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: "EXACT TRANSITION PROBABILITIES FOR THE INDEPENDENCE METROPOLIS SAMPLER"
  Abstract: A recent result of Jun Liu's has shown how to compute explicitly the eigen-values and eigenvectors for the Markov chain derived from a special case of the Hastings sampling algorithm, known as the indepdendence Metropolis sampler. In this note, we show how to extend the result to obtain exact n-step transition probabilities for any n. This is done first for a chain on a finite state space, and then extended to a general (discrete or continuous) state space. The paper concludes with some implications for diagnostic tests of convergence of Markov chain samplers.

Connected through hyperedge HE-1 (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"
    - "Estimating L 1 Error of Kernel Estimator: Monitoring Convergence of Markov Samplers"
    - "A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms"
    - "Exponential Convergence of Langevin Diffusions and Their Discrete Approximations"

Connected through hyperedge HE-2 (induced by source paper "A note on acceptance rate criteria for CLTs for Hastings-Metropolis algorithms"):
  with members:
    - "Rates of convergence of the Hastings and Metropolis algorithms"
    - "Geometric Ergodicity and Hybrid Markov Chains"
    - "Exponential Convergence of Langevin Diffusions and Their Discrete Approximations"

Connected through hyperedge HE-3 (induced by source paper "Self Regenerative Markov Chain Monte Carlo  Summary"):
  with members:
    - "Adaptation for Self Regenerative MCMC  SUMMARY"
    - "Adaptive Markov Chain Monte Carlo through Regeneration  Summary"
    - "Adaptive proposal distribution for random walk Metropolis algorithm"

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