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: "A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms"
  Abstract: This note considers positive recurrent Markov chains where the probability of remaining in the current state is arbitrarily close to 1. Specifically, conditions are given which ensure the non-existence of central limit theorems for ergodic averages of functionals of the chain. The results are motivated by applications for Metropolis-Hastings algorithms which are constructed in terms of a rejection probability, (where a rejection involves remaining at the current state). Two examples for commonly used algorithms are given, for the independence sampler and the Metropolis adjusted Langevin algorithm. The examples are rather specialised, although in both cases, the problems which arise are typical of problems commonly occurring for the particular algorithm being used. 0 I would like to thank Kerrie Mengersen Jeff Rosenthal and Richard Tweedie for useful conversations on the subject of this paper.

Connected through hyperedge HE-1 (induced by source paper "EXACT TRANSITION PROBABILITIES FOR THE INDEPENDENCE METROPOLIS SAMPLER"):
  with members:
    - "Rates of convergence of the Hastings and Metropolis algorithms"
    - "Self Regenerative Markov Chain Monte Carlo  Summary"

Connected through hyperedge HE-2 (induced by source paper "Exponential Convergence of Langevin Diffusions and Their Discrete Approximations"):
  with members:
    - "Rates of convergence of the Hastings and Metropolis algorithms"
    - "Self-Targeting Candidates for Metropolis-Hastings Algorithms"
    - "Geometric and Subgeometric Convergence of Diffusions with Given Stationary Distributions, and Their Discretizations"

Connected through hyperedge HE-3 (induced by source paper "Rates of convergence of the Hastings and Metropolis algorithms"):
  with members:
    - "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration"
    - "Theoretical rates of convergence for Markov chain Monte Carlo"
    - "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"
    - "EXACT TRANSITION PROBABILITIES FOR THE INDEPENDENCE METROPOLIS SAMPLER"
    - "Estimating L 1 Error of Kernel Estimator: Monitoring Convergence of Markov Samplers"
    - "Exponential Convergence of Langevin Diffusions and Their Discrete Approximations"

Connected through hyperedge HE-4 (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"
    - "Outperforming the Gibbs sampler empirical estimator for nearest neighbor random fields"

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