J. A. Fill, M. Machida, D. J. Murdoch, and J. S. Rosenthal, "Extension of Fill's perfect rejection sampling algorithm to general chains (extended abstract)," in Monte Carlo Methods, N. Madras, Ed. New York: Amer. Math. Soc., 2000, vol. 26, pp. 37--52.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... are some extensions to continuous and unbounded state spaces, these require sophisticated, problem speci c tricks to reduce the number of chains under consideration to a nite number (see e.g. Murdoch and Green, 1998; Hobert, Robert and Titterington, 1999; Mira, M ller and Roberts, 1999; and Fill, Machida, Murdoch and Rosenthal, 2000). A common theme of the perfect samplers that have so far been developed is the use of coupling ; that is, running chains from di erent starting points and waiting until they enter the same state at the same time. In contrast, simulating from via (1) is unrelated to coupling. The distributions ....

....an viable option. Otherwise, getting close to would be a mute point. It is possible to nd n by constructing exact upper bounds on kP n ( k through drift and minorization conditions (Rosenthal, 1995; Roberts and Tweedie, 1999) The phrase dicult theoretical analysis is used by Fill, Machida, Murdoch and Rosenthal (2000) to describe this method. While this approach has been successfully applied to a few relatively simple MCMC algorithms (Roberts and Rosenthal, 1999; Jones and Hobert, 2000) it is not clear how useful it will be in more complex situations. We now present a slightly less rigorous and much simpler ....

Fill, J. A., Machida, M., Murdoch, D. J. and Rosenthal, J. S. (2000). Extension of Fill's perfect rejection sampling algorithm to general chains, Technical report, The Johns Hopkins University.

....introduced. 5 Concluding remarks and further reading Remark 1 (Fill s algorithm) Fill (1998) introduces a clever form of rejection sampling, assuming a nite state space and a monotone setting with unique minimal and maximal states. Applications and extensions of Fill s algorithm can be found in Fill et al. 2000) and the references therein. The advantage of Fill s algorithm compared to CFTP is that it is interruptible in the sense that the output is independent on the running time (like in any rejection sampler) The disadvantages may be problems with storage and that it seems more limited for ....

Fill, J.A., Machida, M., Murdoch, D.J. and Rosenthal, J.S. (2000). Extensions of Fill's perfect rejection sampling algorithm to general chains. Random Structures and Algorithms, 16. To appear.

.... interruptible algorithm can be aborted without biasing output; see the discussion in [6] For active case algorithms, the leading example of a non interruptible algorithm is coupling from the past [12] while interruptible algorithms include cycle popping [13] Fill s rejection based algorithm [6] [8], and the Randomness Recycler [7] The results of this paper, both positive and negative, are for interruptible algorithms. 4 A terminating algorithm for interruptible exact sampling in the passive case In this section we present a terminating algorithm for interruptible exact stationary ....

Fill, J. A., Machida, M., Murdoch, D. J., and Rosenthal, J. S. Extension of Fill's perfect rejection sampling algorithm to general chains. Random Structures & Algorithms 17 (2000), 290--316.

....of their own. These algorithms are noninterruptible, which means that the user must commit to running such an algorithm for its entire (random) running time even though that time is not known ahead of time. Failure to do so can introduce bias into the sample. Other algorithms, such as FMMR [1], are interruptible, but require storage of random bits used by the algorithm. Because FMMR needs to read these bits twice, it is a read twice algorithm. The method we present will be both interruptible and read once, with no storage of random bits needed. In addition, algorithms like CFTP and ....

James A. Fill, Motoya Machida, Duncan J. Murdoch, and Je#rey S. Rosenthal. Extension of Fill's perfect rejection sampling algorithm to general chains. Random Structures & Algorithms, 17:290--316, 2000.

....drawbacks of their own. These algorithms are noninterruptible, which means that the user must commit to running such an algorithm for its entire (random) running time even though that time is not known in advance. Failure to do so can introduce bias into the sample. Other algorithms, such as FMMR [3], are interruptible (when time is measured in Markov chain steps) but require storage and subsequent rereading of random bits used by the algorithm. The method we will present is both interruptible and readonce, with no storage of random bits needed. In addition, algorithms like CFTP and FMMR ....

....time (if measured in number of iterations of the basic Repeat loop) without introducing bias into the sample. Like read once coupling from the past [20] this algorithm does not require storage of any random bits. Another perfect sampling approach, that of Fill, Machida, Murdoch, and Rosenthal [3] is also interruptible but not read once, and so does requires storage of random bits) We wish to stress that these existing means for perfect sampling rely on finding a good Markov chain for the problem at hand. RR does away with the chain, and in doing so breaks the O(n ln n) barrier that has ....

James A. Fill, Motoya Machida, Duncan J. Murdoch, and Jeffrey S. Rosenthal. Extension of Fill's perfect rejection sampling algorithm to general chains. Random Structures & Algorithms, 2000. To appear.

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Preprint. J.A. Fill, M. Machida, D.J. Murdoch, and J.S. Rosenthal (1999), Extension of Fill's perfect rejection sampling algorithm to general chains. Random Structures and Algorithms, to appear.

....are the same. Remark 2.3 (a) Note that no assumption is made in Algorithm 2.1 concerning monotonicity or discreteness of the state space. b) This algorithm is, like Fill s original algorithm [11] a form of rejection sampling (see, e.g. Devroye [6] This is explained in Section 2 of [14]. c) We have reversed the direction of time, and the roles of the kernels K and f K, compared to Fill [11] d) Algorithm 2.1 is interruptible, in the sense of Fill [11] e) Fill s original algorithm [11] also incorporated a search for a good value of t by doubling the previous value of t ....

Fill, J. A., Machida, M., Murdoch, D., and Rosenthal, J. (2000). Extension of Fill's perfect rejection sampling algorithm to general chains (extended abstract). Pages 37--52 in Monte Carlo Methods (ed.: N. Madras), Fields Institute Communications 26, American Mathematical Society.

....drawbacks of their own. These algorithms are noninterruptible, which means that the user must commit to running such an algorithm for its entire (random) running time even though that time is not known in advance. Failure to do so can introduce bias into the sample. Other algorithms, such as FMMR [3], are interruptible (when time is measured in Markov chain steps) but require storage and subsequent rereading of random bits used by the algorithm. The method we will present is both interruptible and readonce, with no storage of random bits needed. In addition, algorithms like CFTP and FMMR ....

....time (if measured in number of iterations of the basic Repeat loop) without introducing bias into the sample. Like read once coupling from the past [20] this algorithm does not require storage of any random bits. Another perfect sampling approach, that of Fill, Machida, Murdoch, and Rosenthal [3] is also interruptible but not read once, and so does requires storage of random bits) We wish to stress that these existing means for perfect sampling rely on finding a good Markov chain for the problem at hand. RR does away with the chain, and in doing so breaks the O(n ln n) barrier that has ....

James A. Fill, Motoya Machida, Duncan J. Murdoch, and Jeffrey S. Rosenthal. Extension of Fill's perfect rejection sampling algorithm to general chains. Random Structures & Algorithms, 2000. To appear.

....be able to do the first coupling conditional on a realized path from C t . This requires us to be able to calculate U t values conditional on the C t values; it is often quite difficult to do in practice. However, we have a great deal of freedom in choosing C t . Fill s perfect sampling algorithm [1, 2] also requires ex post facto coupling, though there the values of U t must be simulated conditional on an X t path instead: dominated CFTP has an easier task. With these ingredients, we proceed as follows. 1. Simulate C 0 from the equilibrium distribution of C t . 2. Choose T 0. 3. Simulate ....

James Allen Fill, Motoya Mochida, Duncan J. Murdoch, and Jeffrey S. Rosenthal. Extension of Fill's perfect rejection sampling algorithm to general chains. Technical Report 592, John's Hopkins University, 1999.

....We have strived to keep to the spirit of the talks presented at the Workshop on Monte Carlo Methods held at the Fields Institute for Research in Mathematical Sciences in Toronto in October, 1998 and make our results accessible to a broad audience. Technical details are provided in the full paper [14]. Following is our interruptible algorithm for generic chains. We discuss some of the terminology used and other details of the algorithm in Section 3. Algorithm 1.1 Choose and fix a positive integer t, choose an initial state X t from any distribution absolutely continuous with respect to #, ....

....may choose X t deterministically and arbitrarily. As mentioned above, we will discuss the details of Algorithm 1.1 in Section 3. First, in Section 2, we motivate our algorithm in the context of a rather general rejection sampling framework. A more rigorous treatment may be found in the full paper [14]. In Section 4 we discuss how the computational burden of tracking all of the trajectories Y(x) can be eased by the use of coalescence detection events in general and bounding processes in particular; these processes take on a very simple form (see Section 4.3) when the state space is partially ....

[Article contains additional citation context not shown here]

Fill, J. A., Machida, M., Murdoch, D., and Rosenthal, J. Extension of Fill's perfect rejection sampling algorithm to general chains. Preprint (1999). Available from http://www.mts.jhu.edu/~fill/.

....We have strived to keep to the spirit of the talks presented at the Workshop on Monte Carlo Methods held at the Fields Institute for Research in Mathematical Sciences in Toronto in October, 1998 and make our results accessible to a broad audience. Technical details are provided in the full paper [14]. Following is our interruptible algorithm for generic chains. We discuss some of the terminology used and other details of the algorithm in Section 3. Algorithm 1.1 Choose and fix a positive integer t, choose an initial state X t from any distribution absolutely continuous with respect to , ....

....may choose X t deterministically and arbitrarily. As mentioned above, we will discuss the details of Algorithm 1.1 in Section 3. First, in Section 2, we motivate our algorithm in the context of a rather general rejection sampling framework. A more rigorous treatment may be found in the full paper [14]. In Section 4 we discuss how the computational burden of tracking all of the trajectories Y(x) can be eased by the use of coalescence detection events in general and bounding processes in particular; these processes take on a very simple form (see Section 4.3) when the state space is partially ....

[Article contains additional citation context not shown here]

Fill, J. A., Machida, M., Murdoch, D., and Rosenthal, J. Extension of Fill's perfect rejection sampling algorithm to general chains. Preprint (1999). Available from http://www.mts.jhu.edu/~fill/.

No context found.

J. A. Fill, M. Machida, D. J. Murdoch, and J. S. Rosenthal, "Extension of Fill's perfect rejection sampling algorithm to general chains (extended abstract)," in Monte Carlo Methods, N. Madras, Ed. New York: Amer. Math. Soc., 2000, vol. 26, pp. 37--52.

No context found.

Fill, J.A., M. Machida, D.J. Murdoch and J.S. Rosenthal. "Extension of Fill's Perfect Rejection Sampling Algorithm to General Chains". Mimeo.

No context found.

Fill, J.A., Machida, M., Murdoch, D.J., and Rosenthal, J.S. (1999) Extension of Fill's perfect rejection sampling algorithm to general chains, 1999. Preprint, John Hopkins.

No context found.

J. A. Fill, M. Machida, D. J. Murdoch, and J. S. Rosenthal. Extension of Fill's perfect rejection sampling algorithm to general chains, 1999. Preprint.

No context found.

James Allen Fill, Motoya Machida, Duncan J. Murdoch, and Jerey S. Rosenthal. Extension of Fill's perfect rejection sampling algorithm to general chains. Technical report, The Johns Hopkins University, Dept. of Mathematical Sciences, 1999.

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