Rosenbluth sampling

Wu and Kofke discuss the significance of the overlap of the phase space domain of diflerent states in the testing and use of FRs. They also introduce Rosenbluth sampling to assist in convergence of the JE to the correct value. 

In principle, this method can also be applied to multichain systems, but the problem of correcting for the bias becomes even more severe. In practice, one therefore has to resort to the configurational bias method which is an extension of the Rosenbluth sampling (see Chapter 7). But, inversely restricted sampling is still one of the possible options for not too large... 

Square-lattice example for the bias implied by Rosenbluth sampling. Both walks shown are grown from the monomer labeled "1". Although the shapes are identical, they are created with different probabilities (left p=1/108, right ... 

In Chapter 4, it has already been stated that it is an advantage of the simple-sampling algorithms based on Rosenbluth sampling [33], compared to importance-sampling methods, that they allow for the approximation of the degeneracy ( density ) of states absolutely, i.e., free energy and entropy can be explicitly determined. 

Rosenbluth algorithm can also be used as the basis for a more efficient way to perform ite Carlo sampling for fully flexible chain molecules [Siepmann and Frenkel 1992], ch, as we have seen, is difficult to do as bond rotations often give rise to high energy rlaps with the rest of the system. 

Metropolis NA, Rosenbluth AW, Teller AH, Teller E (1953) Generalizing Swendsen-Wang to sampling - arbitrary posterior probabilities, J Chem Phys, 21 1087... 

This method of sampling is ineffective for very long chains, in which case enrichment techniques need to be employed to increase efficiency. An example is the technique introduced by Rosenbluth and Rosenbluth. " Here if an intersection of bonds occurs, one does not start the configuration from the beginning. Instead one goes back one step and chooses another possible step. Because this causes an imbalance in the a priori probabilities, one must weight the new step in a way that is consistent with unbias. 

The first molecular simulations were performed almost five decades ago by Metropolis et al. (1953) on a system of hard disks by the Monte Carlo (MC) method. Soon after, hard spheres (Rosenbluth and Rosenbluth, 1954) and Lennard-Jones (Wood and Parker, 1957) particles were also studied by both MC and molecular dynamics (MD). Over the years, the simulation techniques have evolved to deal with more complex systems by introducing different sampling or computational algorithms. Molecular simulation studies have been made of molecules ranging from simple systems (e.g., noble gases, small organic molecules) to complex molecules (e.g., polymers, biomolecules). 

Recently, recursive sampling has been combined with configurational bias methods (see Section III.D). In the Pruned-enriched Rosenbluth method of Grassberger [11], the number of copies of a growing chain is either reduced (pruning) or increased (enrichment) based on the chain s... 

One chain can then be accepted based on its Rosenbluth weight. This strategy of multiple chain growth has been tried on a scalar machine, and has been shown to improve sampling efficiency within configuration bias MC [37]. It should also translate to parallel machines because a reasonable amount of computational time is required to generate a chain (or multiple chains) on each processor, relative to the inter-processor communication required at the end of chain regrowth. 

We next discuss the inversely restricted sampling already proposed by Rosenbluth and Rosenbluth. ° Rather than adding the next bond to the existing part of the SAW blindly, as one does in simple sampling, one scans the local environment of the last monomer and excludes all trail directions that lead... 

Configurational-bias methods trace their ancestry to biased sampling for lattice polymer configurations proposed by Rosenbluth and Rosenbluth [85]. Development of configurational-bias methods for canonical and grand canonical simulations and for continuous-space models took place in the early 1990s [86-90] and dramatically expanded the range of intermolecular potential models that can be studied by the methods described in the previous sections. 

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