Linganisha mbinu

	Takwimu za Kuelezea za Kibayesiani	Bayesian chi-square test
Nyanja	Takwimu	Takwimu
Familia	Hypothesis test	Hypothesis test
Mwaka wa asili	1763/1812	1967
Mwanzilishi	Thomas Bayes / Pierre-Simon Laplace	I. J. Good; extended by Gunel, Dickey, and Wagenmakers et al.
Aina	Bayesian parameter estimation	Bayesian nonparametric association test
Chanzo asilia	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Good, I. J. (1967). A Bayesian significance test for multinomial distributions. Journal of the Royal Statistical Society: Series B (Methodological), 29(3), 399–418.
Majina mbadala	Bayesian summaries, posterior descriptives, Bayesian parameter estimation, credible-interval summaries	Bayesian contingency table test, Bayes factor chi-square, Bayesian goodness-of-fit test, Bayesian association test
Zinazohusiana	5	3
Muhtasari	Bayesian descriptive statistics summarizes data by combining observed information with prior knowledge through Bayes' theorem, yielding posterior distributions over parameters such as the mean and variance. Instead of point estimates and p-values, results are expressed as posterior means, medians, and credible intervals that carry a direct probability interpretation.	The Bayesian chi-square test evaluates independence or goodness-of-fit in frequency tables using Bayes factors rather than classical p-values. It quantifies evidence for or against an association between categorical variables, updating prior beliefs with observed counts and delivering an odds-like ratio that distinguishes 'no evidence' from 'evidence of no effect'.