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: "Outperforming the Gibbs sampler empirical estimator for nearest neighbor random fields"
  Abstract: Given a Markov chain sampling scheme, does the standard empirical estimator make best use of the data? We show that this is not so and construct better estimators. We restrict attention to nearest neighbor random fields and to Gibbs samplers with deterministic sweep, but our approach applies to any sampler that uses reversible variable-at-a-time updating with deterministic sweep. The structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance. The extra computational cost is negligible. When the random field is spatially homogeneous, symmetrizations of our estimator lead to further variance reduction. The performance of the estimators is evaluated in a simulation study of the Ising model.

Connected through hyperedge HE-1 (induced by source paper "Von Mises type statistics for single site updated local interaction random fields"):
  with members:
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"

Connected through hyperedge HE-2 (induced by source paper "Geometric Ergodicity and Hybrid Markov Chains"):
  with members:
    - "A simulation approach to convergence rates for Markov chain Monte Carlo algorithms"
    - "A note on convergence rates of Gibbs sampling for nonparametric mixtures"
    - "APPLICATIONS OF CHEEGER'S CONSTANT TO THE CONVERGENCE RATE OF MARKOV CHAINS ON R n"
    - "A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms"

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