mlegp (version 2.2.6)

plotMainEffects: Sensitivity Analysis for Gaussian Processes and Gaussian Process Lists

Description

Plots main effects of Gaussian process design parameters

Usage

plotMainEffects(gp, ylab = "predicted output", graphStyle = 2, verbose = FALSE, no.plot = FALSE, ...)

Value

• If no.plot is TRUE, a list with components:
• index
  vector of parameter values
• preds
  vector of corresponding predicted values

Additional Arguments (General)

• FANOVA

{ if TRUE, and graphStyle is 1 or 2, FANOVA results (% of total functional variance of each effect) is reported in the legend; this option is not implmented for functional output } lower{ a vector for the minimum values of all parameters of the gp design matrix, defaulting to the minimum value of each parameter in the design } upper{ a vector for the maximum values of all parameters of the gp design matrix, defaulting to the maximum value of each parameter in the design }

Additional Arguments (for single Gaussian processes)

• effects

{ a vector of parameter names (or numbers) to plot main effects for, corresponding to the column of the design matrix (default is all parameters) } length.out{ the number of values to plot for each parameter }

Additional Arguments (for Gaussian process lists)

• effects

{ the name (or number) of the parameter to plot main effects for; only one main effect can be plotted at a time } gp.nums{ a vector of the Gaussian process numbers to plot (all Gaussian processes in list are analyzed by default) } length.out{ the number of values of each parameter to plot (but does not apply for main effects of functional output } PC.weights{ if the component UD of gp is not NULL, set PC.weights to FALSE (the default) to plot the main effects of observed response; otherwise the main effects of the principle component weights are plotted } param.values{ if calculating the main effect of output using principle component weights, the parameter values to look at } xlab{ if calculating the main effect of output using principle component weights, optional x-axis label (default is 'time') } xValues{ for plotting main effects of functional output, the values to plot along the x-axis }

Details

Implements main effects plots described in Schonlau and Welch (2006), using a prior distribution of all components that is ~ independent U(a,b), where (a,b) corresponds to the (min, max) value of that component in the design. For all parameters, (a,b) can be overwritten via the arguments lower and upper.

For a single Gaussian process, main effects of the specified parameters are plotted; for Gaussian process lists, the main effects of a single parameter for (a subset of) all Gaussian processes in the list are plotted; for functional output, the main effect is caculated by calculating the main effect for each Gaussian process and premultiplying by the UD matrix to obtain the main effect on the functional output.

Main effects for the parameter x of non-functional output will plot the main effect of x evaluated at values seq(min(x), max(x), length.out), where length.out can be specified by the user. For functional output, plotMainEffects considers values of x with length.out equal to 3; the parameter values can also be specified directly via the argument param.values.

If main effects for several parameters are plotted on the same graph, and the ranges for parameters are not identical, they are automatically sclaed to be between 0 and 1.

Additional arguments (described below) will vary depending on whether gp is of type gp or type gp.list.

References

Schonlau, M. and Welch, W. 2006. Screening the Input Variables to a Computer Model Via Analysis of Variance and Visualization, in Screening: Methods for Experimentation in Industry, Drug Discovery, and Genetics. A Dean and S. Lewis, eds. (New York: Springer).

http://users.nsula.edu/dancikg/mlegp/

See Also

FANOVADecomposition for quantifying the importance of main effects

Examples

## fit a Gaussian process ##
x1 = rep(-5:5,3); x2 = kronecker(1:3, rep(1,11))
y = sin(x1) + 2*x2 + rnorm(length(x1),sd=.001)
fit = mlegp(cbind(x1,x2), y)

## plot all main effects
plotMainEffects(fit) 

## library adapt must be loaded for FANOVA=TRUE 
## plot all main effects with FANOVA contributions in legend
plotMainEffects(fit, FANOVA = TRUE)

## plotMainEffects for x2 'manually'
main = plotMainEffects(fit, effects = 2, no.plot=TRUE)
plot(main$index, main$preds, xlab = "x2", ylab = "predicted output")

## fit multiple Gaussian processes ##
x = seq(-5,5)
z1 = 10 - 5*x + rnorm(length(x))
z2 = 4 - 5*x + rnorm(length(x))
z3 = 7*sin(x) + rnorm(length(x))
fitMulti = mlegp(x, cbind(z1,z2,z3), param.names = "x")

# for each gaussian process, plot main effects for parameter 1
plotMainEffects(fitMulti, effects = 1)

# plot the main effect of the first parameter for gaussian processes 1 and 3
plotMainEffects(fitMulti, effects = 1, gp.nums = c(1,3))


## fit multiple Gaussian processes using principle component weights ##
x = seq(-5,5,by=.2)
p = 1:50
y = matrix(0,length(p), length(x))
for (i in p) {
        y[i,] = sin(x) + i + rnorm(length(x), sd  = .01)
}

numPCs = 2
fitPC = mlegp(p, t(y), PC.num = numPCs)

# plot main effects on the functional output ##
plotMainEffects(fitPC, effects = 1, xValues = x)