NormalToeplitz | R Documentation |

Provides methods for the Normal-Toeplitz (NTz) distribution defined as

z ~ NTz(acf) <=> z ~ Normal(0, toeplitz(acf)),

i.e., for a multivariate normal with mean zero and variance `Tz = toeplitz(acf)`

.

`new()`

Class constructor.

NormalToeplitz$new(N)

`N`

Size of the NTz random vector.

A `NormalToeplitz`

object.

`size()`

Get the size of the NTz random vector.

NormalToeplitz$size()

Size of the NTz random vector.

`logdens()`

Log-density function.

NormalToeplitz$logdens(z, acf)

`z`

Density argument. A vector of length

`N`

or an`N x n_obs`

matrix where each column is an`N`

-dimensional observation.`acf`

A vector of length

`N`

containing the autocorrelation (i.e., first row/column) of the Toeplitz variance matrix.

A scalar or vector of length `n_obs`

containing the log-density of the NTz evaluated at its arguments.

`grad()`

Gradient of the log-density with respect to parameters.

NormalToeplitz$grad(z, dz, acf, dacf, full_out = FALSE)

`z`

Density argument. A vector of length

`N`

.`dz`

An

`N x n_theta`

matrix containing the gradient`dz/dtheta`

.`acf`

A vector of length

`N`

containing the autocorrelation of the Toeplitz variance matrix.`dacf`

An

`N x n_theta`

matrix containing the gradient`dacf/dtheta`

.`full_out`

If

`TRUE`

, returns the log-density as well (see 'Value').

A vector of length `n_theta`

containing the gradient of the NTz log-density with respect to `theta`

, or a list with elements `ldens`

and `grad`

consisting of the log-density and the gradient vector.

`hess()`

Hessian of log-density with respect to parameters.

NormalToeplitz$hess(z, dz, d2z, acf, dacf, d2acf, full_out = FALSE)

`z`

Density argument. A vector of length

`N`

.`dz`

An

`N x n_theta`

matrix containing the gradient`dz/dtheta`

.`d2z`

An

`N x n_theta x n_theta`

array containing the Hessian`d^2z/dtheta^2`

.`acf`

A vector of length

`N`

containing the autocorrelation of the Toeplitz variance matrix.`dacf`

An

`N x n_theta`

matrix containing the gradient`dacf/dtheta`

.`d2acf`

An

`N x n_theta x n_theta`

array containing the Hessian`dacf^2/dtheta^2`

.`full_out`

If

`TRUE`

, returns the log-density and its gradient as well (see 'Value').

An `n_theta x n_theta`

matrix containing the Hessian of the NTz log-density with respect to `theta`

, or a list with elements `ldens`

, `grad`

, and `hess`

consisting of the log-density, its gradient (a vector of size `n_theta`

), and the Hessian matrix, respectively.

`grad_full()`

Full gradient of log-density function.

NormalToeplitz$grad_full(z, acf, calc_dldz = TRUE, calc_dlda = TRUE)

`z`

Density argument. A vector of length

`N`

.`acf`

A vector of length

`N`

containing the autocorrelation of the Toeplitz variance matrix.`calc_dldz`

Whether or not to calculate the gradient with respect to

`z`

.`calc_dlda`

Whether or not to calculate the gradient with respect to

`acf`

.

A list with elements:

`ldens`

The log-density evaluated at

`z`

and`acf`

.`dldz`

The length-

`N`

gradient vector with respect to`z`

, if`calc_dldz = TRUE`

.`dlda`

The length-

`N`

gradient vector with respect to`acf`

, if`calc_dlda = TRUE`

.

`clone()`

The objects of this class are cloneable with this method.

NormalToeplitz$clone(deep = FALSE)

`deep`

Whether to make a deep clone.

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