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Practitioners of Markov chain Monte Carlo (MCMC) may hesitate to use random walk Metropolis-Hastings algorithms, especially variable-at-a-time algorithms with many parameters, because these algorithms require users to select values of…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
Based on the algorithm Informed Importance Tempering (IIT) proposed by Li et al. (2023) we propose an algorithm that uses an adaptive bounded balancing function. We argue why implementing parallel tempering where each replica uses a…
Properties of the self-adjusted Monte Carlo algorithm applied to 2d Ising ferromagnet are studied numerically. The endogenous feedback form expressed in terms of the instant running averages is suggested in order to generate a biased random…
We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic…
The Metropolis Monte Carlo algorithm with the Finite Element method applied to compute electrostatic interaction energy between charge densities is described in this work. By using the Finite Element method to integrate numerically the…
The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the…
Optimal scaling has been well studied for Metropolis-Hastings (M-H) algorithms in continuous spaces, but a similar understanding has been lacking in discrete spaces. Recently, a family of locally balanced proposals (LBP) for discrete spaces…
In order to gain a deeper understanding of complex systems and infer key information using minimal data, I classify all configurations based on classical probability, starting from the dimensions of energy and different categories of…
We analyse computational efficiency of Metropolis-Hastings algorithms with stochastic AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g.…
This paper studies the mixing time of certain adaptive Markov Chain Monte Carlo algorithms. Under some regularity conditions, we show that the convergence rate of Importance Resampling MCMC (IRMCMC) algorithm, measured in terms of the total…
In Markov Chain Monte Carlo (MCMC) simulations, the thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the…
Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing…
We apply a new entropic scheme to study the critical behavior of the square-lattice Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions. Estimates of the present scheme are compared with those of the…
In detailed microcanonical analyses of densities of states obtained by extensive multicanonical Monte Carlo computer simulations, we investigate the caloric properties of conformational transitions adsorbing polymers experience near…
The Monte Carlo with Absorbing Markov Chains (MCAMC) method is introduced. This method is a generalization of the rejection-free method known as the $n$-fold way. The MCAMC algorithm is applied to the study of the very low-temperature…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…