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Related Concept Videos

Contingency Table01:29

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A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; The table helps determine conditional probabilities quite quickly and can help systematically organize, analyze and quantify data. The table displays sample values concerning two variables that may be dependent or contingent on one...
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Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
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In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
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A default prior distribution for contingency tables with dependent factor levels.

Antony M Overstall1, Ruth King1

  • 1School of Mathematics & Statistics, University of St Andrews, St Andrews, Fife, KY16 9SS, United Kingdom.

Statistical Methodology
|April 22, 2014
PubMed
Summary
This summary is machine-generated.

A novel default prior distribution is introduced for Bayesian contingency table analysis, accounting for factor level dependence. This method is applied to estimate injecting drug users across Scottish regions, considering geographical relationships.

Keywords:
Contingency tableDefault priorDependence structure

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Contingency Table Analysis

Background:

  • Bayesian analysis of contingency tables often requires specifying prior distributions.
  • Existing methods may not adequately capture dependence structures between factor levels.
  • Accurate modeling is crucial for applications like epidemiological estimations.

Purpose of the Study:

  • To propose a flexible default prior distribution for Bayesian contingency table analysis.
  • To incorporate dependence structures between factor levels within the prior.
  • To demonstrate the utility of the proposed prior using a real-world dataset.

Main Methods:

  • Development of a default prior distribution allowing for dependence.
  • Consideration of various dependence structures (e.g., conditional autoregressive, distance correlation).
  • Application to an incomplete contingency table for estimating injecting drug users in Scotland.

Main Results:

  • The proposed prior effectively models dependence between factor levels.
  • The method provides a robust framework for analyzing incomplete contingency tables.
  • Estimation of injecting drug users in Scottish regions was demonstrated.

Conclusions:

  • The proposed default prior offers a valuable tool for Bayesian contingency table analysis.
  • The approach accommodates complex dependence structures, enhancing model flexibility.
  • This methodology has practical implications for public health data analysis and estimation.