marginalLikelihood_bySufficientStatistics.GaussianNIW {bbricks} R Documentation

## Marginal likelihood of a "GaussianNIW" object, using sufficient statistics

### Description

Generate the marginal likelihood of a set of observations of the following 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 model structure and prior parameters are stored in a "GaussianNIW" object.
Marginal likelihood = p(x|m,k,v,S)

### Usage

```## S3 method for class 'GaussianNIW'
marginalLikelihood_bySufficientStatistics(obj, ss, LOG = TRUE, ...)
```

### Arguments

 `obj` A "GaussianNIW" object. `ss` Sufficient statistics of x. In Gaussian-NIW case the sufficient statistic of sample x is a object of type "ssGaussian", it can be generated by the function sufficientStatistics(). `LOG` Return the log density if set to "TRUE". `...` Additional arguments to be passed to other inherited types.

### Value

numeric, the marginal likelihood.

### 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).

`GaussianNIW`, `marginalLikelihood.GaussianNIW`

### Examples

```x <- rGaussian(1000,mu = c(1,1),Sigma = matrix(c(1,0.5,0.5,3),2,2))
obj <- GaussianNIW(gamma=list(m=c(0,0),k=1,v=2,S=diag(2)))
marginalLikelihood(obj = obj,x=x)
## or...
ss <- sufficientStatistics(obj=obj,x=x,foreach = FALSE)
marginalLikelihood_bySufficientStatistics(obj = obj,ss=ss)
```

[Package bbricks version 0.1.4 Index]