Bayes factors for independence in contingency tables

Günel, Erdoǵan; Dickey, James

doi:10.1093/biomet/61.3.545

Cited by 114 publications

(91 citation statements)

References 10 publications

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“…These priors, which do not depend on the null, are not appropriate for testing problems since they do not concentrate mass around the null; that is, they do not satisfy the Savage continuity condition (Jeffreys, 1961, Ch. 5;Gûnel and Dickey, 1974;Berger and Sellke, 1987;Casella and Berger, 1987;Morris, 1987a,b;Berger, 1994). When the prior concentrates its mass around the null hypothesis, as the intrinsic priors do with a degree of concentration controlled by the training sample size, the resulting likelihood of the alternative model will be a much more serious competitor of the null likelihood, and in this case the null can be rejected.…”

Section: Elías Moreno (Universidad De Granada Spain)mentioning

confidence: 99%

Integrated Objective Bayesian Estimation and Hypothesis Testing

Bernardo

2011

Bayesian Statistics 9

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SummaryThe complete final product of Bayesian inference is the posterior distribution of the quantity of interest. Important inference summaries include point estimation, region estimation, and precise hypotheses testing. Those summaries may appropriately be described as the solution to specific decision problems which depend on the particular loss function chosen. The use of a continuous loss function leads to an integrated set of solutions where the same prior distribution may be used throughout. Objective Bayesian methods are those which use a prior distribution which only depends on the assumed model and the quantity of interest. As a consequence, objective Bayesian methods produce results which only depend on the assumed model and the data obtained. The combined use of the intrinsic discrepancy, an invariant information-based loss function, and appropriately defined reference priors, provides an integrated objective Bayesian solution to both estimation and hypothesis testing problems. The ideas are illustrated with a large collection of non-trivial examples.

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Section: Elías Moreno (Universidad De Granada Spain)mentioning

confidence: 99%

Integrated Objective Bayesian Estimation and Hypothesis Testing

Bernardo

2011

Bayesian Statistics 9

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“…As the models relate to p and π, this does not seem to be a serious restriction. Gûnel and Dickey (1974) consider the Bayes factor for comparing independence and saturated models in a two-way contingency table, and give an example where inference under Poisson and multinomial models differs when this condition is violated.…”

Section: Bayesian Inferencementioning

confidence: 99%

Bayesian inference for Poisson and multinomial log-linear models

Forster

2010

Statistical Methodology

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Categorical data frequently arise in applications in the social sciences. In such applications,the class of log-linear models, based on either a Poisson or (product) multinomial response distribution, is a flexible model class for inference and prediction. In this paper we consider the Bayesian analysis of both Poisson and multinomial log-linear models. It is often convenient to model multinomial or product multinomial data as observations of independent Poisson variables. For multinomial data, Lindley (1964) showed that this approach leads to valid Bayesian posterior inferences when the prior density for the Poisson cell means factorises in a particular way. We develop this result to provide a general framework for the analysis of multinomial or product multinomial data using a Poisson log-linear model. Valid finite population inferences are also available, which can be particularly important in modelling social data.We then focus particular attention on multivariate normal prior distributions for the log-linear model parameters.Here, an improper prior distribution for certain Poisson model parameters is required for valid multinomial analysis, and we derive conditions under which the resulting posterior distribution is proper.We also consider the construction of prior distributions across models, and for model parameters, when uncertainty exists about the appropriate form of the model. We present classes of Poisson and multinomial models, invariant under certain natural groups of permutations of the cells. We demonstrate that, if prior belief concerning the model parameters is also invariant, as is the case in a `reference' analysis, then choice of prior distribution is considerably restricted. The analysis of multivariate categorical data in the form of a contingency table is considered in detail. We illustrate the methods with two examples. Bayesian Inference for Poisson and MultinomialLog-linear Models Lindley (1964) showed that this approach leads to valid Bayesian posterior inferences when the prior density for the Poisson cell means factorises in a particular way. We develop this result to provide a general framework for the analysis of multinomial or product multinomial data using a Poisson log-linear model. Valid finite population inferences are also

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“…Like the previous analysis of correlational data, this does not provide any evidence for the null hypothesis nor provide any confidence that the true log odds ratio lies between the CI bounds. Bayesian frequency distribution analysis was performed using independent multinomial sampling, as the crucial test was a comparison of two proportions and the number of people assigned to receive each treatment was presumably fixed [28,29]. The median log odds ratio was -0.86, with a 95% credible interval of -2.31 and 0.51.…”

Section: Frequency Distributionsmentioning

confidence: 99%

Bayesian alternatives for common null-hypothesis significance tests in psychiatry: A non-technical guide using JASP

Quintana¹,

Williams²

2017

Preprint

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Background: Despite its popularity as an inferential framework, classical null hypothesis significance testing (NHST) has several restrictions. Bayesian analysis can be used to complement NHST, however, this approach has been underutilized largely due to a dearth of accessible software options. JASP is a recently developed open-source statistical package that facilitates both Bayesian and NHST analysis using a graphical interface. This article provides an applied introduction to Bayesian inference with Bayes factors using JASP.

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Bayes factors for independence in contingency tables

Cited by 114 publications

References 10 publications

Integrated Objective Bayesian Estimation and Hypothesis Testing

Integrated Objective Bayesian Estimation and Hypothesis Testing

Bayesian inference for Poisson and multinomial log-linear models

Bayesian alternatives for common null-hypothesis significance tests in psychiatry: A non-technical guide using JASP

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