LaplacesDemon (version 16.1.4)

predict.demonoid: Posterior Predictive Checks

Description

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

Usage

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

Arguments

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.

Value

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:

y

This stores the vectorized form of $\mathbf{\text{y}}$, the dependent variable.

yhat

This is a $N\times S$ matrix, where $N$ is the number of records of $\mathbf{\text{y}}$ and $S$ is the number of posterior samples.

Deviance

This is a vector of predictive deviance.

Details

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 $\mathbf{\text{y}}$, given the samples, model specification, and data. Stationary samples are used if detected, otherwise non-stationary samples will be used. To predict ${\mathbf{\text{y}}}^{rep}$, simply supply the data set used to estimate the model. To predict ${\mathbf{\text{y}}}^{new}$, supply a new data set instead (though for some model specifications, this cannot be done, and ${\mathbf{\text{y}}}_{new}$ must be specified in the Model function). If the new data set does not have $\mathbf{\text{y}}$, 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.

See Also

LaplacesDemon