Above are papers related to the following paper: [Paper_ID] Paper #645016. 	[Title] Extensions of Fill's algorithm for perfect simulation [Abstract] Fill's algorithm for perfect simulation for attractive finite state space models, unbiased for user impatience, is presented in terms of stochastic recursive sequences and extended in two ways. Repulsive discrete Markov random fields with two coding sets like the auto-Poisson distribution on a lattice with 4-neighbourhood can be treated as monotone systems if a particular partial ordering and quasi-maximal and quasi-minimal states are used. Fill's algorithm then applies directly. Combining Fill's rejection sampling with sandwiching leads to a version of the algorithm, which works for general discrete conditionally specified repulsive models. Extensions to other types of models are briefly discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #644361. 	[Title] Perfect Sampling of Harris Recurrent Markov Chains [Abstract] We develop an algorithm for simulating "perfect" random samples from the invariant measure of a Harris recurrent Markov chain. The method uses backward coupling of embedded regeneration times, and works most effectively for finite chains and for stochastically monotone chains even on continuous spaces, where paths may be sandwiched below "upper" and "lower" processes. Examples show that more naive approaches to constructing such bounding processes may be considerably biased, but that the algorithm can be simplified in certain cases to make it easier to run. We give explicit analytic bounds on the backward coupling times in the stochastically monotone case. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131274. 	[Title] Perfect Simulation in Stochastic Geometry [Abstract] Simulation plays an important role in stochastic geometry and related fields, because all but the simplest random set models tend to be intractable to analysis. Many simulation algorithms deliver (approximate) samples of such random set models, for example by simulating the equilibrium distribution of a Markov chain such as a spatial birth-and-death process. The samples usually fail to be exact because the algorithm simulates the Markov chain for a long but finite time, and thus convergence to equilibrium is only approximate. The seminal work by Propp and Wilson made an important contribution to simulation by proposing a coupling method, Coupling from the Past (CFTP), which delivers perfect, that is to say exact, simulations of Markov chains. In this paper we introduce this new idea of perfect simulation and illustrate it using two common models in stochastic geometry: the dead leaves model and a Boolean model conditioned to cover a finite set of points. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #644363. 	[Title] EXACT SIMULATION USING MARKOV CHAINS [Abstract] This reports gives a review of the new exact simulation algorithms using Markov chains. The first part covers the discrete case. We consider two different algorithms, Propp and Wilsons coupling from the past (CFTP) technique and Fills rejection sampler. The algorithms are tested on the Ising model, with and without an external field. The second part covers continuous state spaces. We present several algorithms developed by Murdoch and Green, all based on coupling from the past. We discuss the applicability of these methods on a Bayesian analysis problem of surgical failure rates. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #645452. 	[Title] An extension of Fill's exact sampling algorithm to non-monotone chains* [Abstract] We provide an extension of Fill's (1998) exact sampler algorithm. Our algorithm is similar to Fill's, however it makes no assumptions regarding stochastic monotonicity, discreteness of the state space, the existence of densities, etc. We illustrate our algorithm on a simple example. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #644843. 	[Title] Perfect Simulation of some Point Processes for the Impatient User [Abstract] Recently Propp and Wilson [14] have proposed an algorithm, called Coupling from the Past (CFTP), which allows not only an approximate but perfect (i.e. exact) simulation of the stationary distribution of certain finite state space Markov chains. Perfect Sampling using CFTP has been successfully extended to the context of point processes, amongst other authors, by Haggstrom et al. [5]. In [5] Gibbs sampling is applied to a bivariate point process, the penetrable spheres mixture model [19]. However, in general the running time of CFTP in terms of number of transitions is not independent of the state sampled. Thus an impatient user who aborts long runs may introduce a subtle bias, the user impatience bias. Fill [3] introduced an exact sampling algorithm for finite state space Markov chains which, in contrast to CFTP, is unbiased for user impatience. Fill's algorithm is a form of rejection sampling and similar to CFTP requires sufficient mono-tonicity properties of the transition kernel used. We show how Fill's version of rejection sampling can be extended to an infinite state space context to produce an exact sample of the penetrable spheres mixture process and related models. Following [5] we use Gibbs sampling and make use of the partial order of the mixture model state space. Thus Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1154071. 	[Title] PERFECT SIMULATION OF CONDITIONALLY SPECIFIED MODELS [Abstract] We discuss how the ideas of producing perfect simulations based on coupling from the past for finite state space models naturally extend to mul-tivariate distributions with infinite or uncountable state spaces such as auto-gamma, auto-Poisson and auto-negative-binomial models, using Gibbs sampling in combination with sandwiching methods originally introduced for perfect simulation of point processes. Please summarise all the given information.

Paper #645016 has the title `Extensions of Fill's algorithm for perfect simulation  
` and the abstract `Fill's algorithm for perfect simulation for attractive finite state space models, unbiased for user impatience, is presented in terms of stochastic recursive sequences and extended in two ways. Repulsive discrete Markov random fields with two coding sets like the auto-Poisson distribution on a lattice with 4-neighbourhood can be treated as monotone systems if a particular partial ordering and quasi-maximal and quasi-minimal states are used. Fill's algorithm then applies directly. Combining Fill's rejection sampling with sandwiching leads to a version of the algorithm, which works for general discrete conditionally specified repulsive models. Extensions to other types of models are briefly discussed. 
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Question: Which category should Paper #645016 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #645016 has the title `Extensions of Fill's algorithm for perfect simulation  
` and the abstract `Fill's algorithm for perfect simulation for attractive finite state space models, unbiased for user impatience, is presented in terms of stochastic recursive sequences and extended in two ways. Repulsive discrete Markov random fields with two coding sets like the auto-Poisson distribution on a lattice with 4-neighbourhood can be treated as monotone systems if a particular partial ordering and quasi-maximal and quasi-minimal states are used. Fill's algorithm then applies directly. Combining Fill's rejection sampling with sandwiching leads to a version of the algorithm, which works for general discrete conditionally specified repulsive models. Extensions to other types of models are briefly discussed. 
`.
Question: Which category should Paper #645016 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods