posterior_predictive: Compute Posterior Predictive Distribution

In bpr: Fitting Bayesian Poisson Regression

Compute Posterior Predictive Distribution

Description

This function is a method for class poisreg. Compute the posterior predictive distribution and summary statistics for posterior check of the model; optionally, it also computes the predictive distribution with new values of the explanatory variables.

Usage

posterior_predictive(object, new_X = NULL)

Arguments

object	object of class "poisreg" (usually, the result of a call to sample_bpr).
new_X	(optional) a data frame in which to look for variables with which to predict.

Value

The call to this function returns an object of S3 class posterior_check. The object is a list with the following elements:

data : the component from object (list with covariates X and response variable y).

y_pred : matrix of dimension [n, iter] (with n sample size), each column is a draw from the posterior predictive distribution.

y_MAP_pred : vector of length n containing a draw from the posterior distribution obtained using the maximum a posteriori estimates (MAP) of the parameters.

diagnostics : list containing 2 elements: CPO, i.e. the Conditional Predictive Ordinate (Gelfand et al. 1992); and LPML, i.e. the logarithm of the pseudo-marginal likelihood (Ibrahim et al. 2014).

newdata : if the matrix new_X of new values of the covariates is provided, list of three elements:

• new_X : the provided matrix of explanatory variables;

• y_newdata : a matrix of dimension [nrow(new_X), iter], each column is a draw from the posterior predictive distribution using new_X;

• y_MAP_newdata : vector of length nrow(new_X) containing a draw from the posterior distribution obtained using the MAP estimate of the parameters, computed on the new data new_X.

perc_burnin : the component from object.

References

Gelfand, A., Dey, D. and Chang, H. (1992), Model determination using predictive distributions with implementation via sampling-based-methods (with discussion), in ‘Bayesian Statistics 4’, University Press.

Ibrahim, J. G., Chen, M.H. and Sinha, D. (2014), Bayesian Survival Analysis, American Cancer Society.

bpr documentation built on May 29, 2024, 11:28 a.m.