scholarly journals Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding

2011 ◽  
pp. 64-90 ◽  
Author(s):  
G. K. Ambler ◽  
B. W. Silverman
Keyword(s):  
Point Processes ◽  
Wavelet Thresholding ◽  
Perfect Simulation ◽  
Interaction Point ◽  
The Past ◽  
Coupling From The Past

Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes

2000 ◽  
Vol 32 (3) ◽  
pp. 844-865 ◽  
Author(s):  
Wilfrid S. Kendall ◽  
Jesper Møller
Keyword(s):  
Point Process ◽  
Discrete Time ◽  
Point Processes ◽  
Random Point ◽  
Perfect Simulation ◽  
Stable Point ◽  
Birth And Death Processes ◽  
The Past ◽  
Coupling From The Past ◽  
Equilibrium Distributions

In this paper we investigate the application of perfect simulation, in particular Coupling from the Past (CFTP), to the simulation of random point processes. We give a general formulation of the method of dominated CFTP and apply it to the problem of perfect simulation of general locally stable point processes as equilibrium distributions of spatial birth-and-death processes. We then investigate discrete-time Metropolis-Hastings samplers for point processes, and show how a variant which samples systematically from cells can be converted into a perfect version. An application is given to the Strauss point process.

Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes

2000 ◽  
Vol 32 (03) ◽  
pp. 844-865 ◽  
Author(s):  
Wilfrid S. Kendall ◽  
Jesper Møller
Keyword(s):  
Point Process ◽  
Discrete Time ◽  
Point Processes ◽  
Random Point ◽  
Perfect Simulation ◽  
Stable Point ◽  
Birth And Death Processes ◽  
The Past ◽  
Coupling From The Past ◽  
Equilibrium Distributions

In this paper we investigate the application of perfect simulation, in particular Coupling from the Past (CFTP), to the simulation of random point processes. We give a general formulation of the method of dominated CFTP and apply it to the problem of perfect simulation of general locally stable point processes as equilibrium distributions of spatial birth-and-death processes. We then investigate discrete-time Metropolis-Hastings samplers for point processes, and show how a variant which samples systematically from cells can be converted into a perfect version. An application is given to the Strauss point process.

scholarly journals Exact Monte Carlo simulation for fork-join networks

2011 ◽  
Vol 43 (02) ◽  
pp. 484-503 ◽  
Author(s):  
Hongsheng Dai
Keyword(s):  
Monte Carlo ◽  
Response Times ◽  
Simulation Method ◽  
Perfect Simulation ◽  
Analytic Approximations ◽  
The Past ◽  
Coupling From The Past ◽  
Service Stations ◽  
Explicit Formulae ◽  
Queue Lengths

In a fork-join network each incoming job is split into K tasks and the K tasks are simultaneously assigned to K parallel service stations for processing. For the distributions of response times and queue lengths of fork-join networks, no explicit formulae are available. Existing methods provide only analytic approximations for the response time and the queue length distributions. The accuracy of such approximations may be difficult to justify for some complicated fork-join networks. In this paper we propose a perfect simulation method based on coupling from the past to generate exact realisations from the equilibrium of fork-join networks. Using the simulated realisations, Monte Carlo estimates for the distributions of response times and queue lengths of fork-join networks are obtained. Comparisons of Monte Carlo estimates and theoretical approximations are also provided. The efficiency of the sampling algorithm is shown theoretically and via simulation.

scholarly journals Exact Monte Carlo simulation for fork-join networks

2011 ◽  
Vol 43 (2) ◽  
pp. 484-503 ◽  
Author(s):  
Hongsheng Dai
Keyword(s):  
Monte Carlo ◽  
Response Times ◽  
Simulation Method ◽  
Perfect Simulation ◽  
Analytic Approximations ◽  
The Past ◽  
Coupling From The Past ◽  
Service Stations ◽  
Explicit Formulae ◽  
Queue Lengths

In a fork-join network each incoming job is split into K tasks and the K tasks are simultaneously assigned to K parallel service stations for processing. For the distributions of response times and queue lengths of fork-join networks, no explicit formulae are available. Existing methods provide only analytic approximations for the response time and the queue length distributions. The accuracy of such approximations may be difficult to justify for some complicated fork-join networks. In this paper we propose a perfect simulation method based on coupling from the past to generate exact realisations from the equilibrium of fork-join networks. Using the simulated realisations, Monte Carlo estimates for the distributions of response times and queue lengths of fork-join networks are obtained. Comparisons of Monte Carlo estimates and theoretical approximations are also provided. The efficiency of the sampling algorithm is shown theoretically and via simulation.

scholarly journals Attractive regular stochastic chains: perfect simulation and phase transition

2013 ◽  
Vol 34 (5) ◽  
pp. 1567-1586 ◽  
Author(s):  
SANDRO GALLO ◽  
DANIEL Y. TAKAHASHI
Keyword(s):  
Phase Transition ◽  
Infinite Order ◽  
Concentration Of Measure ◽  
Finite Alphabet ◽  
Perfect Simulation ◽  
Exponential Rate ◽  
The Past ◽  
Coupling From The Past ◽  
Probability Kernel ◽  
Independent And Identically Distributed

AbstractWe prove that uniqueness of the stationary chain, or equivalently, of the$g$-measure, compatible with an attractive regular probability kernel is equivalent to either one of the following two assertions for this chain: (1) it is a finitary coding of an independent and identically distributed (i.i.d.) process with countable alphabet; (2) the concentration of measure holds at exponential rate. We show in particular that if a stationary chain is uniquely defined by a kernel that is continuous and attractive, then this chain can be sampled using a coupling-from-the-past algorithm. For the original Bramson–Kalikow model we further prove that there exists a unique compatible chain if and only if the chain is a finitary coding of a finite alphabet i.i.d. process. Finally, we obtain some partial results on conditions for phase transition for general chains of infinite order.

scholarly journals Perfect posterior simulation for mixture and hidden Markov models

2010 ◽  
Vol 13 ◽  
pp. 246-259
Author(s):  
Kasper K. Berthelsen ◽  
Laird A. Breyer ◽  
Gareth O. Roberts
Keyword(s):  
Bayesian Inference ◽  
Statistical Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Perfect Simulation ◽  
Unknown Parameters ◽  
The Past ◽  
Coupling From The Past ◽  
Posterior Simulation ◽  
Unknown Mixture

AbstractIn this paper we present an application of the read-once coupling from the past algorithm to problems in Bayesian inference for latent statistical models. We describe a method for perfect simulation from the posterior distribution of the unknown mixture weights in a mixture model. Our method is extended to a more general mixture problem, where unknown parameters exist for the mixture components, and to a hidden Markov model.

scholarly journals Relating Time and Customer Averages for Queues Using ‘forward’ Coupling from the Past

2008 ◽  
Vol 45 (02) ◽  
pp. 568-574
Author(s):  
Erol A. Peköz ◽  
Sheldon M. Ross
Keyword(s):  
Queueing System ◽  
Steady State Distribution ◽  
State Distribution ◽  
The Past ◽  
Coupling From The Past ◽  
Poisson Arrivals ◽  
Time Averages ◽  
Time Average ◽  
New Better Than Used ◽  
Better Than

We give a new method for simulating the time average steady-state distribution of a continuous-time queueing system, by extending a ‘read-once’ or ‘forward’ version of the coupling from the past (CFTP) algorithm developed for discrete-time Markov chains. We then use this to give a new proof of the ‘Poisson arrivals see time averages’ (PASTA) property, and a new proof for why renewal arrivals see either stochastically smaller or larger congestion than the time average if interarrival times are respectively new better than used in expectation (NBUE) or new worse than used in expectation (NWUE).

scholarly journals On exact sampling of stochastic perpetuities

2011 ◽  
Vol 48 (A) ◽  
pp. 165-182 ◽  
Author(s):  
Jose H. Blanchet ◽  
Karl Sigman
Keyword(s):  
Fixed Point ◽  
Net Present Value ◽  
Positive Density ◽  
Simulation Algorithm ◽  
Present Value ◽  
The Past ◽  
Coupling From The Past ◽  
Fixed Point Equation ◽  
Point Equation ◽  
The Right

A stochastic perpetuity takes the formD∞=∑n=0∞exp(Y1+⋯+Yn)Bn, whereYn:n≥0) and (Bn:n≥0) are two independent sequences of independent and identically distributed random variables (RVs). This is an expression for the stationary distribution of the Markov chain defined recursively byDn+1=AnDn+Bn,n≥0, whereAn=eYn;D∞then satisfies the stochastic fixed-point equationD∞D̳AD∞+B, whereAandBare independent copies of theAnandBn(and independent ofD∞on the right-hand side). In our framework, the quantityBn, which represents a random reward at timen, is assumed to be positive, unbounded with EBnp<∞ for somep>0, and have a suitably regular continuous positive density. The quantityYnis assumed to be light tailed and represents a discount rate from timenton-1. The RVD∞then represents the net present value, in a stochastic economic environment, of an infinite stream of stochastic rewards. We provide an exact simulation algorithm for generating samples ofD∞. Our method is a variation ofdominated coupling from the pastand it involves constructing a sequence of dominating processes.

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