Ising modelMarkov Chain Monte CarloThe Ising model is one of the simplest and most famous models of interacting systems. It was originally proposed to model ferromagnetic interactions in statistical physics and
3. For the Ising Model and the RBM trained on MNIST, when using the uniform reference distribution and a small number of bridging distributions, AIS started with relatively high error rates, but improved by over an order of magnitude in error when the number of bridging distributions was ...
This section concludes with an evaluation of the Laplace approximation to the model evidence, in relation to Monte Carlo–Markov chain (MCMC) sampling estimates. The final section revisits model selection using automatic model selection (AMS) and relevance determination (ARD). We show how suitable ...
It’s no wonder that sometimes I feel cognitively closer to my salad than my coworkers when the lunch conversation turns to Bayesian models, Markov chain analysis and Monte-Carlo simulations. Thankfully the lunch breaks I’m told have gotten shorter too. Don’t put your faith in research inv...
Fig. 1: Asymmetric kinetic SK model. a The asymmetric kinetic Ising model describes a Markov chain where states at time su depend on pairwise couplings to states su−1. This model shows disordered dynamics for large coupling variance both at high and low temperatures (b and c), ordered dy...
The classicalGlauber dynamicsfor the Ising model picks a random vertexat each step and resamples the spin atxaccording to the correct conditional distribution given its neighboring spins; this Markov chain converges to the Gibbs distribution (1.3) from any initial configuration. The analogous nonlinear...
Results are the mean of estimated median detection probability P and the expected number of animal passes (lambda), and their 95% credible interval (CI) coverage of the densities. Parameter estimation of the capture-recapture model was performed using the Markov chain Monte Carlo (MCMC) method,...
Jerrum, M.: Mathematical Foundations of the Markov Chain Monte Carlo Method. In: Probabilistic Methods for Algorithmic Discrete Mathematics, pp. 116–165. Springer, New York (1998) Laanait, L., Messager, A., Miracle-Solé, S., Ruiz, J., Shlosman, S.: Interfaces in the Potts model I...
This method uses stochastic models derived from Markov Chain Monte Carlo methods in discrete time (Michelot et al., 2020; Michelot, Blackwell, et al., 2019) and continuous time (Michelot, Gloaguen, et al., 2019), allowing joint inference at multiple scales (Blackwell & Matthiopoulos, ...
Depending on the subset S, the problem falls into one of the following categories: in P; NP-complete; polynomial-time equivalent to the Ising model with transverse magnetic fields; or QMA-complete. The third of these classes has been shown to be StoqMA-complete by Bravyi and Hastings. The...