Related papers: Markov bases and subbases for bounded contingency …
We present a computational approach for generating Markov bases for multi-way contingency tables whose cells counts might be constrained by fixed marginals and by lower and upper bounds. Our framework includes tables with structural zeros…
It has been well-known that for two-way contingency tables with fixed row sums and column sums the set of square-free moves of degree two forms a Markov basis. However when we impose an additional constraint that the sum of a subtable is…
Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via Markov chain Monte Carlo method. In this paper we derive explicit forms of Markov bases for change point…
We study Markov bases of decomposable graphical models consisting of primitive moves (i.e., square-free moves of degree two) by determining the structure of fibers of sample size two. We show that the number of elements of fibers of sample…
We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist…
We construct examples of contingency tables on $n$ binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/upper bounds on cell entries is exponentially large. These examples provide…
This paper is concerned with the topological invariant of a graph given by the maximum degree of a Markov basis element for the corresponding graph model for binary contingency tables. We describe a degree four Markov basis for the model…
In this work we define log-linear models to compare several square contingency tables under the quasi-independence or the quasi-symmetry model, and the relevant Markov bases are theoretically characterized. Through Markov bases, an exact…
To evaluate a fitting of a statistical model to given data, calculating a conditional $p$ value by a Markov chain Monte Carlo method is one of the effective approaches. For this purpose, a Markov basis plays an important role because it…
A reference set, or a fiber, of a contingency table is the space of all realizations of the table under a given set of constraints such as marginal totals. Understanding the geometry of this space is a key problem in algebraic statistics,…
In this paper, we introduce the fundamental notion of a Markov basis, which is one of the first connections between commutative algebra and statistics. The notion of a Markov basis is first introduced by Diaconis and Sturmfels (1998) for…
We discuss connecting tables with zero-one entries by a subset of a Markov basis. In this paper, as a Markov basis we consider the Graver basis, which corresponds to the unique minimal Markov basis for the Lawrence lifting of the original…
We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. Such a problem relates to recent developments in copula modeling for discrete random vectors.…
It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we…
In this paper we consider a Bayesian analysis of contingency tables allowing for the possibility that cells may have probability zero. In this sense we depart from standard log-linear modeling that implicitly assumes a positivity…
In two-way contingency tables we sometimes find that frequencies along the diagonal cells are relatively larger(or smaller) compared to off-diagonal cells, particularly in square tables with the common categories for the rows and the…
We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. This is an old question which relates to recent advances in copula modeling for discrete random…
We study random walks on contingency tables with fixed marginals, corresponding to a (log-linear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with the same marginals that are not connected.…
Exact conditional tests for contingency tables require sampling from fibers with fixed margins. Classical Markov basis MCMC is general but often impractical: computing full Markov bases that connect all fibers of a given constraint matrix…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…