sufficientStatistics.GaussianInvWishart: Sufficient statistics of a "GaussianInvWishart" object

In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

Description

For following model 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 sufficient statistics of a set of samples x (each row of x is a sample) are:

• the effective number of samples N=nrow(x)

• the centered sample scatter matrix S = (t(x)-mu)^T

Usage

## S3 method for class 'GaussianInvWishart'
sufficientStatistics(obj, x, foreach = FALSE, ...)

Arguments

obj	A "GaussianInvWishart" object.
x	matrix, Gaussian samples, when x is a matrix, each row is a sample of dimension ncol(x). when x is a vector, x is length(x) samples of dimension 1.
foreach	logical, specifying whether to return the sufficient statistics for each observation. Default FALSE.
...	Additional arguments to be passed to other inherited types.

Value

If foreach=TRUE, will return a list of sufficient statistics for each row of x, otherwise will return the sufficient statistics of x as a whole.

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, sufficientStatistics_Weighted.GaussianInvWishart

Examples

obj <- GaussianInvWishart(gamma=list(mu=c(-1.5,1.5),v=3,S=diag(2)))
x <- rGaussian(10,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2))
sufficientStatistics(obj=obj,x=x,foreach = FALSE)
sufficientStatistics(obj=obj,x=x,foreach = TRUE)

bbricks documentation built on July 8, 2020, 7:29 p.m.