human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent groups of papers sharing a common citing paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function"):
  with members:
    - "Continuous sigmoidal belief networks trained using slice sampling"
    - "Convergence properties of perturbed Markov chains"
    - "Analysis of a Non-Reversible Markov Chain Sampler"
    - "SUPPRESSING RANDOM WALKS IN MARKOV CHAIN MONTE CARLO USING ORDERED OVERRELAXATION"

Connected through hyperedge HE-2 (induced by source paper "Convergence properties of perturbed Markov chains"):
  with members:
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "Analysis of the Gibbs sampler for a model related to James-Stein estimators"
    - "Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function"
    - "A note on convergence rates of Gibbs sampling for nonparametric mixtures"

Connected through hyperedge HE-3 (induced by source paper "A note on convergence rates of Gibbs sampling for nonparametric mixtures"):
  with members:
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Convergence properties of perturbed Markov chains"
    - "Geometric Ergodicity and Hybrid Markov Chains"
    - "A Note on the Dirichlet Process Prior in Bayesian Nonparametric Inference with Partial Exchangeability 1"

Question: Please tell me which class the center node 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