multivator (version 1.1-4)

optimal_params: Optimization of the hyperparameters

Description

Optimization of the hyperparameters using a sequence of subfunctions.

Usage

optimal_params     (expt, LoF, start_hp, option = "a", ...)
optimal_B          (expt, LoF, start_hp, option = "a", verbose=FALSE, ...)
optimal_identical_B(expt, LoF, start_hp, verbose=FALSE, ...)
optimal_diag_M     (expt, LoF, start_hp)
optimal_M          (expt, LoF, start_hp, ...)

Arguments

expt

Object of class experiment

LoF

List of functions

start_hp

Start value for the hyperparameters, an object of class mhp. The various optimization routines use the different parts of start_hp as start points, and incrementally update it

option

In function optimal_B() and consequently optimal_params(), a character indicating whether to allow the scales to differ or not.

• Default option “a” is the simplest: each univariate B matrix is a multiple of the identity matrix.
• Option “b” allows the B matrices to be any (positive definite) diagonal matrix.
• Option “c” specifies that B[,,j] is diagonal for each j and furthermore that B[i,i,1]=B[i,i,2]=...=B[i,i,r]. This option calls optimal_identical_B().

verbose

In function optimal_B(), Boolean with TRUE meaning to print debugging information and default FALSE meaning not to print anything

...

Further arguments passed to the optimization routine

Value

Returns a mhp object.

Details

The user-friendly wrapper function is optimal_params(). This calls function optimal_B() first, as most of the analysis is conditional on B. Then optimal_diag_M() is called; this places the maximum likelihood estimate for $sigma^2$ on the diagonal of M. Finally, optimal_M() is called, which assigns the off-diagonal elements of M.

Each of the subfunctions returns an object appropriate for insertion into a mhp object.

The “meat” of optimal_params() is

       B(out)  <- optimal_B     (mm, d, LoF, start_hp=out, option=option, ...)
  diag(M(out)) <- optimal_diag_M(mm, d, LoF, start_hp=out, ...)
       M(out)  <- optimal_M     (mm, d, LoF, start_hp=out, ...)
  return(out)

See how object out is modified sequentially, it being used as a start point for the next function.

Examples

data(mtoys)

optimal_params(toy_expt,toy_LoF,toy_mhp,option='c',control=list(maxit=1))