze the reversibility and ergodicity properties of our generalized PT algorithms. Numerical results on sampling from different target distributions, show that the proposed methods significantly improve sampling efficiency over more traditional sampling algorithms such as Random Walk Metropolis, preconditioned Crank–Nicolson, and (standard) Parallel Tempering.