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 "BAYESIAN STATISTICS 6, pp. 000--000  Exact sampling for Bayesian inference: towards general purpose algorithms"):
  Abstract: There are now methods for organising a Markov chain Monte Carlo simulation so that it can be guaranteed that the state of the process at a given time is exactly drawn from the target distribution. The question of assessing convergence totally vanishes. Such methods are known as exact or perfect sampling. The approach that has received most attention uses the protocol of coupling from the past devised by Propp and Wilson (Random Structures and Algorithms,1996), in which multiple dependent paths of the chain are run from different initial states at a sequence of initial times going backwards into the past, until they satisfy the condition of coalescence by time 0. When this is achieved the state at time 0 is distributed according to the required target. This process must be implemented very carefully to assure its validity (including appropriate re-use of random number streams), and also requires one of various tricks to enable us to follow infinitely many sample paths with a finite amount of work. With the ultimate objective of Bayesian MCMC with guaranteed convergence, the purpose of this paper is to describe recent efforts to construct exact sampling methods for continuous-state Markov chains. We review existing methods based on gamma-coupling and rejection sampling (Murdoch and Green, Scandinavian Journal of Statistics, 1998), that are quite straightforward to understand, but require a closed form for the transition kernel and entail cumbersome algebraic manipulation. We then introduce two new methods based on random walk Metropolis, that offer the prospect of more automatic use, not least because the difficult, continuous, part of the transition mechanism can be coupled in a generic way, using a proposal distribution of convenience. One of the methods is based on a neat decomposition of any unimodal (multivariate) symmetric density into pieces that may be re-assembled to construct any translated copy of itself: that allows coupling of a continuum of Metropolis proposals to a finite set, at least for a compact state space. We discuss methods for economically coupling the subsequent accept/reject decisions. Our second new method deals with unbounded state spaces, using a trick due to W. S. Kendall of running a coupled dominating process in parallel with the sample paths of interest. The random subset of the state space below the dominating path is compact, allowing efficient coupling and coalescence. We look towards the possibility that application of such methods could become sufficiently convenient that they could become the basis for routine Bayesian computation in the foreseeable future.

Includes members:
  Member "Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review")
  Member "Bayesian Forecasting of Multinomial Time Series through Conditionally Gaussian Dynamic Models":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "Change Point and Change Curve Modeling in Stochastic Processes and Spatial Statistics")
  Member "On Bayesian analysis of mixtures with an unknown number of components  Summary":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "Finding Overlapping Distributions with MML")
  Member "An Approach to Diagnosing Total Variation Convergence of MCMC Algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "Assessing Convergence of Markov Chain Monte Carlo Algorithms")

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