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Monte Carlo Methods

Abstracts

  • 12:00 - 12:40 Gareth Roberts (Warwick, Statistics)
    Introduction to adaptive Markov Chain Monte Carlo (slides)

    This talk will motivate and introduce adaptive mcmc and will discuss theory underpinning its use, including the 'diminishing adaptation' and 'containment' conditions for ergodicity.

  • 12:40 - 13:10 Mike Allen, Adam Swetnam (Warwick, Physics), Charles Brett (Warwick, Mathematics)
    Lattice peptide simulations using the Wang-Landau Monte Carlo method (slides)

    We report our recent simulations of lattice polymers and peptides adsorbed on a planar surface, and confined between two planar surfaces. Following the approach of Bachmann and Janke [1,2] we attempt to determine the full density of states for a single molecule in the vicinity of the surface. This allows the construction of a pseudophase diagram as a function of temperature and the parameters controlling the adsorption or confinement, specifically the surface energy and the compressive or tensile force respectively. We use the Wang-Landau sampling method combined with pull moves [3], and study both simple lattice homopolymers and the HP model of peptides. The talk will summarize some of the techniques that we have developed to study surface-adsorbed chains [4] and to improve the convergence of the simulations [5], as well as our recent studies of ring polymers exploring the different behaviour exhibited by different topological knot states.
    References:
    [1] M. Bachmann and W. Janke, Phys. Rev. Lett., 91, 208105 (2003).
    [2] M. Bachmann and W. Janke, J. Chem. Phys., 120, 6779 (2004).
    [3] T. Wüst and D. P. Landau, Comput. Phys. Commun., 179, 124 (2008).
    [4] A. D. Swetnam and M. P. Allen, Phys. Chem. Chem. Phys., 11, 2046 (2009).
    [5] A. D. Swetnam and M. P. Allen, J Comput. Chem. 32, 816 (2011).

  • 14:00 - 14:40 David Wild (Warwick, Systems Biology)
    Exploring the energy landscapes of protein folding simulations with Bayesian computation

    Nested sampling is a technique developed to explore probability distributions localised in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence (marginal likelihood) of the model. Previous applications of the algorithm have yielded large effciency gains over other sampling techniques, including parallel tempering. In this work we apply the nested sampling algorithm to the problem of protein folding in a Go-type force eld of empirical potentials that were designed to stabilize secondary structure elements in room-temperature simulations. A topological analysis of the posterior samples is performed to produce energy landscape charts, which give a high level description of the potential energy surface for the protein folding simulations. These charts provide qualitative insights into both the folding process and the nature of the model and force eld used.
    We demonstrate the method by conducting folding simulations on a number of small proteins which are commonly used for testing protein folding procedures: protein G, the SH3 domain of Src tyrosine kinase and chymotrypsin inhibitor 2. We compare our results for protein G to those obtained using parallel tempering with the same model. The topology of the protein molecule emerges as a major determinant of the shape of the energy landscape. The nested sampling algorithm also provides an effcient way to calculate free energies and the expectation value of thermodynamic observables at any temperature, through a simple post-processing of the output.
    This is joint work with Nikolas S. Burkoff.

  • 14:40 - 15:20 Adam Johansen (Warwick, Statistics)
    Monte Carlo Solution of Integral Equations (of the Second Kind) (slides)

    We propose an original approach to solve Fredholm equations of the second kind. We interpret the standard von Neumann expansion of the solution as an expectation with respect to a probability distribution defined on an union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov Chain Monte Carlo (MCMC) methods such as Reversible Jump MCMC to approximate the solution numerically. This can be an attractive alternative to standard Sequential Importance Sampling (SIS) methods routinely used in this context. Computational results will be presented to motivate the method.
  • 15:50 - 16:30 David Cheung (Warwick, Chemistry)
    Monte Carlo simulations of interfaces (slides)

    There has been much interest in the adsorption of nanoscale particles onto soft interfaces, as a means to the formation of dense, ordered nanoparticle structures and to stabilise nanocomposite materials. In this presentation I will discuss some recent simulation work studying the behaviour of nanoparticles at soft interfaces. Using Monte Carlo simulations the adhesion of nanoparticles on a model liquid-liquid interface is studied, with particular emphasis on the nanoparticle-interface interaction and how this is affected by changes to particle size and structure [1,2]. Simulations of the patterning of polymer vesicles by nanoparticles in order to reproduce the patterns seen experimentally and to study the factors that control this will also be presented [3].
    References:
    [1] D. L. Cheung and S. A. F. Bon, Phys. Rev. Lett., 102, 066103 (2009)
    [2] D. L. Cheung and S. A. F. Bon, Soft Matter, 5, 3969 (2009)
    [3] R. Chen et al, J. Am. Chem. Soc., 133, 2151 (2011)

  • 16:30 - 17:10 Markus Kraft (Cambridge, Chemical Engineering)
    Stochastic numerics for the gas-phase synthesis of nanoparticles (slides)

    The aim of this work is threefold: first, to present the mathematical description of a detailed multivariate population balance model for silica nanoparticles; second, to state a Stochastic Particle Algorithm which approximates the solution to the model; third, to investigate the numerical properties of this algorithm. Silica nanoparticles are formed by the interaction of silicic acid monomers (Si(OH)4) in the gas-phase. Each particle is described by its constituent primary particles and the connectivity between these primaries. Each primary, in turn, has internal variables that describe its chemical composition, i.e. the number of Si, free O and OH units. The particles change in time due to surface reaction with gas-phase species, coagulation and sintering with other particles, and intra-particulate processes.

  • 17:10 - 17:50 Anthony Lee/Chris Holmes (Oxford, Statistics)
    On the utility of graphics cards to perform massively parallel simulation with advanced Monte Carlo methods (slides)

    Advances in computational methods and computing power have been instrumental in the development of statistics in the last fifty years. A recent trend in desktop computer architecture is the move from traditional, single-core processors to multi-core processors and further to many-core or massively multi-core processors. Therefore, statistical methods that can take advantage of many-core architectures can make the best use of the latest technology. A particularly promising avenue in this regard is the design and implementation of statistical algorithms for execution on graphics processing units (GPUs) since they are dedicated, low cost, low maintenance, energy-efficient devices that are becoming increasingly easy to program. We present an introduction to this architecture and a case study on the suitability of using GPUs for three population-based Monte Carlo algorithms - population-based MCMC, sequential Monte Carlo samplers and the particle filter - with speedups ranging from 35 to 500 fold over conventional single-threaded computation. These results suggest that GPUs and other many-core devices are likely to change the landscape of high performance statistical computing in the near future.

  • 17:50 - 18:10 Dan Barker (Warwick, Complexity)
    Tempering Algorithm for Large-sample Network Inference (slides)

    Bayesian networks and their variants are widely used for modeling gene regulatory and protein signaling networks. In many settings, it is the underlying network structure itself that is the object of inference. Within a Bayesian framework inferences regarding network structure are made via a posterior probability distribution over graphs. However, in practical problems, the space of graphs is usually too large to permit exact inference, motivating the use of approximate approaches. An MCMC-based algorithm known as MC3 is widely used for network inference in this setting. We argue that recent trends towards larger sample size datasets, while otherwise advantageous, can, for reasons related to concentration of posterior mass, render inference by MC3 harder. We therefore exploit an approach known as parallel tempering to put forward an algorithm for network inference which we call MC4 . We show empirical results on both synthetic and proteomic data which highlight the ability of MC4 to converge faster and thereby yield demonstrably accurate results, even in challenging settings where MC3 fails.

  • 18:10 - 18:30 Peter Man (Cambridge, Chemical Engineering)
    Bayesian inference for expensive computer models in chemical engineering (slides)

    We consider the problem of parameter estimation in chemical engineering based on limited experimental data and a very computationally expensive simulator that attempts to predict the experimental data. However, the simulator is a function of unknown parameters, and it is desired to find the value which best calibrates the simulator for prediction. Since the simulator is expensive, Gaussian Process regression techniques are chosen for its emulation. Furthermore, the parameter estimation is executed through a Bayesian approach. The method is applied and discussed using a toy example and a first attempt to apply the method to a real granulation problem is presented.