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: "Estimating Ratios of Normalizing Constants for Densities with Different Dimensions"
  Abstract: In Bayesian inference, a Bayes factor is defined as the ratio of posterior odds versus prior odds where posterior odds is simply a ratio of the normalizing constants of two posterior densities. In many practical problems, the two posteriors have different dimensions. For such cases, the current Monte Carlo methods such as the bridge sampling method (Meng and Wong 1996), the path sampling method (Gelman and Meng 1994), and the ratio importance sampling method (Chen and Shao 1994) cannot directly be applied. In this article, we extend importance sampling, bridge sampling, and ratio importance sampling to problems of different dimensions. Then we find global optimal importance sampling, bridge sampling, and ratio importance sampling in the sense of minimizing asymptotic relative mean-square errors of estimators. Implementation algorithms, which can asymptotically achieve the optimal simulation errors, are developed and two illustrative examples are also provided.

Connected through hyperedge HE-1 (induced by source paper "MARKOV CHAIN MONTE CARLO SAMPLING FOR EVALUATING MULTIDIMENSIONAL INTEGRALS WITH APPLICATION TO BAYESIAN COMPUTATION"):
  with members:
    (none)

Connected through hyperedge HE-2 (induced by source paper "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review"):
  with members:
    - "Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses"
    - "Decision Analysis by Augmented Probability Simulation"
    - "Bounding Convergence Time of the Gibbs Sampler in Bayesian Image Restoration"
    - "Perfect Simulation in Stochastic Geometry"
    - "Theoretical rates of convergence for Markov chain Monte Carlo"
    - "Maximum Working Likelihood Inference with Markov Chain Monte Carlo"
    - "Markov Chain Monte Carlo in Practice: A Roundtable Discussion"
    - "A simulation approach to convergence rates for Markov chain Monte Carlo 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