SHIFT AND SCALE COUPLING METHODS FOR PERFECT SIMULATION

2003 ◽  
Vol 17 (3) ◽  
pp. 277-303 ◽  
Author(s):  
J.N. Corcoran ◽  
U. Schneider
Keyword(s):  
Markov Chains ◽  
Sampling Procedure ◽  
Attractive Alternative ◽  
Density Functions ◽  
Perfect Simulation ◽  
Perfect Sampling ◽  
Slice Sampling ◽  
Sample Paths ◽  
Coupling Methods ◽  
Sampling Algorithms

We describe and develop a variation on a layered multishift coupler due to Wilson that uses a slice sampling procedure to allow one to obtain potentially common draws from two different distributions. Our main application is coupling sample paths of Markov chains for use in perfect sampling algorithms. The coupler is based on slicing density functions and we describe a “folding” mechanism as an attractive alternative to the accept/reject step commonly used in slice sampling algorithms. Applications of the coupler are given to storage models and to auto-gamma distribution sampling.

Exact Markov Chain Monte Carlo Algorithms and Their Applications in Probabilistic Data Analysis and Inference

2009 ◽  
pp. 161-183
Author(s):  
Dominic Savio Lee
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Data Analysis ◽  
Markov Chain Monte Carlo ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Probabilistic Data ◽  
Perfect Sampling ◽  
Monte Carlo Algorithms ◽  
Sampling Algorithms

This chapter describes algorithms that use Markov chains for generating exact sample values from complex distributions, and discusses their use in probabilistic data analysis and inference. Its purpose is to disseminate these ideas more widely so that their use will become more widespread, thereby improving Monte Carlo simulation results and stimulating greater research interest in the algorithms themselves. The chapter begins by introducing Markov chain Monte Carlo (MCMC), which stems from the idea that sample values from a desired distribution f can be obtained from the stationary states of an ergodic Markov chain whose stationary distribution is f. To get sample values that have distribution f exactly, it is necessary to detect when the Markov chain has reached its stationary distribution. Under certain conditions, this can be achieved by means of coupled Markov chains—these conditions and the resulting exact MCMC or perfect sampling algorithms and their applications are described.

The Move-to-Front Rule: A Case Study for two Perfect Sampling Algorithms

1998 ◽  
Vol 12 (3) ◽  
pp. 283-302 ◽  
Author(s):  
James Allen Fill
Keyword(s):  
Finite Population ◽  
Mixing Time ◽  
Test Case ◽  
Perfect Sampling ◽  
Mcmc Algorithms ◽  
Time Result ◽  
Elementary Problem ◽  
Sampling Algorithms ◽  
Coupling Algorithm

The elementary problem of exhaustively sampling a finite population without replacement is used as a nonreversible test case for comparing two recently proposed MCMC algorithms for perfect sampling, one based on backward coupling and the other on strong stationary duality. The backward coupling algorithm runs faster in this case, but the duality-based algorithm is unbiased for user impatience. An interesting by-product of the analysis is a new and simple stochastic interpretation of a mixing-time result for the move-to-front rule.

Asymptotic and monotonicity properties of some repairable systems

1998 ◽  
Vol 30 (4) ◽  
pp. 1089-1110 ◽  
Author(s):  
Günter Last ◽  
Ryszard Szekli
Keyword(s):  
Markov Chains ◽  
Total Variation ◽  
Repairable Systems ◽  
Lifetime Distributions ◽  
Failure Times ◽  
Imperfect Repair ◽  
Coupling Methods ◽  
Monotonicity Properties ◽  
Heavy Tailed

The paper studies a model of repairable systems which is flexible enough to incorporate the standard imperfect repair and many other models from the literature. Palm stationarity of virtual ages, inter-failure times and degrees of repair is studied. A Loynes-type scheme and Harris recurrent Markov chains combined with coupling methods are used. Results on the weak total variation and moment convergences are obtained and illustrated by examples with IFR, DFR, heavy-tailed and light-tailed lifetime distributions. Some convergences obtained are monotone and/or at a geometric rate.

scholarly journals Perfect sampling of Markov chains with piecewise homogeneous events

2012 ◽  
Vol 69 (6) ◽  
pp. 247-266 ◽  
Author(s):  
Ana Bušić ◽  
Bruno Gaujal ◽  
Furcy Pin
Keyword(s):  
Markov Chains ◽  
Perfect Sampling

scholarly journals Probabilistic Cellular Automata, Invariant Measures, and Perfect Sampling

2013 ◽  
Vol 45 (04) ◽  
pp. 960-980 ◽  
Author(s):  
Ana Bušić ◽  
Jean Mairesse ◽  
Irène Marcovici
Keyword(s):  
Markov Chain ◽  
Cellular Automaton ◽  
Invariant Measures ◽  
Sampling Procedure ◽  
Monotonicity Property ◽  
Local Rule ◽  
Probabilistic Cellular Automata ◽  
Perfect Sampling ◽  
One Dimensional ◽  
Probabilistic Cellular Automaton

A probabilistic cellular automaton (PCA) can be viewed as a Markov chain. The cells are updated synchronously and independently, according to a distribution depending on a finite neighborhood. We investigate the ergodicity of this Markov chain. A classical cellular automaton is a particular case of PCA. For a one-dimensional cellular automaton, we prove that ergodicity is equivalent to nilpotency, and is therefore undecidable. We then propose an efficient perfect sampling algorithm for the invariant measure of an ergodic PCA. Our algorithm does not assume any monotonicity property of the local rule. It is based on a bounding process which is shown to also be a PCA. Last, we focus on the PCA majority, whose asymptotic behavior is unknown, and perform numerical experiments using the perfect sampling procedure.

scholarly journals Adipose tissue-derived stem cells show considerable promise for regenerative medicine applications

2013 ◽  
Vol 18 (4) ◽  
Author(s):  
Izabela Harasymiak-Krzyżanowska ◽  
Alicja Niedojadło ◽  
Jolanta Karwat ◽  
Lidia Kotuła ◽  
Paulina Gil-Kulik ◽  
...  
Keyword(s):  
Stem Cells ◽  
Adipose Tissue ◽  
Regenerative Medicine ◽  
Stromal Cells ◽  
Pluripotent Stem Cells ◽  
Sampling Procedure ◽  
Patient Comfort ◽  
Attractive Alternative ◽  
Isolated Cells ◽  
Alternative Source

AbstractThe stromal-vascular cell fraction (SVF) of adipose tissue can be an abundant source of both multipotent and pluripotent stem cells, known as adipose-derived stem cells or adipose tissue-derived stromal cells (ADSCs). The SVF also contains vascular cells, targeted progenitor cells, and preadipocytes. Stromal cells isolated from adipose tissue express common surface antigens, show the ability to adhere to plastic, and produce forms that resemble fibroblasts. They are characterized by a high proliferation potential and the ability to differentiate into cells of meso-, ecto- and endodermal origin. Although stem cells obtained from an adult organism have smaller capabilities for differentiation in comparison to embryonic and induced pluripotent stem cells (iPSs), the cost of obtaining them is significantly lower. The 40 years of research that mainly focused on the potential of bone marrow stem cells (BMSCs) revealed a number of negative factors: the painful sampling procedure, frequent complications, and small cell yield. The number of stem cells in adipose tissue is relatively large, and obtaining them is less invasive. Sampling through simple procedures such as liposuction performed under local anesthesia is less painful, ensuring patient comfort. The isolated cells are easily grown in culture, and they retain their properties over many passages. That is why adipose tissue has recently been treated as an attractive alternative source of stem cells. Essential aspects of ADSC biology and their use in regenerative medicine will be analyzed in this article.

scholarly journals Perfect simulation for a class of positive recurrent Markov chains

2007 ◽  
Vol 17 (3) ◽  
pp. 781-808 ◽  
Author(s):  
Stephen B. Connor ◽  
Wilfrid S. Kendall
Keyword(s):  
Markov Chains ◽  
Perfect Simulation ◽  
Positive Recurrent
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