human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge groups papers that share a common citing paper.

Details of the hypergraph:
Center hyperedge (induced by source paper "MARKOV CHAIN MONTE CARLO SAMPLING FOR EVALUATING MULTIDIMENSIONAL INTEGRALS WITH APPLICATION TO BAYESIAN COMPUTATION"):
  Abstract: Recently, Markov chain Monte Carlo (MCMC) sampling methods have become widely used for determining properties of a posterior distribution. Alternative to the Gibbs sampler, we elaborate on the Hit-and-Run sampler and its generalization, a black-box sampling scheme, to generate a time-reversible Markov chain from a posterior distribution. The proof of convergence and its applications to Bayesian computation with constrained parameter spaces are provided and comparisons with the other MCMC samplers are made. In addition, we propose an importance weighted marginal density estimation (IWMDE) method. An IWMDE is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w. The asymptotic properties for the IWMDE and the guidelines for choosing a weighting conditional density w are also considered. The generalized version of IWMDE for estimating marginal posterior densities when the full joint posterior density contains analytically intractable normalizing constants is developed. Furthermore, we develop Monte Carlo methods based on Kullback-Leibler divergences for comparing marginal posterior density estimators. This article is a summary of the author's Ph.D. thesis and it was presented in the Savage Award session.

Includes members:
  Member "Estimating Ratios of Normalizing Constants for Densities with Different Dimensions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review")

Question: Please tell me which class the citing paper (i.e., the source paper of the center hyperedge) 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