sufficientStatistics_Weighted.GaussianInvWishart {bbricks} R Documentation

## Weighted sufficient statistics of a "GaussianInvWishart" object

### 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) and weights w are:

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

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

### Usage

```## S3 method for class 'GaussianInvWishart'
sufficientStatistics_Weighted(obj, x, w, 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. `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.

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

`GaussianInvWishart`, `sufficientStatistics.GaussianInvWishart`
```obj <- GaussianInvWishart(gamma=list(mu=c(-1.5,1.5),v=4,S=diag(2)))