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: "Convergence properties of perturbed Markov chains"
  Abstract: Acknowledgements. We thank Neal Madras, Radford Neal, Peter Rosenthal, and Richard Tweedie for helpful conversations. This work was partially supported by EPSRC of the U.K., and by NSERC of Canada.

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"
    - "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications"
    - "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 "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
    - "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration"
    - "Theoretical rates of convergence for Markov chain Monte Carlo"
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "Analysis of the Gibbs sampler for a model related to James-Stein estimators"
    - "Rates of convergence of the Hastings and Metropolis algorithms"
    - "A note on convergence rates of Gibbs sampling for nonparametric mixtures"
    - "Adaptive Markov Chain Monte Carlo through Regeneration  Summary"

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"
    - "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications"
    - "Geometric Ergodicity and Hybrid Markov Chains"
    - "A Note on the Dirichlet Process Prior in Bayesian Nonparametric Inference with Partial Exchangeability 1"

Connected through hyperedge HE-4 (induced by source paper "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "On Convergence of the EM Algorithm and the Gibbs Sampler  SUMMARY"
    - "Assessing Convergence of Markov Chain Monte Carlo Algorithms"
    - "Rates of convergence of the Hastings and Metropolis algorithms"

Connected through hyperedge HE-5 (induced by source paper "Analysis of the Gibbs sampler for a model related to James-Stein estimators"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
    - "Theoretical rates of convergence for Markov chain Monte Carlo"
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "Rates of convergence of the Hastings and Metropolis algorithms"
    - "APPLICATIONS OF CHEEGER'S CONSTANT TO THE CONVERGENCE RATE OF MARKOV CHAINS ON R n"

Connected through hyperedge HE-6 (induced by source paper "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications"):
  with members:
    - "Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function"
    - "A note on convergence rates of Gibbs sampling for nonparametric mixtures"

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