bayesics - Bayesian Analyses for One- and Two-Sample Inference and Regression Methods

Perform fundamental analyses using Bayesian parametric and non-parametric inference (regression, anova, 1 and 2 sample inference, non-parametric tests, etc.). (Practically) no Markov chain Monte Carlo (MCMC) is used; all exact finite sample inference is completed via closed form solutions or else through posterior sampling automated to ensure precision in interval estimate bounds. Diagnostic plots for model assessment, and key inferential quantities (point and interval estimates, probability of direction, region of practical equivalence, and Bayes factors) and model visualizations are provided. Bayes factors are computed either by the Savage Dickey ratio given in Dickey (1971) <doi:10.1214/aoms/1177693507> or by Chib's method as given in xxx. Interpretations are from Kass and Raftery (1995) <doi:10.1080/01621459.1995.10476572>. ROPE bounds are based on discussions in Kruschke (2018) <doi:10.1177/2515245918771304>. Methods for determining the number of posterior samples required are described in Doss et al. (2014) <doi:10.1214/14-EJS957>. Bayesian model averaging is done in part by Feldkircher and Zeugner (2015) <doi:10.18637/jss.v068.i04>. Methods for contingency table analysis is described in Gunel et al. (1974) <doi:10.1093/biomet/61.3.545>. Variational Bayes (VB) methods are described in Salimans and Knowles (2013) <doi:10.1214/13-BA858>. Mediation analysis uses the framework described in Imai et al. (2010) <doi:10.1037/a0020761>. The loss-likelihood bootstrap used in the non-parametric regression modeling is described in Lyddon et al. (2019) <doi:10.1093/biomet/asz006>. Non-parametric survival methods are described in Qing et al. (2023) <doi:10.1002/pst.2256>. Methods used for the Bayesian Wilcoxon signed-rank analysis is given in Chechile (2018) <doi:10.1080/03610926.2017.1388402> and for the Bayesian Wilcoxon rank sum analysis in Chechile (2020) <doi:10.1080/03610926.2018.1549247>. Correlation analysis methods are carried out by Barch and Chechile (2023) <doi:10.32614/CRAN.package.DFBA>, and described in Lindley and Phillips (1976) <doi:10.1080/00031305.1976.10479154> and Chechile and Barch (2021) <doi:10.1016/j.jmp.2021.102638>. See also Chechile (2020, ISBN: 9780262044585).