This may be used to predict either new, unobserved instances of
\(\textbf{y}\) (called \(\textbf{y}^{new}\)) or
replicates of \(\textbf{y}\) (called
\(\textbf{y}^{rep}\)), and then perform posterior
predictive checks. Either \(\textbf{y}^{new}\) or
\(\textbf{y}^{rep}\) is predicted given an object of
class `demonoid`

, the model specification, and data.

```
# S3 method for demonoid
predict(object, Model, Data, CPUs=1, Type="PSOCK", …)
```

object

An object of class `demonoid`

is required.

Model

The model specification function is required.

Data

A data set in a list is required. The dependent variable
is required to be named either `y`

or `Y`

.

CPUs

This argument accepts an integer that specifies the number
of central processing units (CPUs) of the multicore computer or
computer cluster. This argument defaults to `CPUs=1`

, in which
parallel processing does not occur.

Type

This argument specifies the type of parallel processing to
perform, accepting either `Type="PSOCK"`

or
`Type="MPI"`

.

…

Additional arguments are unused.

This function returns an object of class `demonoid.ppc`

(where
ppc stands for posterior predictive checks). The returned object is
a list with the following components:

This stores the vectorized form of \(\textbf{y}\), the dependent variable.

This is a \(N \times S\) matrix, where \(N\) is the number of records of \(\textbf{y}\) and \(S\) is the number of posterior samples.

This is a vector of predictive deviance.

This function passes each iteration of marginal posterior samples
along with data to `Model`

, where the fourth component in the
return list is labeled `yhat`

, and is a vector of expectations of
\(\textbf{y}\), given the samples, model specification, and
data. Stationary samples are used if detected, otherwise
non-stationary samples will be used. To predict
\(\textbf{y}^{rep}\), simply supply the data set used to
estimate the model. To predict \(\textbf{y}^{new}\), supply
a new data set instead (though for some model specifications, this
cannot be done, and \(\textbf{y}_{new}\) must be specified
in the `Model`

function). If the new data set does not have
\(\textbf{y}\), then create `y`

in the list and set it
equal to something sensible, such as `mean(y)`

from the
original data set.

The variable `y`

must be a vector. If instead it is matrix
`Y`

, then it will be converted to vector `y`

. The vectorized
length of `y`

or `Y`

must be equal to the vectorized length
of `yhat`

, the fourth component of the return list of the
`Model`

function.

Parallel processing may be performed when the user specifies
`CPUs`

to be greater than one, implying that the specified number
of CPUs exists and is available. Parallelization may be performed on a
multicore computer or a computer cluster. Either a Simple Network of
Workstations (SNOW) or Message Passing Interface is used (MPI). With
small data sets and few samples, parallel processing may be slower,
due to computer network communication. With larger data sets and more
samples, the user should experience a faster run-time.

For more information on posterior predictive checks, see https://web.archive.org/web/20150215050702/http://www.bayesian-inference.com/posteriorpredictivechecks.