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Topic: Gibbs sampling

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	Gibbs Sampling
		Gibbs sampling is well suited to coping with incomplete information and is often suggested for such applications.
		Geman and Geman [1984] place the idea of Gibbs sampling in a general setting in which the collection of variables is structured in a graphical model and each variable has a neighborhood corresponding to a local region of the graphical structure.
		Gibbs sampling can be used to learn Bayesian networks with missing data.
	www.cs.brown.edu /research/ai/dynamics/tutorial/Documents/GibbsSampling.html (821 words)

	Gibbs sampling - Wikipedia, the free encyclopedia
		Gibbs sampling is a special case of the Metropolis-Hastings algorithm, and thus an example of a Markov chain Monte Carlo algorithm.
		Gibbs sampling is applicable when the joint distribution is not known explicitly, but the conditional distribution of each variable is known.
		Gibbs sampling is particularly well-adapted to sampling the posterior distribution of a Bayesian network, since Bayesian networks are typically specified as a collection of conditional distributions.
	en.wikipedia.org /wiki/Gibbs_sampling (436 words)

	Gibbs sampling - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-30)
		Gibbs sampling is an algorithm to generate a sequence of samples from the joint probability distribution of two or more random variables.
		Gibbs sampling is a special case of the Metropolis-Hastings algorithm,
		The algorithm is named after the physicist J.W. Gibbs, in reference to an analogy between the sampling algorithm and statistical physics.
	encyclopedia.worldsearch.com /gibbs_sampling.htm (424 words)

	[No title]
		Gibbs sampling updates are then done for the Y values, with # lambda1 and lambda2 integrated away.
		Values for lambda1 and lambda2 # to go with each Y are sampled as well, from their conditional # distributions given Y. The result is a list with vectors matrix Y # and lambda1 and lambda2, holding the K+1 values for Y from the # Markov chain along with sampled lambdas.
		library(ts) acf (g1$lambda2[burnin:iters], lag.max=30, main="First Gibbs Sampler") acf (g2$lambda2[burnin:iters], lag.max=30, main="Second Gibbs Sampler") dev.off() }
	www.cs.toronto.edu /~radford/csc2541/ass1-prog (891 words)

	Gibbs Sampling - Gelfand (ResearchIndex)
		Gibbs sampling provides a Monte Carlo approach for carrying...
		Gelfand, A.E. Gibbs sampling (a contribution to the Encyclopedia of Statistical Science).
		1 The Gibbs stopper and the griddy Gibbs sampler (context) - Ritter, Tanner - 1992
	citeseer.ist.psu.edu /gelfand95gibbs.html (1071 words)

	[No title]
		The dft-mc program is the specialization of xxx-mc to the task of sampling from the posterior distribution of the overall model hyperparameters, the diffusion tree parameters, the latent vectors for training cases, and the structures, divergence times, and node locations of the diffusion trees.
		Locations for terminal nodes are also generated before the K Gibbs sampling updates, and discarded afterwards, as are case-by-case noise variances, if there is a third level in the prior for the noise.
		The single variable slice sampling procedure is used, applied to the logarithms (base e) of the parameters, using an initial interval of width "scale" (default one), which is not expanded.
	www.cs.toronto.edu /~radford/fbm.2003-06-29.doc/dft-mc.html (2740 words)

	Web Site for Perfectly Random Sampling with Markov Chains:
		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.
		Instead of obtaining a sample of this model with approximately the stationary distribution by Monte Carlo simulation, it is possible to obtain a result which is exactly distributed according to the stationary distribution.
	dimacs.rutgers.edu /~dbwilson/exact.html (14686 words)

	Gibbs sampling (Site not responding. Last check: 2007-10-30)
		Implement in R a Gibbs sampler for sampling from the posterior distribution for the Normal model with unknown mean and precision and independent normal and gamma priors.
		Your main loop should take as arguments the number of samples required, the sufficient statistics for the data (the sample size, the mean, and sample variance) and all the hyper-parameters which specify the prior.
		Suppose further that you observe a sample of size 15 with mean 25 and sample variance 20.
	www.mas.ncl.ac.uk /~ndjw1/teaching/sim/gibbs (458 words)

	CGIL Publication (Site not responding. Last check: 2007-10-30)
		Gibbs sampling has been used for models with linear (with respect to coefficients) regressions and normality assumptions for random effects.
		Those problems are illustrated through comparison of Gibbs sampling schemes for single-trait random regression test-day models with different model parameterizations, different functions used for regressions and posterior chains of different sizes.
		Gibbs sampling under hierarchical model parameterization had a lower level of autocorrelation and required less time for computation.
	cgil.uoguelph.ca /pub/abstracts/jamrozik2.html (245 words)

	Sampling from Gibbs Distributions (Site not responding. Last check: 2007-10-30)
		The standard approach to sampling from the Gibbs distribution is the "Markov Chain Monte Carlo" method.
		At the heart of this method is a Markov chain whose stationary distribution is the Gibbs distribution and which quickly converges to stationarity.
		We study the properties of the Glauber dynamics in two models of particular combinatorial interest: the Potts model, whose configurations are the set of proper colorings of a graph; and the hard core model, whose configurations are the set of independent sets of a graph.
	sunsite.berkeley.edu /TechRepPages/CSD-99-1088 (385 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.
		This approach is often easier to implement than Gibbs sampling and more efficient than simple Metropolis updates, due to the ability of slice sampling to adaptively choose the magnitude of changes made.
		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 (2023 words)

	R: Performs Gibbs sampling for the Bayesian model used in analyze climate model experiments
		The default values for the Gibbs sampler are the same as those used in the analysis of the paper.
		The function implements a Gibbs sampler for the Gaussian-based statistical model for present and future model biases as described in Quantifying Uncertainty in Projections of Regional Climate Change: A Bayesian Approach to the Analysis of Multimodel Ensembles (2004), Tebaldi, Smith Nychka and Mearns.
		Another detail of the sampling is that a burn in period is required for the Gibbs time series to move away from transient effects from particular initial conditions.
	www.cgd.ucar.edu /~nychka/REA/REA.Gibbs.html (783 words)

	Gibbs Sampling (Site not responding. Last check: 2007-10-30)
		In mid-September, Healy resident Chris Gibbs gave Beth Scheen a small orange and white cat.
		In mathematics and physics, Gibbs sampling is an algorithm to generate a sequence of samples from the joint distribution of two or more variables.
		Gibbs sampling is a variation on the Metropolis-Hastings algorithm, and thus it is an example of a Markov chain Monte Carlo algorithm.
	www.wikiverse.org /gibbs-sampling (436 words)

	Gibbs Sampling (Site not responding. Last check: 2007-10-30)
		Gibbs Sampling combines these by performing a modified Line Search but using a probabilistic selection to determine which solution is selected.
		Gibbs Sampling is similar to Simulated Annealing in that the user needs to choose the initial and final effective temperature, as well as the cooling schedule and the number of times a new solution is generated at each temperature.
		The steps involved in a Gibbs Sampling for all of the problems described in the Introduction are as follows.
	members.aol.com /btluke/featur06.htm (708 words)

	Recent Research (Site not responding. Last check: 2007-10-30)
		Importance sampling densities are derived from multivariate normal of Student t approximations to local behavior of the posterior density at its mode.
		The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical accuracy of the approximations to the expected value of functions of interest under the posterior.
		Overall, the Gibbs sampling algorithm has a slight edge, with the relative performance of MSM and SML based on the GHK simulator being difficult to evaluate.
	www.biz.uiowa.edu /faculty/jgeweke/papers.html (8826 words)

	Gibbs: Gibbs Sampling for Aligning RNA (Site not responding. Last check: 2007-10-30)
		A new method of discovering the common secondary structure of a family of homologous RNA sequences using Gibbs sampling and stochastic context-free grammars is proposed.
		Given an unaligned set of sequences, a Gibbs sampling step simultaneously estimates the secondary structure of each sequence and a set of statistical parameters describing the common secondary structure of the set as a whole.
		After the Gibbs sampling has produced a crude statistical model for the family, this model is translated into a stochastic context-free grammar, which is then refined by an Expectation Maximization (EM) procedure to produce a more complete model.
	www.cse.ucsc.edu /research/compbio/gibbs.html (319 words)

	Bayesian separation of discrete sources via Gibbs sampling
		In fact, MCMC methods such as Metropolis Hastings algorithms or Gibbs sampling (see [3], [4], [5], [6]) enable to sample from any general distribution.
		The aim of Gibbs sampling is to draw a multidimensional random variable through a given probability density.
		The main hypothesis its application requires is the possibility to easily simulate through marginal densities or the knowledge of their analytic formulae.
	www.supelec.fr /lss/MaxEnt2000/htm/Abstracts/senecal.html (475 words)

	Query-driven biclustering of microarray data by Gibbs sampling (Site not responding. Last check: 2007-10-30)
		Given the knowledge that a certain set of genes belongs to a specific pathway, an interesting question for biologists is to discover other genes that might share the same function as the given set of genes.
		In the case of query-driven biclustering to recruit patients of a certain pathological type while identifying the responsible genes, we use gene expression levels of the known set of patients to construct a prior for bicluster model of the bicluster.
		As in the original biclustering algorithm, Gibbs sampling technique is used for the parameter estimation.
	www.iscb.org /ismb2004/posters/qizheng.shengATesat.kuleuven.ac.be_169.html (386 words)

	Phylogenetic footprinting of co-expressed genes by Tree-Gibbs sampling (Site not responding. Last check: 2007-10-30)
		Phylogenetic footprinting of co-expressed genes by Tree-Gibbs sampling
		Motivation: Site/motif Gibbs sampling is a valuable technique for the detection and alignment of locally conserved regions (motifs) in both amino acids and nucleic acids sequences.
		It is an extension of the existing site/motif Gibbs sampler, programmed in C. On simulated data, the Tree-Gibbs algorithm works in situations where the classic site/motif sampler fails, but scores worse in others.
	www.iscb.org /ismb2003/posters/StefanATbiomath.rug.ac.be_56.html (243 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		In Gibbs sampling, we are given N sequences x1, ., xN, a motif length K, and a background model B, which is a set of probabilities that gives us the ratio of a residue being in the background model versus the true model.
		Gibbs Sampling: Algorithm: There are two basic steps to the Gibbs sampling algorithm, an initialization step followed by a predictive update step which involves iterative sampling.
		Sampling Iterations: (Predictive Update) Remove a sequence x = xi Recalculate model M Pick a new location of motif in xi according to probability that the location is a motif occurrence.
	www.stanford.edu /class/cs262/Spring2003/Notes/16.doc (2802 words)

	Laboratory of Computational Engineering: Teaching: S-114.600
		In this case the proposal distribution q is a Gaussian distribution with mean tt_i and diagonal covariance matrix, that is, the distribution is isotropic (equally wide in all directions).
		For the sake of the exercise we assume that we can not draw samples directly from our target distribution but can compute the probability density in a specified point (this is the usual case with models and distributions more complex than the Gaussian).
		In Gibbs sampling we have to be able to draw samples from the conditional distributions of the target distribution.
	www.lce.hut.fi /teaching/S-114.600/ex/sampling_en.html (526 words)

	Gibbs Sampling (Site not responding. Last check: 2007-10-30)
		Efficiency of proposal density is an issue, but where the form of the full conditional distributions is known, these may be used to obtain proposals for the above algorithm.
		In this case Gibbs sampling is combined with for example Metropolis-Hastings techniques.
		Such a sampling method is sometimes referred to as Metropolis-Hastings within Gibbs; although since Gibbs sampling is a special case of Metropolis-Hastings, this terminology is incorrect [9].
	www.maths.tcd.ie /~chas/node56.html (140 words)

	Abstract (Site not responding. Last check: 2007-10-30)
		The Gibbs sampler permits one to simulate realizations from complicated stochastic models in high dimensions by making use of the model's associated full conditional distributions, which will generally have a much simpler and more manageable form.
		In its most extreme version, the Gibbs sampler reduces the analysis of a complicated multivariate stochastic model to the consideration of that model's associated univariate full conditional distributions.
		The fourth example describes a reasonably sophisticated application of the Gibbs sampler in the important arena of credibility for classification ratemaking via hierarchical models, and involves the Bayesian prediction of frequency counts in workers compensation insurance.
	www.math.ucalgary.ca /~scollnik/balducci/abstracts/abstract.pcas94.html (202 words)

	Finding scientific topics -- Griffiths and Steyvers 101 (Supplement 1): 5228 -- Proceedings of the National Academy of ...
		by using importance sampling as in ref. 9, and the estimates
		We applied this analysis to the sample used to generate Fig.
		The superscripts indicate the topics to which individual words were assigned in a single sample, whereas the contrast level reflects the probability of a word being assigned to the most prevalent topic in the abstract, computed across samples.
	www.pnas.org /cgi/content/full/101/suppl_1/5228 (5127 words)

	Biclustering Microarray Data by Gibbs Sampling (Site not responding. Last check: 2007-10-30)
		Gibbs sampling has become a method of choice for the discovery of noisy patterns, known as motifs, in DNA and protein sequences.
		Gibbs sampling has the key advantage of providing transparent probabilistic interpretation of the biclusters.
		Furthermore, Gibbs sampling does not suffer from the problem of local minima that often characterizes Expectation-Maximizatoin.
	iscb.org /ismb2003/posters/qizheng.shengATesat.kuleuven.ac.be_3.html (143 words)

	GIBBS
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		Gibbs motif sampling: detection of bacterial outer membrane protein repeats.
		Lawrence, Altschul, Boguski, Liu, Neuwald and Wootton (1993) Detecting Subtle Sequence Signals: A Gibbs Sampling Strategy for Multiple Alignment, Science 262:208-214.
	bioweb.pasteur.fr /seqanal/interfaces/gibbs-simple.html (133 words)

	Bayesian Factor Analysis By Gibbs Sampling and Iterated Conditional Modes (ResearchIndex) (Site not responding. Last check: 2007-10-30)
		Abstract: Press and Shigemasu proposed a Bayesian factor analysis model in which factor scores, factor loadings, and disturbance variances and covariances were estimated in closed form using a large sample approximation for one of the terms in the posterior distribution.
		This paper shows that by using Gibbs sampling or Iterated Conditional Modes approaches to estimation instead of the large sample approximation, we can obtain improved point estimators in small samples.
		Bayesian Factor Analysis By Gibbs Sampling and Iterated..
	citeseer.csail.mit.edu /270003.html (343 words)

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