human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge groups papers that share a common citing paper.

Details of the hypergraph:
Center hyperedge (induced by source paper "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications"):
  Abstract: Suppose one wishes to sample from the density (x) using Markov chain Monte Carlo (MCMC). An auxiliary variable u and its conditional distribution (ujx) can be defined, giving the joint distribution (x; u) = (x)(ujx). A MCMC scheme which samples over this joint distribution can lead to substantial gains in efficiency compared to standard approaches. The revolutionary algorithm of Swendsen and Wang (1987) is one such example. In addition to reviewing the Swendsen-Wang algorithm and its generalizations, this paper introduces a new auxiliary variable method called partial decoupling. Two applications in Bayesian image analysis are considered. The first is a binary classification problem in which partial decoupling out performs SW and single site Metropolis. The second is a PET reconstruction which uses the gray level prior of Geman and McClure (1987). A generalized Swendsen-Wang algorithm is developed for this problem, which reduces the computing time to the point that MCMC is a viable method of posterior exploration.

Includes members:
  Member "Convergence properties of perturbed Markov chains":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function")
  Member "Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "Continuous sigmoidal belief networks trained using slice sampling")
  Member "A note on convergence rates of Gibbs sampling for nonparametric mixtures":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms")

Question: Please tell me which class the citing paper (i.e., the source paper of the center hyperedge) belongs to. The 7 classes are: Neural_Networks, Reinforcement_Learning, Probabilistic_Methods, Theory, Genetic_Algorithms, Case_Based, Rule_Learning. Directly output the class name.

gpt: Probabilistic_Methods