bbricks (version 0.1.4)

dPosteriorPredictive.GaussianInvWishart: Posterior predictive density function of a "GaussianInvWishart" object

Description

Generate the the density value of the posterior predictive distribution of the following structure: $$x \sim Gaussian(mu,Sigma)$$ $$Sigma \sim InvWishart(v,S)$$ mu is known. Gaussian() is the Gaussian distribution. See ?dGaussian and ?dInvWishart for the definition of the distributions. The model structure and prior parameters are stored in a "GaussianInvWishart" object. Posterior predictive density is p(x|v,S,mu).

Usage

# S3 method for GaussianInvWishart
dPosteriorPredictive(obj, x, LOG = TRUE, ...)

Arguments

obj

A "GaussianInvWishart" object.

x

matrix, or the ones that can be converted to matrix, each row of x is an observation.

LOG

Return the log density if set to "TRUE".

...

Additional arguments to be passed to other inherited types.

Value

A numeric vector of the same length as nrow(x), the posterior predictive density.

References

Gelman, Andrew, et al. Bayesian data analysis. CRC press, 2013.

MARolA, K. V., JT KBNT, and J. M. Bibly. Multivariate analysis. AcadeInic Press, Londres, 1979.

See Also

GaussianInvWishart, dPosteriorPredictive.GaussianInvWishart, marginalLikelihood.GaussianInvWishart

Examples

# NOT RUN {
obj <- GaussianInvWishart(gamma=list(mu=c(-1.5,1.5),v=3,S=diag(2)))
x <- rGaussian(100,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2))
xNew <- rGaussian(100,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2))
ss <- sufficientStatistics(obj=obj,x=x,foreach = FALSE)
## update piror with x
posterior(obj=obj,ss = ss)
## use the posterior to calculate the probability of observing each xNew
dPosteriorPredictive(obj = obj,x = xNew,LOG = TRUE)
# }