# Computational Methods for Statistical Mechanics - At the Interface Between Mathematical Statistics and Molecular Simulation

*02 - 06 Jun 2014*

*ICMS, 15 South College Street Edinburgh*

#### Scientific Organisers:

**Carsten Hartmann**, Freie Universität Berlin**Grigorios Pavliotis**, Imperial College London**Gabriel Stoltz**, École des Ponts ParisTech

By bringing together researchers in computational statistical mechanics and molecular dynamics this workshop fostered closer contact and facilitated the exchange of ideas and expertise. The programme explored recent examples of cross-fertilisation between molecular dynamics and statistics through a series of lectures which laid the basics of each field.

#### Speakers:

**Michael Allen,**University of Warwick*- Molecular Simulation and Statistical Mechanics from a Practical Viewpoint*

**Omiros Papaspiliopoulos,**Universitat Pompeu Fabra*- The Gibbs Sampler: Geometry and Algorithms***Ben Leimkuhler**, University of Edinburgh*- Weak Convergence of Numerical Methods for Stochastic Gradient Systems in the T->Infinity Limit***Christophe Andrieu,**University of Bristol*- Exact Approximate Monte Carlo***Tony Lelièvre,**École Nationale des Ponts et Chaussées*- Numerical Methods in Molecular Dynamics***Maria Cameron,**University of Maryland*- Analysis Tools for Networks Representing Energy Landscapes***Pierre Jacob**, University of Oxford*- On Non-Negative Unbiased Estimators***Francis Pinski,**University of Cincinnati*- Theory of Fluctuations in a Thermodynamic System and the Limitations of the Onsager-Machlup Functional***Rosalind Allen,**University of Edinburgh*- Trajectory Reweighting: Smart Sampling in Non-Equilibrium Simulations***Jonathan Weare,**University of Chicago*- Stratification of Markov Processes for Rare Event Simulation***Gabriel Stoltz**, École des Ponts & Inria Rocquencourt*- Computer Simulations: the Third Way of Doing Science***Arnaud Guyader,**Université de Rennes*- Rare Event Simulation for Molecular Dynamics***Michela Ottobre,**Imperial College London*- Diffusion Limit for Random Walk Metropolis Algorithm Started Out of Stationarity***Christophe Chipot,**Université de Lorraine/CNRS*- Efficient Determination of Protein-Ligand Standard Binding Free Energies and Permeabilities with a Computational Microcalorimeter***Jérôme Hénin,**Laboratoire de Biochimie Théorique*- Ergodic Sampling in Biomolecular Simulations Using Adaptive Collective Variable Biases***Antonietta Mira,**Università della Svizzeria Italiana*- Variance Reduction Strategies for MCMC Simulation***Hilbert Kappen,**Radboud University*- Optimal Sampling for Optimal Control***Johannes Zimmer,**University of Bath*- Entropic Flows and Their Stochastic Corrections for Particle Models***Christian Robert,**Université Paris-Dauphine & University of Warwick*- Selection of Summary Statistics for ABC***Hugo Touchette,**University of Stellenbosch*- Nonequilibrium Markov Processes Conditioned on Large Deviations***Benjamin Jourdain,**École des Ponts*- Optimal Scaling of the Transient Phase of Metropolis Hastings Algorithms***Alexandros Beskos**, University College London*- Sequential Monte Carlo Methods for Applications in High Dimensions*

**Financial support for this workshop has been provided by The Centre for Numerical Algorithms and Intelligent Software (NAIS).**

### Presentations

Random Walk Metropolis is a popular Metropolis-Hastings algorithm which samples from a given probability distribution by creating a reversible Markov chain which has the target distribution as unique invariant measure.

When the target measure is in product form, a diffusion limit for the resulting Markov chain has been first studied by G.Roberts et al (1997), assuming the chain is started in stationarity.

More recently, diffusion limits for RWM have been considered in J.Mattingly et al (2011) and Jourdain et al (2012): in the first paper the target measure is in non-product form and the chain is started in stationarity; in the second one the authors examine the transient phase as well by relaxing the stationarity assumption, for measures in product form. In this talk we will explain how to extend the results in the literature by considering measures in non-product form, when the chain is started out of stationarity. We use methods close to the diffusion approximation framework. The diffusion limit for the considered chain is given by an SDE on an appropriate infinite dimensional Hilbert space, with time dependent coefficients.

### Participants

Name | Institution |
---|---|

Sergios, Agapiou | University of Warwick |

Michael, Allen | University of Warwick |

Rosalind, Allen | University of Edinburgh |

Christophe, Andrieu | University of Bristol |

Tomasz, Badowski | Freie Universität Berlin |

Janis, Bajars | University of Edinburgh |

Ralf, Banisch | Freie Universität Berlin |

Alexandros, Beskos | University College London |

Maria, Cameron | University of Maryland |

Frédéric, Cérou | Inria Rennes - Bretagne Atlantique |

Christophe, Chipot | Université de Lorraine/CNRS |

Matt, Dunlop | University of Warwick |

Alain, Durmus | Telecom ParisTech |

Gersende, Fort | Telecom ParisTech/LTCI/CNRS |

Gianpaolo, Gobbo | University of Edinburgh |

Ben, Goddard | University of Edinburgh |

Arnaud, Guyader | Université de Rennes |

Jérôme, Hénin | Laboratoire de Biochimie Théorique/IBPC/CNRS |

Pierre, Jacob | University of Oxford |

Benjamin, Jourdain | École Nationale des Ponts et Chaussées |

Hilbert, Kappen | Radboud University |

Ben, Leimkuhler | University of Edinburgh |

Tony, Lelièvre | École Nationale des Ponts et Chaussées |

Han Cheng, Lie | Freie Universität Berlin |

Charles, Matthews | University of Edinburgh |

Antonietta, Mira | Università della Svizzera Italiana, Switzerland and Università dell’Insubria, Italy |

Boris, Nectoux | École Nationale des Ponts et Chaussées |

Nikolas, Nüsken | Imperial College London |

Michela, Ottobre | Heriot-Watt University |

Omiros, Papaspiliopoulos | Universitat Pompeu Fabra |

Grigorios, Pavliotis | Imperial College London |

Francis, Pinski | University of Cincinnati |

Christian, Robert | Université Paris-Dauphine & University of Warwick |

Matthias, Sachs | University of Edinburgh |

Markus, Schmuck | Heriot-Watt University |

Xiaocheng, Shang | University of Edinburgh |

Konstantinos, Spiliopoulos | Boston University |

Gabriel, Stoltz | École des Ponts ParisTech |

Hugo, Touchette | University of Stellenbosch |

Jonathan, Weare | University of Chicago |

Johannes, Zimmer | University of Bath |