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Strong Markov Random Field Model
"... The strong Markov random field (MRF) model is a submodel of the more general MRFGibbs model. The strongMRF model defines a system whereby not only is the field Markovian with respect to a defined neighbourhood, but all subneighbourhoods also define a Markovian system. A checkerboard pattern is a ..."
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The strong Markov random field (MRF) model is a submodel of the more general MRFGibbs model. The strongMRF model defines a system whereby not only is the field Markovian with respect to a defined neighbourhood, but all subneighbourhoods also define a Markovian system. A checkerboard pattern is a perfect example of a strong Markovian system. Although the strong Markovian system requires a more stringent assumption about the field, it does have some very nice mathematical properties. One mathematical property, is the ability to define the strong Markov random field model with respect to its marginal distributions over the cliques. This property allows a direct equivalence to the ANOVA loglinear construction to be proved. From this proof, the general ANOVA loglinear construction formula is derived.
Simulate and Reject Monte Carlo Exact Conditional Tests for Quasiindependence
 In Proceedings of COMPSTAT
, 1994
"... this paper, we propose improvements to a naive simulate and reject procedure for generating r \Theta c tables under quasiindependence for an arbitrary pattern of fixed cells. Although some of the algorithmic improvements are described for generating under QI for the offdiagonal cells of a square t ..."
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this paper, we propose improvements to a naive simulate and reject procedure for generating r \Theta c tables under quasiindependence for an arbitrary pattern of fixed cells. Although some of the algorithmic improvements are described for generating under QI for the offdiagonal cells of a square table, the ideas are applicable to other patterns of fixed cells. Apart from complete enumeration, which is only viable for small tables, the simulate and reject procedure is currently the only method for generating independent tables from the exact null distribution under QI. Our improvements to the naive procedure greatly increase its efficiency. Smith, McDonald and Forster (1994) discuss another method for generating tables under QI using a Gibbs sampling approach, based on theoretical results in Forster, McDonald and Smith (1994). However, the generated tables are not necessarily independent and are only realizations from an approximation to the exact null distribution. When using a single Markov chain, the observed table is the obvious starting value. For multiple chains, obtaining other starting values with the same sufficient statistics for the nuisance parameters as the observed data is problematic. A possible solution is to generate a small number of independent starting values using the simulate and reject algorithms proposed. Acknowledgements
Exact Tests for TwoWay Symmetric Contingency Tables
"... this paper, we review exact tests and the computing problems involved. We propose new recursive algorithms for exact goodnessoffit tests of quasiindependence, quasisymmetry, linearbylinear association and some related models. We propose that all computations be carried out using symbolic comput ..."
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this paper, we review exact tests and the computing problems involved. We propose new recursive algorithms for exact goodnessoffit tests of quasiindependence, quasisymmetry, linearbylinear association and some related models. We propose that all computations be carried out using symbolic computation and rational arithmetic in order to calculate the exact pvalues accurately and describe how we implemented our proposals. Two examples are presented.
Monte Carlo Exact Conditional Tests for Quasiindependence using Gibbs Sampling
, 1994
"... this paper, is the hypothesis of QI for the offdiagonal cells of a r \Theta r square table, where the sufficient statistics for the nuisance parameters are x i+ ; x +j and x ii , for i; j = 1; : : : ; r. ..."
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this paper, is the hypothesis of QI for the offdiagonal cells of a r \Theta r square table, where the sufficient statistics for the nuisance parameters are x i+ ; x +j and x ii , for i; j = 1; : : : ; r.
Exact Tests via Complete Enumeration: A Distributed Computing Approach
, 1997
"... The analysis of categorical data often leads to the analysis of a contingency table. For large samples, asymptotic approximations are sufficient when calculating pvalues, but for small samples the tests can be unreliable. In these situations an exact test should be considered. This bases the test o ..."
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The analysis of categorical data often leads to the analysis of a contingency table. For large samples, asymptotic approximations are sufficient when calculating pvalues, but for small samples the tests can be unreliable. In these situations an exact test should be considered. This bases the test on the exact distribution of the test statistic. Sampling techniques can be used to estimate the distribution. Alternatively, the distribution can be found by complete enumeration. This thesis develops a number of new algorithms for complete enumeration of various models. Recursive algorithms are developed to test for independence in r × c tables. The algorithm is extended for multidimensional tables. One algorithm is extended to enumerate tables under the model of quasiindependence, and a rejection stage enables testing of models such as quasisymmetry and uniform association. A new algorithm is developed that enables a model to be defined by a model matrix, and all tables that satisfy the model are found. This provides a more efficient enumeration mechanism for complex models and extends the range of models that can be tested. The technique can lead to large calculations and a distributed version of the algorithm is developed that enables a number of machines to work efficiently on the same problem.
The NPAR1WAY Procedure
, 2008
"... For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is ..."
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For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is subject to the Agreement with SAS Institute and the restrictions set forth in FAR 52.22719, Commercial Computer SoftwareRestricted Rights (June 1987).
Other brand and product names are registered trademarks or trademarks of their respective companies. Chapter 35 The FREQ Procedure Contents
, 2009
"... For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is ..."
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For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is subject to the Agreement with SAS Institute and the restrictions set forth in FAR 52.22719, Commercial Computer SoftwareRestricted Rights (June 1987).