# Bayesian inference for categorical data analysis

@article{Agresti2005BayesianIF, title={Bayesian inference for categorical data analysis}, author={Alan Agresti and David B. Hitchcock}, journal={Statistical Methods and Applications}, year={2005}, volume={14}, pages={297-330} }

Abstract.This article surveys Bayesian methods for categorical data analysis, with primary emphasis on contingency table analysis. Early innovations were proposed by Good (1953, 1956, 1965) for smoothing proportions in contingency tables and by Lindley (1964) for inference about odds ratios. These approaches primarily used conjugate beta and Dirichlet priors. Altham (1969, 1971) presented Bayesian analogs of small-sample frequentist tests for 2 x 2 tables using such priors. An alternative…

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## References

SHOWING 1-10 OF 243 REFERENCES

### Bayesian Methods for Contingency Tables

- Mathematics
- 2005

Several Bayes and empirical Bayes approaches to estimating probabilities of categories, testing equiprobability in a one-way table, testing independence in a two-way contingency table, and selecting among generalized linear models, with particular attention to loglinear models, for tables of higher dimension are reviewed.

### Bayesian Methods for Censored Categorical Data

- Mathematics
- 1987

Abstract Bayesian methods are given for finite-category sampling when some of the observations suffer missing category distinctions. Dickey's (1983) generalization of the Dirichlet family of prior…

### Bayesian Full Rank Marginalization for Two-Way Contingency Tables

- Mathematics
- 1986

A general approach is proposed for modeling the structure of anr ×s contingency table and for drawing marginal inferences about all parameters (e.g., interaction effects) in the model. The main…

### On Bayesian Analysis of Generalized Linear Models Using Jeffreys's Prior

- Mathematics
- 1991

Abstract Generalized linear models (GLM's) have proved suitable for modeling various kinds of data consisting of exponential family response variables with covariates. Bayesian analysis of such data…

### Exact Bayesian analysis of two proportions

- Mathematics
- 1987

Altham (1969) derived a relation between the cumulative posterior probability for association and the exact p-value in a 2 x 2 table. But she found that, in general, the exact posterior distribution…

### On the Application of Symmetric Dirichlet Distributions and their Mixtures to Contingency Tables

- Mathematics
- 1976

This paper is a continuation of a paper in the Annals of Statistics (1976), 4 1159-1189 where, among other things, a Bayesian approach to testing independence in contingency tables was developed. Our…

### An Alternative Bayesian Approach to the Bradley-Terry Model for Paired Comparisons

- Mathematics
- 1977

In recent years new Bayesian approaches have been developed for the estimation of parameters in multinomial models and contingency tables. The standard methods involving conjugate prior distributions…

### Prior induction in log-linear models for general contingency table analysis

- Mathematics
- 2001

Log-linear modelling plays an important role in many statistical applications, particularly in the analysis of contingency table data. With the advent of powerful new computational techniques such as…

### Nonparametric Bayesian Analysis for Assessing Homogeneity in k × l Contingency Tables with Fixed Right Margin Totals

- Mathematics
- 1998

Abstract In this work I postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when…

### Bayesian inference for square contingency tables

- Mathematics
- 2003

Inference for multivariate categorical data often proceeds by selecting a log-linear model from a set of competing models or, in a Bayesian approach, by averaging inferences over the set, weighted by…