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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)

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*

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)

- 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)

_{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)

- 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.