computational methods for statistical mechanics [day #3]

Arthur Seat, Edinburgh, Sep. 7, 2011

The third day [morn] at our ICMS workshop was dedicated to path sampling. And rare events. Much more into [my taste] Monte Carlo territory. The first talk by Rosalind Allen looked at reweighting trajectories that are not in an equilibrium or are missing the Boltzmann [normalizing] constant. Although the derivation against a calibration parameter looked like the primary goal rather than the tool for constant estimation. Again papers in J. Chem. Phys.! And a potential link with ABC raised by Antonietta Mira… Then Jonathan Weare discussed stratification. With a nice trick of expressing the normalising constants of the different terms in the partition as solution(s) of a Markov system

v\mathbf{M}=v

Because the stochastic matrix M is easier (?) to approximate. Valleau’s and Torrie’s umbrella sampling was a constant reference in this morning of talks. Arnaud Guyader’s talk was in the continuation of Toni Lelièvre’s introduction, which helped a lot in my better understanding of the concepts. Rephrasing things in more statistical terms. Like the distinction between equilibrium and paths. Or bias being importance sampling. Frédéric Cérou actually gave a sort of second part to Arnaud’s talk, using importance splitting algorithms. Presenting an algorithm for simulating rare events that sounded like an opposite nested sampling, where the goal is to get down the target, rather than up. Pushing particles away from a current level of the target function with probability ½. Michela Ottobre completed the series with an entry into diffusion limits in the Roberts-Gelman-Gilks spirit when the Markov chain is not yet stationary. In the transient phase thus.

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