Metropolis acceptance probability

The value of ATJ is calculated from the potential energy functions given above and used for the Metropolis acceptance probability W for the trial movement,... 

The atom-exchange method was developed by Tsai, Abraham, and Pound to speed barrier crossing in binary (two types of atoms) alloy cluster simulations. During the Metropolis walk two different types of atoms are periodically chosen, and their positions are exchanged. The exchange is accepted or rejected by the standard Metropolis acceptance probability. The utility of this method is naturally limited to systems of this particular type, namely, binary atomic clusters and liquids. 

Based on (1.12), we can implement any complement of MC moves and formulate appropriate acceptance criteria such that the progression of configurations satisfies this distribution. For simple moves in which the proposal probability equals that of its inverse - symmetric moves, such as single-particle displacements - the Metropolis acceptance criterion then reads [141] ... 

Reconsider the Metropolis rejection Monte Carlo method (Kalos and Whitlock, 1986, Section 3.7), and derive the acceptance probability Eq. (8.14) on the basis of the traditional detailed balance specification. 

In the grand-canonical Monte Carlo method, the system volume, temperature, and chemical potential are kept fixed, while the number of particles is allowed to fluctuate.There exist three types of trial move (1) displacement of a particle, (2) insertion of a particle, and (3) removal of a particle. These trial moves are generated at random with equal probability. The acceptance probability of the Metropolis method can be used for the trial moves of type (1). For the two other types, the acceptance probabilities are different. Regarding zeolites, an adsorption isotherm can be calculated with the grand-canonical Monte Carlo method by running a series of simulations at varying chemical potentials. 

The acceptance probability is not uniquely defined by this equation. Metropolis et al. [1] proposed the solution... 

Metropolis acceptance criteria are applied to trial swap moves. Given that simulations are being conducted in a composite ensemble of several rephcas, a trial swap move is accepted with probability... 

Again the limiting probabilities occur only as a ratio and the value of Qc is not required. In most computer simulations, the Metropolis acceptance criterion is chosen, because it appears to sample phase space more efficiently than the other schemes that have been proposed [9]. 

A local algorithm for Metropolis Monte Carlo trajectories must be constructed carefully. Due to the finite probability of exactly repeated states in these paths, the corresponding transition probability includes a singular term [see Eq. (1.14)]. The generation algorithm for local path moves must take this singularity into account properly. Appropriate acceptance probabilities are given in [5]. (H. C. Andersen has drawn our attention to an omission in [5]. In Metropolis Monte Carlo trajectories sequences of multiple rejections can occur. Attempts to modify time slices in the interior... 

It is easy to check that detailed balance holds for the Metropolis algorithm described above with p ff) equal to the canonical ensemble distribution in configuration space. In the Metropolis algorithm, IF(F- F ) = a(F F )min(l,/OM(F )//OM(f)), where q (F F ) is the probability of attempting a move from F to F and Pacc(F -> F ) = min, pijj ) PiJr)) is the probability of accepting that move. In the classical Metropolis algorithm, the attempt step is designed such that q (F -> F ) = q (F F). In the NVT ensemble, the acceptance probability is mi (l,exp[—(V —V)/(k5l)]), as described above. One can easily verify that the detailed balance equation (77) is satisfied under these conditions. 

The Metropolis-Hastinp algorithm restores the balance by introducing an acceptance probability that depends on the current and candidate values and then only accepting some of the transitions. 

The Gibbs sampling algorithm is a special case of blockwise Metropolis-Hastings where the candidate density for each block of parameters is its correct conditional distribution given all other parameters not in its block and the observed data. The acceptance probability is always 1, so every candidate is accepted. 

The choice of poses is made with a traditional Metropolis approach. Metropolis algorithm is a Markov chain Monte Carlo method for obtaining a sequence of random poses from a probability distribution for which direct sampling is difficult. When the energy results are to be higher, the new conformation will be accepted or rejected if an acceptance probability law... 

In the standard Metropolis MC algorithm, the trial move is generated uniformly within a region of space such that 7(x -> x ) = T(x x) = constant. To sample the Boltzmann probability of the system visiting a conformation x relative to another conformation x, given by p x )/p(x) = exp(—At//A 7), the acceptance probability must be given by... 

Obviously, under assumption (18.10), we have T1 = tl = ft. Therefore, the MH algorithm for all three densities are identical with acceptance probability given by (18.11). However, once the assumption is dropped, some terms in the calculation of acceptance probabilities in (18.6) cannot be canceled. The placing of at sfiategic locations in the reptile means that the Metropolis decision needs to be adjusted accordingly. All the variants proposed, which we outline below, take advantage of specific properties of the chosen target densities. 

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