posterior.GaussianInvWishart {bbricks} R Documentation

## Update a "GaussianInvWishart" object with sample sufficient statistics

### Description

For the 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.
Update (v,S) by adding the information of newly observed samples x. The model structure and prior parameters are stored in a "GaussianInvWishart" object, the prior parameters in this object will be updated after running this function.

### Usage

```## S3 method for class 'GaussianInvWishart'
posterior(obj, ss, ...)
```

### Arguments

 `obj` A "GaussianInvWishart" object. `ss` Sufficient statistics of x. In Gaussian and Inverse-Wishart case the sufficient statistic of sample x is a object of type "ssGaussianVar", it can be generated by the function sufficientStatistics(). `...` Additional arguments to be passed to other inherited types.

### Value

None. the gamma stored in "obj" will be updated based on "ss".

### 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`,`posteriorDiscard.GaussianInvWishart`,`sufficientStatistics.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))
ss <- sufficientStatistics(obj=obj,x=x,foreach = FALSE)
obj
posterior(obj,ss = ss)
obj
```

[Package bbricks version 0.1.4 Index]