Bayesian inference for categorical data analysis

  title={Bayesian inference for categorical data analysis},
  author={Alan Agresti and David B. Hitchcock},
  journal={Statistical Methods and Applications},
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… 
Default Bayesian analysis for multi-way tables: a data-augmentation approach
This paper proposes a strategy for regularized estimation in multi-way contingency tables, which are common in meta-analyses and multi-center clinical trials. Our approach is based on data
Preprint ISSN 2198-5855 Simultaneous Bayesian analysis of contingency tables in genetic association studies
Genetic association studies lead to simultaneous categorical data analysis. The sample for every genetic locus consists of a contingency table containing the numbers of observed genotype-phenotype
Bayesian test of independence and conditional independence of two ordinal variables
It is shown that, in contingency tables with ordinal variables, it is better to apply gamma as a measure of association in comparison to kappa, and some sensitivity analysis to the choice of prior are performed.
Bayesian inference on contingency tables with uncertainty about independence for small areas
A Bayesian method to solve the problem when estimation is needed for the cells of a contingency table and there is uncertainty about independence or dependence when Bayesian predictive inference is done for the finite population means corresponding to each cell of the table.
Simultaneous Bayesian analysis of contingency tables in genetic association studies
  • T. Dickhaus
  • Mathematics, Computer Science
    Statistical applications in genetics and molecular biology
  • 2015
An objective Bayesian methodology is presented for these association tests, which relies on the conjugacy of Dirichlet and multinomial distributions and the ordering of the Bayes factors shows a good agreement with that of frequentist p-values.
Doing Bayesian Data Analysis: A Tutorial with R and BUGS
There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis obtainable to a wide audience. Doing Bayesian
Reliable Inference in Highly Stratified Contingency Tables: Using Latent Class Models as Density Estimators
Contingency tables are among the most basic and useful techniques available for analyzing categorical data, but they produce highly imprecise estimates in small samples or for population subgroups
Bayesian Test of Different Association Structures in Two-Way Contingency Tables
Bayesian methods for exact small-sample analysis with categorical data in I × J contingency tables are considered and the Bayesian test of “homogenous association” is applied on a real data set.
Learning for Contingency Tables and Survival Data using Imprecise Probabilities
This work implements imprecise Bayesian inference in two-way contingency tables and generalized to three-way tables by using different families of prior distributions, which is the core of this work.
A hierarchical Bayesian approach for handling missing classification data
Two hierarchical Bayesian models are developed to overcome the assumption of perfect assignment to mutually exclusive categories in the multinomial distribution of categorical counts, when classifications are missing.


Bayesian Methods for Contingency Tables
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
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
Using Gibbs Sampling for Bayesian Inference in Multidimensional Contingency Tables
Abstract : This paper discusses a method suggested by Epstein and Fienberg (1991) for the Bayesian analysis of multidimensional contingency tables in connection with the Gibbs sampler to calculate
Bayesian Full Rank Marginalization for Two-Way Contingency Tables
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
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
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
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
Bayesian Marginal Inference
Abstract A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for
An Alternative Bayesian Approach to the Bradley-Terry Model for Paired Comparisons
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
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