A Primer on Perfect Simulation

Thönnes, Elke

doi:10.1007/3-540-45043-2_13

Cited by 14 publications

(10 citation statements)

References 20 publications

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“…For large state spaces it is infeasible to monitor all initial conditions at time - T . However, this can be done efficiently if one can find a partial ordering over the state space that is preserved by the transition rule [ 12 ]:…”

Section: Preliminaries and Definitionsmentioning

confidence: 99%

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A Dominated Coupling From The Past algorithm for the stochastic simulation of networks of biochemical reactions

Hemberg

Barahona

2008

BMC Syst Biol

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Background: In recent years, stochastic descriptions of biochemical reactions based on the Master Equation (ME) have become widespread. These are especially relevant for models involving gene regulation. Gillespie's Stochastic Simulation Algorithm (SSA) is the most widely used method for the numerical evaluation of these models. The SSA produces exact samples from the distribution of the ME for finite times. However, if the stationary distribution is of interest, the SSA provides no information about convergence or how long the algorithm needs to be run to sample from the stationary distribution with given accuracy.

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Section: Preliminaries and Definitionsmentioning

confidence: 99%

“…The mark process generates a uniform random number each time D is changed. These marks are used to update the original process X according to the adapted functional (3) in a process that is equivalent to the direct simulation of X [ 12 ]. Heuristically, the DCFTP scheme works as follows.…”

Section: Preliminaries and Definitionsmentioning

confidence: 99%

A Dominated Coupling From The Past algorithm for the stochastic simulation of networks of biochemical reactions

Hemberg

Barahona

2008

BMC Syst Biol

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“…Our interest in this paper includes algorithms on state spaces of the form , where is an integer. For further references regarding perfect sampling on both discrete and continuous state spaces, see [32]- [34]. Now, we explain the CFTP algorithm.…”

Section: Perfect Sampling Algorithmsmentioning

confidence: 99%

Multiuser detection of synchronous code-division multiple-access signals by perfect sampling

Huang

Djurić

2002

IEEE Trans. Signal Process.

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Code-division multiple-access (CDMA) is a multiplexing technique that shows significant advantages over analog and conventional time-division multiple access (TDMA) systems. This technology has become a driving force behind the rapidly advancing communications industry. In order to recover the transmitted signal at the receiver in a CDMA system, demodulating techniques are engaged, where a prominent role is played by the multiuser detector. In this paper, we introduce a class of novel Bayesian multiuser detectors that are constructed by employing perfect sampling algorithms: the sandwiched CFTP and the Gibbs coupler. We show that the detector based on the sandwiched CFTP can be applied to systems with negative cross-correlations, whereas the Gibbs coupler detector can be used without restrictions. A salient feature of the proposed detectors is the use of exact (perfect) samples from posterior distributions. This feature provides them with several advantages over detectors based on the Gibbs sampler. Simulation results on systems with and without near-far resistance demonstrate improved performance of the proposed detectors over some other popular detectors. In the end, we also discuss some important computational issues of the proposed detectors.

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“…Some people prefer the explanation of CFTP in (Fill, 1998a). Subsequent to the writing of this primer on CFTP, the author became aware of two additional expositions on perfect sampling with Markov chains: (Dimakos, 1999) and (Thönnes, 1999).…”

Section: Q: Can You Quantify the User-impatience Bias?mentioning

confidence: 99%

Layered multishift coupling for use in perfect sampling algorithms (with a primer on CFTP)

Wilson¹

2000

Monte Carlo Methods

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In this article we describe a new coupling technique which is useful in a variety of perfect sampling algorithms. A multishift coupler generates a random function f () so that for each x ∈ R, f (x) − x is governed by the same fixed probability distribution, such as a normal distribution. We develop the class of layered multishift couplers, which are simple and have several useful properties. For the standard normal distribution, for instance, the layered multishift coupler generates an f () which (surprisingly) maps an interval of length ℓ to fewer than 2 + ℓ/2.35 points -useful in applications which perform computations on each such image point. The layered multishift coupler improves and simplifies algorithms for generating perfectly random samples from several distributions, including the autogamma distribution, posterior distributions for Bayesian inference, and the steady state distribution for certain storage systems. We also use the layered multishift coupler to develop a Markov-chain based perfect sampling algorithm for the autonormal distribution.At the request of the organizers, we begin by giving a primer on CFTP (coupling from the past); CFTP and Fill's algorithm are the two predominant techniques for generating perfectly random samples using coupled Markov chains.

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A Primer on Perfect Simulation

Cited by 14 publications

References 20 publications

A Dominated Coupling From The Past algorithm for the stochastic simulation of networks of biochemical reactions

A Dominated Coupling From The Past algorithm for the stochastic simulation of networks of biochemical reactions

Multiuser detection of synchronous code-division multiple-access signals by perfect sampling

Layered multishift coupling for use in perfect sampling algorithms (with a primer on CFTP)

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