Contingency tables represent the joint distribution of categorical variables. In this chapter we use modern algebraic geometry to update the geometric representation of 2 × 2 contingency tables first explored in (Fienberg 1968) and (Fienberg and Gilbert 1970). Then we use this geometry for a series of new ends including various characterizations of the joint distribution in terms of combination...

The problem of finding the number of rectangular tables of non-negative integers with given row and column sums occurs in many interesting contexts, mainly in combinatorial problems (counting magic squares, enumerating permutation by descents, etc.) and in statistical applications (studying contingency tables with given margins, testing for independence, etc.). In the present paper a new recurs...

In this paper a Markov chain for contingency tables with two rows is deened. The chain is shown to be rapidly mixing using the path coupling method. The mixing time of the chain is quadratic in the number of columns and linear in the logarithm of the table sum. Two extensions of the new chain are discussed: one for three-rowed contingency tables and one for m-rowed contingency tables. We show t...

A framework is proposed for the investigation of planning systems that must deal with bounded uncertainty. A deenition of this new class of contingency planners is given. A general, complete contingency planning algorithm is described. The algorithm is suitable to many incomplete information games as well as planning situations where the initial state is only partially known. A rich domain is i...

On finding a significant association between rows and columns of an r x c contingency table, the next step is to study the nature of the association in more detail. The use of a scree plot to visualize the largest contributions to Χ 2 among all cells in the table in order to determine the nature of the association in more detail is proposed.

A default prior distribution is proposed for the Bayesian analysis of contingency tables. The prior is specified to allow for dependence between levels of the factors. Different dependence structures are considered, including conditional autoregressive and distance correlation structures. To demonstrate the prior distribution, a dataset is considered which involves estimating the number of inje...

This paper is a contribution to the rapidly emerging field of qualitative data analysis in economics. Ordinal data techniques and error measurement in input-output analysis are here combined in order to test the reliability of a low level of measurement and precision of data by means of a stochastic method for transforming ordinal data into cardinal ones by using a minimum number of assumptions...