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	Nonparametric Tests for Conditional Independence
		Liangjun Su As David (1979) puts it, independence and conditional independence form the basis of probability theory and are equally fundamental in the theory of statistical inference.
		In a seminal paper, Granger (1980) introduces the concept of Granger non-causality at the distribution level, which is a particular case of conditional independence.
		Further, conditional independence is often used as an identification condition in econometrics (e.g., Imbens and Newey, 2001; Lechner and Miquel, 2002).
	www.econ.ucsd.edu /~lsu/abstractshtml.html (712 words)

	Conditional independence - Wikipedia, the free encyclopedia
		In probability theory, two events A and B are conditionally independent given a third event C precisely if the occurrence or non-occurrence of A and B are independent events in their conditional probability distribution given C.
		Two random variables X and Y are conditionally independent given an event C if they are independent in their conditional probability distribution given C.
		Conditional independence of more than two events, or of more than two random variables, is defined analogously.
	en.wikipedia.org /wiki/Conditional_independence (345 words)

	[No title]
		Conditional independence in Bayesian Networks It's crucial to keep in mind that the discussion of conditional independence in Bayesian Networks is always about nodes/variables that are necessarily independent, given the structure of the underlying DAG.
		However, B and E are not independent given A. To see this, consider the graph restricted to the nodes {B, E, A}.
		B, E) 0 0 0.001 0 1 0.001 1 0 0.95 1 1 0.95 With this new conditional probability table for the A node in place, it then happens to be the case that B and E are conditionally independent given A. However, this independence does not hold necessarily for the given DAG.
	www1.cs.columbia.edu /~kathy/cs4701/documents/conditional-independence-bn.txt (1257 words)

	Complex Adaptive Systems as Intuitive Statisticians:...
		In the field of animal conditioning, as well as in human categorization and causal induction, various theorists have proposed that animals perform some implicit computation of statistical contingency: the difference between the proportion of events for which an effect occurs when a factor is present and that proportion when it is absent.
		The contingency for cue A conditional on the absence of both B and C cannot be computed because A does not occur in the absence of B. However, A has a contingency of 1.0 in the focal set in which B is present and C is absent (rows 2-3).
		After each phase of the design, subjects in both conditions rated the degree to which the state of each button was predictive of the state of the alarm, using a scale from 0 to 10, where 10 indicated that the cue was a perfect predictor and 0 indicated the cue was not a predictor.
	cogsci.soton.ac.uk /~harnad/Papers/Py104/cheng.complex.html (11895 words)

	Procedures - Conditional Independence - Details (Site not responding. Last check: 2007-10-14)
		Item response theory models are based on the assumption of conditional independence.
		Conditional independence implies that examinees’ response probabilities are unrelated to background variables (y), given their proficiency.
		A second implication of conditional independence is that the item response probabilities depend only on the examinee’s ability and the specified item
	am.air.org /help/NAEPTextbook/htm/dconditionalindependence.htm (200 words)

	Conditional independence (Site not responding. Last check: 2007-10-14)
		In probability theory, two events A and B are conditionally independent given a third event C precisely if the occurrence or non-occurrenceof A and B are independent eventsin their conditional probability distribution given C.
		Two random variables X and Y are conditionally independent given an event C if they are independent in their conditional probabilitydistribution given C.
		In particular,if a large number of the X s are observed to be equal to 1, that would imply a high conditional probability, given thatobservation, that p is near 1, and thus a high conditional probability, given that observation, that the next X to be observed will be equal to 1.
	www.therfcc.org /conditional-independence-218055.html (306 words)

	Extending Mosaic Displays: Marginal, Partial, and Conditional Views of Categorical Data
		Hence, the conditional scatterplot matrix for quantitative variables provide a visualization of the pairwise partial correlations among all variables and of the conditional independence relations studied in Gaussian graphical models.
		Conditional relations among variables may also be visualized by stratifying the data on the given variables, rather than by partialling out.
		for the conditional independence model with (I-1)(J-1)K degrees of freedom is the sum of the values for the ordinary association between A and B over the levels of C (each with (I-1)(J-1) degrees of freedom).
	math.yorku.ca /SCS/Papers/drew (6258 words)

	Abstract for ``On deducing conditional independence from d-separation in causal graphs with feedback'' (Site not responding. Last check: 2007-10-14)
		Abstract for ``On deducing conditional independence from d-separation in causal graphs with feedback''
		Pearl and Dechter (1996) claimed that the d -separation criterion for conditional independence in acyclic causal networks also applies to networks of discrete variables that have feedback cycles, provided that the variables of the system are uniquely determined by the random disturbances.
		Some condition stronger than uniqueness is needed, such as the existence of a causal dynamics guaranteed to lead to the unique solution.
	www.cs.toronto.edu /~radford/dsepcyc.abstract.html (109 words)

	Reichenbach's Common Cause Principle (Site not responding. Last check: 2007-10-14)
		To be precise, they suggest the ‘law of conditional independence&rsquo;: “If A and B are two disjoint 4-regions, and C is any 4-region which divides the union of the pasts of A and B into two parts, one containing A and the other containing B, then A and B are conditionally independent given c.
		Conditional upon the value of X ′ at t ′, the value of X at t will be independent of any value of any quantity at any time.
		For the demand of initial microscopic chaos is a demand that microscopic conditions are uniformly distributed (in canonical coordinates) in the areas of state-space that are compatible with the fundamental laws of physics.
	www.science.uva.nl /~seop/entries/physics-Rpcc (6077 words)

	Joint Marginal and Conditional
		Often these events are not independent, and sadly this is often ignored.
		Note that in general the conditional probability of A given B is not the same as B given A. The probability of both A and B together is P(AB), and P(AB) X P(B) = P(AB) = P(BA) X P(A), if both P(A) and P(B) are non-zero.
		Conditional probability is also the basis for statistical dependence and independence.
	www.statisticalengineering.com /joint_marginal_conditional.htm (486 words)

	The Devilfinder Search Engine - Three Patterns of Conditional Independence and Their Mutual ... - Finding Stuff Since ...
		To the extent that the conditional independence assumption holds and the probability estimates are...
		Independence can be seen as a special kind of conditional independence,...
		Conditional independence asserts that observations are chosen such that the values taken by...
	www.devilfinder.com /find.php?q=Three+Patterns+of+Conditional+Independence+and+Their+Mutual+... (5053 words)

	Appendices
		In testing the conditional independence of two variables given a set of other variables, if the sample size is less than 10 times the number of cells to be fitted we assume the variables are conditionally dependent.
		The Build module uses two algorithms to construct, from independence and conditional independence data, the class of causal graphs that entail the same set of (conditional) independence relations over the measured variables.
		By the Markov condition, if x and y are not adjacent, then x and y are independent conditional on the parents of x or on the parents of y, or on both.
	www.phil.cmu.edu /projects/tetrad/tet3/Appendices.htm#_ftn1 (4393 words)

	Olof Palmes Internationella Centrum (Site not responding. Last check: 2007-10-14)
		Under the Commission's idea of conditional independence, the domestic powers currently reserved to the SRSG (the Special Representative of the Secretary General of the UN - currently Hans Haekkerup of Denmark) would be progressively transferred to the Kosovo government; at the end Kosovo will be independent, however conditional, outside the FRY.
		The power for the international community to intervene, which might or might not continue to be vested in the SRSG, should be restricted to the protection of minorities, the guarantee of individual human rights, and the guarantee of the integrity of the borders.
		The Independent International Commission on Kosovo was established as an initiative of the Prime Minister of Sweden, Mr Göran Persson, to provide an objective analysis of the events before, during, and after the war in Kosovo and to research the lessons to be learned.
	www.palmecenter.se /article_uk.asp?Article_Id=1692 (765 words)

	Extending Mosaic Displays: Marginal, Partial, and Conditional Views of Categorical Data
		Hence, the conditional scatterplot matrix for quantitative variables provide a visualization of the pairwise partial correlations among all variables and of the conditional independence relations studied in Gaussian graphical models.
		Conditional relations among variables may also be visualized by stratifying the data on the given variables, rather than by partialling out.
		For categorical data, models of independence fit to the strata separately have the useful property that they decompose a model of conditional independence fit to the whole table.
	www.math.yorku.ca /SCS/Papers/drew (6221 words)

	Independence and conditional independence
		It would be uncontroversial to assume that A and B are independent.
		In this case A and B are not independent.
		In many real life situations variables which are believed to be independent are actually only independent conditional on some other variable.
	www.dcs.qmul.ac.uk /~norman/BBNs/Independence_and_conditional_independence.htm (458 words)

	Citations: Conditional independence for statistical operations - Dawid (ResearchIndex)
		These independences are represented by missing edges in a graph which consists of vertices depicting the variables 1 and edges depicting associations between them.
		So called Markov properties describe the conditions which have to be ful lled by the distribution model to connect the graph with these independence statements (Frydenberg, 1990, Lauritzen, 1996) Distributions which are able to capture these demands are the multinomial, multivariate normal, and....
		The conditions for marginalization, collapsibility, and decomposition of the ML estimation for graphical models with CG distribution can be found in Frydenberg (1990) and Frydenberg and....
	citeseer.ist.psu.edu /context/283171/0 (569 words)

	Conditional Random Fields
		Conditional random fields (CRFs) are a probabilistic framework for labeling and segmenting structured data, such as sequences, trees and lattices.
		Conditional random fields also avoid a fundamental limitation of maximum entropy Markov models (MEMMs) and other discriminative Markov models based on directed graphical models, which can be biased towards states with few successor states.
		Conditional random fields (CRFs) for sequence modeling have several advantages over joint models such as HMMs, including the ability to relax strong independence assumptions made in those models, and the ability to incorporate arbitrary overlapping features.
	www.inference.phy.cam.ac.uk /hmw26/crf (5235 words)

	Genome Biology \| Full text \| Estimating genomic coexpression networks using first-order conditional independence
		This set of genes is expressed under non-fermentative growth conditions in the absence of glucose, conditions characteristic of the diauxic shift [ 15 ].
		Cases where the marginal and conditional correlations are of opposite sign are examples of 'Simpson's paradox', which usually indicates that there is a lurking or confounding effect of the conditioning variable (see [ 29 ] for a general discussion of such relationships).
		Permutation tests were carried out by independently randomizing the values for each gene expression variable such that each gene had the same mean and variance as its original observation vector, but both the marginal and partial correlations had an expected value of zero.
	www.genomebiology.com /2004/5/12/R100 (10122 words)

	Graphical Models
		The simplest conditional independence relationship encoded in a Bayesian network can be stated as follows: a node is independent of its ancestors given its parents, where the ancestor/parent relationship is with respect to some fixed topological ordering of the nodes.
		If X is hidden, its parents are marginally independent, and hence the ball does not pass through (the ball being "turned around" is indicated by the curved arrows); but if X is observed, the parents become dependent, and the ball does pass through, because of the explaining away phenomenon.
		Finally, consider the case in which we have one incoming and outgoing arrow to X. It is intuitive that the nodes upstream and downstream of X are dependent iff X is hidden, because conditioning on a node breaks the graph at that point.
	www.cs.berkeley.edu /~murphyk/Bayes/bnintro.html (6529 words)

	Human Rights Violations in Chechnya
		As the Chechen government has repeatedly stated, independence is not an end in itself for the Chechen people, but only a means to put an end, as our prominent fellow countryman A. Avtorkhanov correctly noted, to a more than four-century-long mourning of the Chechen people and to ensure its guaranteed security in the future.
		It should be noted that the proposal of conditional independence does not contradict to the Constitution, the Law on protection of state sovereignty of the Chechen Republic of Ichkeria, because it is just an alternative peaceful way of protecting the right of the Chechen people to a free and safe existence.
		Aspiring to open the road to a mutually acceptable peace and to stop endless violence, we have made a step towards peace and suggest a compromise formula of "conditional independence under an international administration." We believe that this formula corresponds to genuine national interests not only of Chechnya, but also of Russia.
	www.hrvc.net /west/22-7-2003.html (783 words)

	The Devilfinder Search Engine - Categorical Analysis - Conditional Logit Regression - Finding Stuff Since 1979.
		to as conditional logit or conditional logistic or McFaddens logit regression.
		Poisson, tobit, conditional logistic, multinomial logit and nested logit regression ;...
		probit regression, multinomial > logit, cumulative logit, conditional logit,...
	www.devilfinder.com /find.php?q=Categorical+Analysis+-+Conditional+Logit+Regression (4172 words)

	contradiction between class unconditional and class unconditional independence conditional Independence
		Then a probability system can be build where one can assume both the class conditional independence and Class unconditional independence without any problem.
		Furthermore, if X1 and X2 are independent, then automatically, they shall be independent inside each class.
		This is a very specific example, which is possible only because the conditional probability from one class to another is the same for one variable.
	cgm.cs.mcgill.ca /~soss/cs644/projects/simon/contradiction.html (306 words)

	Statistical Applications in Genetics and Molecular Biology
		However, full (unconstrained) conditional relationships between random variables can be only estimated accurately if the number of observations is relatively large in comparison to the number of variables, which is usually not fulfilled for high-throughput genomic data.
		For sparse graphical models such as genetic networks, it is assumed that the zero- and first-order conditional independencies still reflect reasonably well the full conditional independence structure between variables.
		Moreover, low-order conditional independencies have the advantage that they can be accurately estimated even when having only a small number of observations.
	www.bepress.com /sagmb/vol5/iss1/art1 (303 words)

	Conditional probability (Site not responding. Last check: 2007-10-14)
		Conditional probability is the probability of some event A assuming event B.
		Conditional probability is written P ( A
		Conditional Moment Estimation of Nonlinear Equation Systems: With an Application to an Oligopoly Model of Cooperative R & D (Lecture Notes in Economics and Mathematical Systems, 497)
	www.freeglossary.com /Conditional_Probability (443 words)

	Massey University (Site not responding. Last check: 2007-10-14)
		Tuesday 13th June, 10am, SST 1.39 Graphical hierarchical log-linear models occur as intersections of finite sets of conditional independence models.
		The model space of a conditional independence model involving categorical variables is a highly structured subset within a simplex.
		In this presentation we will describe this conditional independence model space using notions of "corresponding point convex hull" and "set convex hull" and also the way to find the maximum likelihood estimate of the joint distribution under the model, using this geometric framework.
	www-ist.massey.ac.nz /News/select-news.asp?ID=313 (103 words)

	Build
		Build module takes data and background knowledge and outputs a set of causal models that entail the same set of conditional independence relations among the measured variables and that are compatible with any user-entered background knowledge.
		The algorithms use statistical tests to make judgments about conditional independence relations in the population, and then use these conditional independence judgments to construct a set of causal models that entail the same set of conditional independence relations and that are compatible with any user-entered background knowledge.
		If the conditional independence decisions made by the algorithm are correct, the existence of a bi-directed edge x1 « x2 in a pattern suggests that there is a latent common cause of x1 and x2 (see Chap.
	www.phil.cmu.edu /projects/tetrad/tet3/chp5.htm (4687 words)

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