linear_gradhess: Gradient and Hessian matrix for the "marginal posterior" for...

In feng-li/movingknots: Efficient Bayesian multivariate surface regression

Description

This is the gradient and hessian matrix for the simple spline model with conjugate priors.

Usage

linear_gradhess(
  Params,
  hessMethod,
  Y,
  x0,
  callParam,
  splineArgs,
  priorArgs,
  Params_Transform
)

Arguments

Params	"list". Contains the matrices for the parameters. Params$knots: knots Params$shrinkages: The shrinkages Params$Sigma: The variance
hessMethod	"character". Method to be used in the Hessian approximation.
Y	"matrix". The response matrix, we consider the multivariate case.
x0	"matrix". The covaritates, you should *NOT* provide the intercept. It will be added automatically if necessary.
callParam	NA
splineArgs	"list". Parameters for the spline options to pass to the function, where splineArgs$method should be the spline method for x, see also d.matrix(). splineArgs$method: "character". The method of splines, which can be "thinplate". splineArgs$withInt: "logical". If TRUE, will return design matrix with intercept; if FALSE, design matrix without intercept.
priorArgs	priorArgs$prior_type: gradient type for prior priorArgs$M: mean of B, q-by-q priorArgs$n0: df. of inverse wishart distribution. priorArgs$S0: Covariance matrix from the prior of B. priorArgs$xi.mu0: Mean of the knots locations from the prior priorArgs$xi.Sigma0: Covariance matrix from the prior of knots priorArgs$K.mu0: mean for ka priorArgs$K.Sigma0: variance for ka
Params_Transform	NA
callParams	"character". callParams$id: the calling tag for the gradient. Possible values is "xi". "ka" callParams$subset: not all updated.

Details

This function will only return the gradient and hessian part for the *labeled* knots. It is possiable to provide the full gradient and hessian matrix if the parameter otherArgs$subsets contains the full knots labels.

Value

"list", see bellow. 'gradObs': n*p-by-1 matrix, the observed gradient for xi. 'hessObs: The obsered Hessian matrix for xi.

Author(s)

Feng Li, Dept. of Statistics, Stockholm University, Sweden.

feng-li/movingknots documentation built on March 30, 2021, 11:58 a.m.