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How is simulating data from the posterior predictive distribution useful?
Simulating data from the posterior predictive distribution using the observed predictors is useful for checking the fit of the model. Drawing from the posterior predictive distribution at interesting values of the predictors also lets us visualize how a manipulation of a predictor affects (a function of) the outcome (s).
How to use BRMs for posterior predictive distribution?
The brms function posterior_predict () is a convenient function that gives us samples from the posterior predictive distribution. If we use posterior_predict (fit_press), we obtain the predicted reaction times in a matrix, with the samples as rows and the observations (data-points) as columns.
How to use the posterior predictive distribution in stanreg?
With new observations of predictor variables we can use the posterior predictive distribution to generate predicted outcomes. # S3 method for stanreg posterior_predict ( object , newdata = NULL , draws = NULL , re.form = NULL , fun = NULL , seed = NULL , offset = NULL ,
When to ignore dependent variable in posterior predict?
(Bear in mind that if we fit a model with sample_prior = “only”, the dependent variable is ignored and posterior_predict will give us samples from the prior predictive distribution).
How is the posterior predictive distribution of a conjugate prior determined?
As noted above, when a conjugate prior is being used, the posterior predictive distribution belongs to the same family as the prior predictive distribution, and is determined simply by plugging the updated hyperparameters for the posterior distribution of the parameter (s) into the formula for the prior predictive distribution.
Is the prior predictive distribution a compound distribution?
The prior predictive distribution is in the form of a compound distribution, and in fact is often used to define a compound distribution, because of the lack of any complicating factors such as the dependence on the data X {\\displaystyle \\mathbf {X} } and the issue of conjugacy.