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Topic: Rejection sampling

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	Rejection sampling - Wikipedia, the free encyclopedia
		In mathematics, Rejection sampling is a technique used to generate observations from a distribution.
		It generates sampling values from an arbitrary probability distribution function f(x) by using an instrumental distribution g(x), under the only restriction that f(x) < Mg(x) where M > 1 is an appropriate bound on f(x) / g(x).
		Rejection sampling is usually used in cases where the form of f(x) makes sampling difficult.
	en.wikipedia.org /wiki/Rejection_sampling (395 words)

	Random walk Monte Carlo (Site not responding. Last check: 2007-09-30)
		Rejection sampling : Approximates a distribution with another distribution as a proposal density from which samples be drawn.
		Samples are drawn from the density then conditionally rejected to ensure that samples approximate the target density.
		Adaptive rejection sampling: A variant of rejection sampling that modifies the proposal density on fly.
	www.freeglossary.com /Markov_chain_Monte_Carlo (461 words)

	Random walk Monte Carlo - InformationBlast
		Rejection sampling: Approximates a distribution with another distribution, known as a proposal density, from which samples can be drawn.
		Samples are drawn from the proposal density then conditionally rejected to ensure that the samples approximate the target density.
		Gibbs sampling: Requires all the conditional distributions of the target distribution to be known in closed form.
	www.informationblast.com /Random_walk_Monte_Carlo.html (515 words)

	Web Site for Perfectly Random Sampling with Markov Chains:
		When rejection sampling has been tried, but has proved impractical, it may be possible to convert the rejection algorithm into a perfect tempering algorithm, with a significant gain in algorithm efficiency.
		In perfect sampling algorithms, a sample is drawn exactly from the stationary distribution of a chain, as opposed to methods that run the chain ``for a long time'' and create samples drawn from a distribution that is close to the stationary distribution.
		Some perfect sampling algorithms for point processes are based on an extension of CFTP known as coupling into and from the past; for completeness, we give a read-once version of coupling into and from the past, but it remains unpractical.
	dimacs.rutgers.edu /~dbwilson/exact.html (13008 words)

	[No title] (Site not responding. Last check: 2007-09-30)
		Adaptive Rejection Sampling by Wally Gilks wally.gilks@mrc-bsu.cam.ac.uk MRC Biostatistics Unit, Cambridge, UK Adaptive rejection sampling (ARS) is a method for efficiently sampling from any univariate probability density function which is log-concave.
		ARMS is a generalisation of the method of adaptive rejection sampling (ARS) (Gilks, 1992), which was itself a development of the original method proposed by Gilks and Wild (1992).
		The procedure is exact (in the sense of returning samples from the exact target density), regardless of the degree of convexity in the log density.
	www.mrc-bsu.cam.ac.uk /pub/methodology/adaptive_rejection/readme (1163 words)

	rejection - Hutchinson encyclopedia article about rejection
		If rejection does not respond to treatment, the donated tissue is destroyed.
		The rejection slip was so tactfully worded that he felt kindly toward the editor.
		Moreover, the recollection of the rejection and the part he had played in the affair tortured him with shame.
	encyclopedia.farlex.com /rejection (168 words)

	6.2.6. What is a Sequential Sampling Plan?
		Sequential sampling is different from single, double or multiple sampling.
		How many total samples looked at is a function of the results of the sampling process.
		Efficiency for a sequential sampling scheme is measured by the average sample number (ASN) required for a given Type I and Type II set of errors.
	www.itl.nist.gov /div898/handbook/pmc/section2/pmc26.htm (453 words)

	Sample
		Simple random sampling is the most basic: sample points are located, independently of each other, anywhere within the sampling region and all possible sample points have an equal probability of being selected.
		One way to improve the sampling pattern is to overlay a regular array of cells, or a "grid," on the sample region and to select one or more samples within each cell.
		Sample also records the sample coordinates and grid cell identifiers as attributes in the output shapefile.
	www.quantdec.com /sample/index.htm (2193 words)

	Global Purchasing - Product Inspection, Single Sampling Plan (MIL-105D), Product Rejection, Rework and Re-inspection
		For example, a lot size is 800 and the sample size is 80, if the prior agreement between trader and vendor calls for an AQL% of 0.25, it means that at least one (1) defect found in the lot constitutes grounds for the rejection of the entire lot.
		The product is rejected when its quality level, as determined by the random sampling, does not comply to the contractual requirements.
		In case of a rejection, the trader may conduct 100% inspection of the lot, sort the acceptable from the unacceptable, then ship the acceptable only and return the unacceptable.
	www.export911.com /e911/purch/docMIL.htm (599 words)

	Steve's Projects Page
		Rejection sampling is a method for simulating observations from a given, but complex, density function f, by simulating from a second, simpler, density g and then stochastically accepting or rejecting each observation in such a way that accepted observations do in fact have density f.
		At present, adaptive rejection sampling methods are restricted to univariate densities f, and we are forced to rely upon approximate techniques for sampling from multivariate densities.
		The development of a general algorithm for multivariate adaptive rejection sampling would be an important breakthrough in statistical computing, and would remove the need for approximate sampling techniques such as Markov chain Monte Carlo, for example.
	www.statslab.cam.ac.uk /~steve/Research/Projects (723 words)

	Diagnosis and Grading of Acute Allograft Rejection (Site not responding. Last check: 2007-09-30)
		In a similar fashion as it is seen in unmodified acute allograft pancreas rejection in laboratory animals, the inflammation in the early stages of rejection appears to be localized to the septal areas with accentuation around small veins and capillaries and associated venous endotheliitis.
		Arterial involvement is characteristic of the higher grades of rejection.
		Sampling variations affect the ability to observe the arterial lesions.
	tpis.upmc.edu /tpis/pancreas/PARejOvr.html (345 words)

	Web Site for Perfectly Random Sampling with Markov Chains:
		This is because the computational requirement for simulating such samples increases exponentially with the selection rate, and also due to the need to be able to simulate a sample of size 1 from the population at equilibrium.
		For the only case where the distribution of a sample of size one is known, that of parent independent mutations, more efficient simulation algorithms exist.
		Further, the computation involved in generating such samples appears to be less than that of simulating the ancestral selection graph until its ultimate ancestor.
	www.dbwilson.com /exact (14686 words)

	Metropolized Independent Sampling with Comparisons to Rejection Sampling and Importance Sampling - Liu (ResearchIndex)
		The eigenvalues and eigenvectors of the corresponding Markov chain, as well as a sharp bound for the total variation distance between the n-th updated distribution and the target distribution, are provided.
		Furthermore, the relationship between this scheme, rejection sampling, and importance sampling are studied with emphasizes on their...
		Metropolized independent sampling with comparisons to rejection sampling and importance sampling.
	citeseer.ist.psu.edu /373286.html (336 words)

	Slice sampling, Radford M. Neal
		Markov chain sampling methods that adapt to characteristics of the distribution being sampled can be constructed using the principle that one can ample from a distribution by sampling uniformly from the region under the plot of its density function.
		Such "slice sampling" methods are easily implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn.
		For single-variable slice sampling, the variation of slice sampling proposed by Neal operates analogously to Gibbs sampling in the sense that to obtain the next point x1, y is generated from the conditional distribution [yx0] given the current point x0 and then x1 is drawn from [xy].
	projecteuclid.org /getRecord?id=euclid.aos/1056562461 (1940 words)

	Research Statement
		We considered the perfect rejection sampling algorithm specifically in the continuous and monotone settings, and proved the correctness of the algorithm under certain regularity conditions (Machida, 2001a).
		We proposed a possible extension of the perfect rejection sampling algorithm using a stochastically dominant Markov kernel L in addition to the Markov kernel K originally devised for MCMC (Fill, Machida, Murdoch and Rosenthal, 2000).
		Though this investigation is still in a preliminary stage, we hope to demonstrate that the perfect rejection sampling algorithm has its own advantage in practice and can be a genuinely useful alternative to the CFTP algorithm.
	math.tntech.edu /machida/research.html (775 words)

	Daniel Eaton // Adaptive Rejection Sampling in Matlab
		It's a neat algorithm to sample exactly (all accepted samples are iid) and efficiently from any univariate log-concave distribution.
		In fact, it can also be used to sample from joint multivariate log-concave distributions (conditionally, see paper) as well, or, even as a proposal for the Metropolis-Hastings algorithm for any univariate target (Gilks, W. R., Best, N. and Tan, K. Adaptive rejection Metropolis sampling.
		As in ordinary rejection sampling, the target distribution need not be normalized.
	www.cs.ubc.ca /~deaton/tut/ars.html (131 words)

	On Nonlinear and Nonnormal Filter Using Rejection Sampling - Tanizaki (ResearchIndex)
		Abstract: In this paper, a nonlinear and/or nonnormal filter is proposed using rejection sampling.
		Generating random draws of the state-vector directly from the filtering density, the filtering estimate is simply obtained as the arithmetic average of the random draws.
		Tanizaki, H. On the Nonlinear and Nonnormal Filter Using Rejection Sampling, IEEE Trans.
	citeseer.ist.psu.edu /282592.html (641 words)

	Rejection sampling (Site not responding. Last check: 2007-09-30)
		For sampling values from an arbitrary probability distribution function Also called the acceptance-rejection method.
		These objects provide information about managed nodes supporting packet sampling, including packet sampling capabilities and configuration.
		They also allow to configure packet sampling concerning the IP interface at which packets are sampled and the packet selections methods used for sampling.
	www.serebella.com /encyclopedia/article-Rejection_sampling.html (441 words)

	Perfect simulation of some point processes for the impatient user, Elke Thönnes
		In [5] Gibbs sampling is applied to a bivariate point process, the penetrable spheres mixture model [19].
		Fill's algorithm is a form of rejection sampling and similarly to CFTP requires sufficient monotonicity 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.
	www.projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aap/1029954267 (378 words)

	Free software by Csaba Szepesvári
		The idea is to have a number of generic Monte-Carlo based sampling and integration routines that can accept functions and return the results.
		Note that this is an experimental version (say version 0.1) with a rather limited functionality (but it worked for me).
		The plan is to extend this package to other sampling methods.
	www.sztaki.hu /~szcsaba/software/index.html (340 words)

	Monte Carlo Integration with Acceptance-Rejection
		We consider Monte Carlo integration under rejection sampling or Metropolis-Hastings sampling.
		While taking the likelihood approach of Kong et al., we basically treat the sampling scheme as a random design and define a stratified estimator of the baseline measure.
		We establish that the likelihood estimator has no greater asymptotic variance than the crude Monte Carlo estimator under rejection sampling or independence Metropolis-Hastings sampling.
	www.bepress.com /jhubiostat/paper21 (185 words)

	chapter_11 (Site not responding. Last check: 2007-09-30)
		Exercise 11.7: Gibbs Sampling from the Bivariate Normal
		Exercise 11.17: Gibbs Sampling in a Regression Model with Inequality Constraints: Geweke (1996b)
		Gibbs Sampling Algorithm which imposes diminishing returns to scale
	www.econ.iastate.edu /faculty/tobias/chapter_11.html (125 words)

	Iain Murray (Site not responding. Last check: 2007-09-30)
		Note on Rejection sampling and exact sampling with the Metropolised Independence Sampler
		This short note shows a close relationship between standard rejection sampling and exact sampling by coupling from the past applied to a Metropolised independence sampler.
		I now know that this idea, first presented as a ten-minute tea-time talk, is probably a duplicate of an unavailable work (Cai 1997), and is closely related to a paper by Jun S. Liu (1996), who provides a much more detailed analysis.
	www.gatsby.ucl.ac.uk /~iam23/pub/04rejection_cftp (89 words)

	Citations: Intro to Monte Carlo methods - MacKay (ResearchIndex) (Site not responding. Last check: 2007-09-30)
		Roughly speaking, these methods draw random samples from an unknown target distribution f(X) by biasing the search for this distribution towards higher probability regions.
		The family of stochastic inference methods can be grouped into the independent Monte Carlo methods (importance sampling and rejection sampling [4, 10, 14] and the dependent Markov Chain....
		) and the dependent Markov Chain Monte Carlo (MCMC) methods (Gibbs sampling, Metropolis sampling, and hybrid Monte Carlo) 5, 10, 11, 15] The goal of all these methods is to simulate drawing a random sample from a target distribution P (x) generally defined by a Bayesian network or graphical.
	citeseer.ist.psu.edu /context/1064916/0 (544 words)

	VLDB 1992: 375-382
		In the past, two basic approaches for sampling from B+ trees have been suggested: sampling from the ranked trees and acceptance/rejection sampling from non-ranked trees.
		In this paper we introduce a new sampling method based on pseudo-ranked B+ trees, which are B+ trees supplemented with information loosely describing the estimated rank limits.
		Frank Olken, Doron Rotem: Sampling from Spatial Databases.
	www.vldb.org /dblp/db/conf/vldb/Antoshenkov92.html (580 words)

	Another Look at Rejection Sampling Through Importance Sampling (Site not responding. Last check: 2007-09-30)
		We provide a different view of rejection sampling by putting it in the framework of importance sampling.
		When rejection sampling with an envelope function g is viewed as a special importance sampling algorithm, we show that it is inferior to the importance sampling algorithm with g as the proposal distribution in terms of the Chi-square distance between the proposal distribution and the target distribution.
		Similar conclusions are drawn for comparing rejection control with importance sampling.
	ftp.isds.duke.edu /WorkingPapers/04-30.html (113 words)

	Abstract (Site not responding. Last check: 2007-09-30)
		Abstract: The intervened Poisson distribution (IPD) was introduced by Shanmugam (1985) as a replacement for the zero-truncated Poisson distribution in order to model rare event count data when some intervention process may alter the mean of the rare event generating process under observation.
		This paper will demonstrate how a full Bayesian analysis of an intervened Poisson model may proceed by making use of the Gibbs sampler and adaptive rejection sampling methods for log-concave densities.
		The posterior analysis based upon the simulation consistent Gibbs sampling methodology is also compared to the exact analysis developed on the basis of numerical integration.
	www.math.ucalgary.ca /~scollnik/balducci/abstracts/abstract.p4.html (166 words)

	David Draper
		The likelihood (and approximate likelihood) approaches we examine are based on the methods most widely used in current applied multilevel analyses: maximum likelihood (ML) and restricted ML (REML) for Gaussian outcomes, and marginal and penalised quasi-likelihood (MQL and PQL) for Bernoulli outcomes.
		Sampling errors under non-probability sampling (with Bowater R; January 1999): Chapter 4 in Model Quality Reports in Business Statistics: Theory and Methods for Quality Evaluation, by Bowater R, Chambers C, Davies P, Draper D, Skinner C, Smith P. Luxembourg: Eurostat.
		Even nonparametric bootstrap confidence intervals, which can be regarded as crude approximations to posterior distribution summaries of particular interest, perform surprisingly poorly with fairly large samples of long-tailed data, because the empirical CDF has nothing to say about the tails of the distribution beyond the largest observation.
	www.cse.ucsc.edu /~draper/old-index.html (6091 words)

	DMTCS Conference vol AD (2005), pp. 125-138
		It combines the Boltzmann framework, a judicious use of rejection, a new combinatorial bijection found by Fusy, Poulalhon and Schaeffer, as well as a precise analytic description of the generating functions counting planar graphs, which was recently obtained by Giménez and Noy.
		Then, for each generation, the time complexity is quadratic for exact-size uniform sampling and linear for approximate-size sampling.
		If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files.
	www.dmtcs.org /proceedings/abstracts/dmAD0112.abs.html (354 words)

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