dPosteriorPredictive.GaussianInvWishart {bbricks} R Documentation

## Posterior predictive density function of a "GaussianInvWishart" object

### Description

Generate the the density value of the posterior predictive distribution of the following 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 model structure and prior parameters are stored in a "GaussianInvWishart" object.
Posterior predictive density is p(x|v,S,mu).

### Usage

```## S3 method for class 'GaussianInvWishart'
dPosteriorPredictive(obj, x, LOG = TRUE, ...)
```

### Arguments

 `obj` A "GaussianInvWishart" object. `x` matrix, or the ones that can be converted to matrix, each row of x is an observation. `LOG` Return the log density if set to "TRUE". `...` Additional arguments to be passed to other inherited types.

### Value

A numeric vector of the same length as nrow(x), the posterior predictive density.

### 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`, `dPosteriorPredictive.GaussianInvWishart`, `marginalLikelihood.GaussianInvWishart`

### Examples

```obj <- GaussianInvWishart(gamma=list(mu=c(-1.5,1.5),v=3,S=diag(2)))
x <- rGaussian(100,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2))
xNew <- rGaussian(100,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)
## update piror with x
posterior(obj=obj,ss = ss)
## use the posterior to calculate the probability of observing each xNew
dPosteriorPredictive(obj = obj,x = xNew,LOG = TRUE)
```

[Package bbricks version 0.1.4 Index]