`fgpm-class.Rd`

This is the formal representation of Gaussian process models within the funGp package. Gaussian process models are useful statistical tools in the modeling of complex input-output relationships.

**Main methods**

fgpm: creation of funGp regression models

predict: output estimation at new input points based on a funGp model

simulate: random sampling from a funGp Gaussian process model

update: modification of data and hyperparameters of a funGp model**Plotters**

plotLOO: leave-one-out diagnostic plot for a funGp model

plotPreds: plot for predictions of a funGp model

plotSims: plot for simulations of a funGp model

`howCalled`

Object of class

`"modelCall"`

. User call reminder.`type`

Object of class

`"character"`

. Type of model based on type of inputs. To be set from "scalar", "functional", "hybrid".`ds`

Object of class

`"numeric"`

. Number of scalar inputs.`df`

Object of class

`"numeric"`

. Number of functional inputs.`f_dims`

Object of class

`"numeric"`

. An array with the original dimension of each functional input.`sIn`

Object of class

`"matrix"`

. The scalar input points. Variables are arranged by columns and coordinates by rows.`fIn`

Object of class

`"list"`

. The functional input points. Each element of the list contains a functional input in the form of a matrix. In each matrix, curves representing functional coordinates are arranged by rows.`sOut`

Object of class

`"matrix"`

. The scalar output values at the coordinates specified by sIn and/or fIn.`n.tot`

Object of class

`"integer"`

. Number of observed points used to compute the training-training and training-prediction covariance matrices.`n.tr`

Object of class

`"integer"`

. Among all the points loaded in the model, the amount used for training.`f_proj`

Object of class

`"fgpProj"`

. Data structures related to the projection of functional inputs. Check fgpProj for more details.`kern`

Object of class

`"fgpKern"`

. Data structures related to the kernel of the Gaussian process model. Check fgpKern for more details.`nugget`

Object of class

`"numeric"`

. Variance parameter standing for the homogeneous nugget effect.`preMats`

Object of class

`"list"`

. L and LInvY matrices pre-computed for prediction. L is a lower diagonal matrix such that \(L'L\) equals the training auto-covariance matrix \(K.tt\). On the other hand, \(LInvY = L^(-1) * sOut\).