# interp.loess: Lowess 2-d interpolation onto a uniform grid In tgp: Bayesian Treed Gaussian Process Models

## Description

Use the `loess` function to interpolate the two-dimensional `x`, `y`, and `z` data onto a uniform grid. The output produced is an object directly usable by the plotting functions `persp`, `image`, and `contour`, etc.

This function is designed as an alternative to the `interp` functions from the akima library.

## Usage

 `1` ```interp.loess(x, y, z, gridlen = c(40,40), span = 0.1, ...) ```

## Arguments

 `x` Vector of `X` spatial input locations `y` Vector of `Y` spatial input locations `z` Vector of `Z` responses interpreted as `Z = f(X,Y)` `gridlen` Size of the interpolated grid to be produced in x and y. The default of `gridlen = c(40,40)` causes a `40 * 40` grid of `X`, `Y`, and `Z` values to be computed. `span` Kernel span argument to the `loess` function with default setting `span = 0.1` set significantly lower than the the `loess` default – see note below. `...` Further arguments to be passed to the `loess` function

## Details

Uses `expand.grid` function to produce a uniform grid of size `gridlen` with domain equal to the rectangle implied by `X` and `Y`. Then, a `loess` a smoother is fit to the data `Z = f(X,Y)`. Finally, `predict.loess` is used to predict onto the grid.

## Value

The output is a list compatible with the 2-d plotting functions `persp`, `image`, and `contour`, etc.

The list contains...

 `x ` Vector of with `length(x) == gridlen` of increasing `X` grid locations `y ` Vector of with `length(y) == gridlen` of increasing `Y` grid locations `z ` `matrix` of interpolated responses `Z = f(X,Y)` where `z[i,j]` contains an estimate of `f(x[i],y[j])`

## Note

As mentioned above, the default `span = 0.1` parameter is significantly smaller that the default `loess` setting. This asserts a tacit assumption that the input is densely packed and that the noise in `z`'s is small. Such should be the case when the data are output from a tgp regression – this function was designed specifically for this situation. For data that is random or sparse, simply choose higher setting, e.g., the default `loess` setting of ```span = 0.75```, or a more intermediate setting of `span = 0.5` as in the example below

## Author(s)

Robert B. Gramacy, rbg@vt.edu, and Matt Taddy, mataddy@amazon.com

## See Also

`interp`, `loess`, `persp`, `image`, `contour`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```# random data ed <- exp2d.rand() # higher span = 0.5 required because the data is sparse # and was generated randomly ed.g <- interp.loess(ed\$X[,1], ed\$X[,2], ed\$Z, span=0.5) # perspective plot persp(ed.g) ```

tgp documentation built on Jan. 13, 2021, 3:49 p.m.