sufficientStatistics_Weighted.GaussianNIW {bbricks} R Documentation

## Weighted sufficient statistics for a "GaussianNIW" object

### Description

For following Gaussian-NIW model structure:

mu,Sigma|m,k,v,S \sim NIW(m,k,v,S)

x|mu,Sigma \sim Gaussian(mu,Sigma)

Where NIW() is the Normal-Inverse-Wishart distribution, Gaussian() is the Gaussian distribution. See `?dNIW` and `dGaussian` for the definitions of these 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)

• the uncentered scatter matrix S = t(w*x)

### Usage

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

### Arguments

 `obj` A "GaussianNIW" 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, 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. `...` 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

Murphy, Kevin P. "Conjugate Bayesian analysis of the Gaussian distribution." def 1.22 (2007): 16.

Gelman, Andrew, et al. "Bayesian Data Analysis Chapman & Hall." CRC Texts in Statistical Science (2004).

### See Also

`GaussianNIW`, `sufficientStatistics.GaussianNIW`

### Examples

```x <- rGaussian(10,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2))
obj <- GaussianNIW()                    #an GaussianNIW object
w <- runif(10)
sufficientStatistics_Weighted(obj=obj,x=x,w=w,foreach = FALSE)
sufficientStatistics_Weighted(obj=obj,x=x,w=w,foreach = TRUE)
```

[Package bbricks version 0.1.4 Index]