sufficientStatistics_Weighted.GaussianGaussian: Weighted sufficient statistics of a "GaussianGaussian" object

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

Description

For following model structure:

x \sim Gaussian(mu,Sigma)

mu \sim Gaussian(m,S)

Where Sigma is known. Gaussian() is the Gaussian distribution. See ?dGaussian for the definition of Gaussian distribution.
The sufficient statistics of a set of samples x (each row of x is a sample) and weights w are:

• the effective number of samples N=sum(w)

• the sample sum xsum = colSums(x*w)

Usage

## S3 method for class 'GaussianGaussian'
sufficientStatistics_Weighted(obj, x, w, foreach = FALSE, ...)

Arguments

obj	A "GaussianGaussian" 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.
w	numeric, sample weights.
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.

See Also

GaussianGaussian, sufficientStatistics.GaussianGaussian

Examples

obj <- GaussianGaussian(gamma=list(Sigma=matrix(c(2,1,1,2),2,2),m=c(0.2,0.5),S=diag(2)))
x <- rGaussian(100,c(0,0),Sigma = matrix(c(2,1,1,2),2,2))
w <- runif(100)
sufficientStatistics_Weighted(obj=obj,x=x,w=w,foreach = FALSE)
sufficientStatistics_Weighted(obj=obj,x=x,w=w,foreach = TRUE)

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