ContRespPP: Predictive Probability for a Continuous Response with an ANOVA
A Bayesian approach to using
predictive probability in an ANOVA construct with a continuous normal response,
when threshold values must be obtained for the question of interest to be
evaluated as successful (Sieck and Christensen (2021) <doi:10.1002/qre.2802>).
The Bayesian Mission Mean (BMM) is used to evaluate a question
of interest (that is, a mean that randomly selects combination of factor levels
based on their probability of occurring instead of averaging over the factor
levels, as in the grand mean). Under this construct, in contrast to a Gibbs
sampler (or Metropolis-within-Gibbs sampler), a two-stage sampling method is
required. The nested sampler determines the conditional posterior distribution
of the model parameters, given Y, and the outside sampler determines the marginal
posterior distribution of Y (also commonly called the predictive distribution for Y).
This approach provides a sample from the joint posterior distribution of Y and
the model parameters, while also accounting for the threshold value that must be
obtained in order for the question of interest to be evaluated as successful.
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