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: "MCMC CONVERGENCE DIAGNOSTIC VIA THE CENTRAL LIMIT THEOREM"
  Abstract: Markov Chain Monte Carlo (MCMC) methods, as introduced by Gelfand and Smith (1990), provide a simulation based strategy for statistical inference. The application fields related to these methods, as well as theoretical convergence properties, have been intensively studied in the recent literature. However, many improvements are still expected to provide workable and theoretically well-grounded solutions to the problem of monitoring the convergence of actual outputs from MCMC algorithms (i.e. the convergence assessment problem). In this paper, we introduce and discuss a methodology based on the Central Limit Theorem for Markov chains to assess convergence of MCMC algorithms. Instead of searching for approximate stationarity, we primarily intend to control the precision of estimates of the invariant probability measure, or of integrals of functions with respect to this measure, through confidence regions based on normal approximation. The first proposed control method tests the normality hypothesis for normalized averages of functions of the Markov chain over independent parallel chains. This normality control provides good guarantees that the whole state space has been explored, even in multimodal situations. It can lead to automated stopping rules. A second tool connected with the normality control is based on graphical monitoring of the stabilization of the variance after n iterations near the limiting variance appearing in the CLT. Both methods require no knowledge of the sampler driving the chain. In this paper, we mainly focus on finite state Markov chains, since this setting allows us to derive consistent estimates of both the limiting variance and the variance after n iterations. Heuristic procedures based on Berry-Esseen bounds are investigated. An extension to the continuous case is also proposed. Numerical simulations illustrating the performance of these methods are given for several examples: a finite chain with multimodal invariant probability, a finite state random walk for which the theoretical rate of convergence to stationarity is known, and a continuous state chain with multimodal invariant probability issued from a Gibbs sampler.

Connected through hyperedge HE-1 (induced by source paper "Discretization of continuous Markov chains and MCMC convergence assessment"):
  with members:
    - "Looking at Markov Samplers through Cusum Path Plots: a simple diagnostic idea"
    - "Adaptive Markov Chain Monte Carlo through Regeneration  Summary"

Connected through hyperedge HE-2 (induced by source paper "Convergence controls for MCMC algorithms, with applications to hidden Markov chains"):
  with members:
    - "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"
    - "Assessing Convergence of Markov Chain Monte Carlo Algorithms"

Connected through hyperedge HE-3 (induced by source paper "Assessing Convergence of Markov Chain Monte Carlo Algorithms"):
  with members:
    - "Decision Analysis by Augmented Probability Simulation"
    - "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration"
    - "Convergence controls for MCMC algorithms, with applications to hidden Markov chains"
    - "Rate of Convergence of the Gibbs Sampler by Gaussian Approximation  SUMMARY"
    - "An Approach to Diagnosing Total Variation Convergence of MCMC 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