gevcdn.bootstrap: Bootstrapped confidence intervals for GEV CDN parameters and...
In GEVcdn: GEV Conditional Density Estimation Network

Description Usage Arguments Details Value References See Also Examples

Used to assist in the calculation of bootstrapped confidence intervals for GEV location, scale, and shape parameters, as well as for specified quantiles. Residual and parametric bootstrap estimates are supported.

gevcdn.bootstrap(n.bootstrap, x, y, iter.max = 1000, n.hidden = 2,
                 Th = gevcdn.logistic, fixed = NULL,
                 init.range = c(-0.25, 0.25),
                 scale.min = .Machine$double.eps,
                 beta.p = 3.3, beta.q = 2, sd.norm = Inf,
                 n.trials = 5, method = c("BFGS", "Nelder-Mead"),
                 boot.method = c("residual", "parametric"),
                 init.from.prev = TRUE, max.fails = 100,
                 probs = c(0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9,
                 0.95, 0.99), ...)

`n.bootstrap`	number of bootstrap trials used to calculate confidence intervals.
`x`	covariate matrix with number of rows equal to the number of samples and number of columns equal to the number of variables.
`y`	column matrix of target values with number of rows equal to the number of samples.
`iter.max`	maximum number of iterations of optimization algorithm.
`n.hidden`	number of hidden nodes in each GEV CDN ensemble member.
`Th`	hidden layer transfer function; defaults to `gevcdn.logistic`.
`fixed`	vector indicating GEV parameters to be held constant; elements chosen from `c("location", "scale", "shape")`
`init.range`	range for random weights on [`min(init.range)`, `max(init.range)`]
`scale.min`	minimum allowable value for the GEV scale parameter.
`beta.p`	`shape1` parameter for shifted beta distribution prior for GEV shape parameter
`beta.q`	`shape2` parameter for shifted beta distribution prior for GEV shape parameter
`sd.norm`	`sd` parameter for normal distribution prior for the magnitude of input-hidden layer weights; equivalent to weight penalty regularization.
`n.trials`	number of repeated trials used to avoid shallow local minima during optimization
`method`	optimization method for `optim` function; must be chosen from `c("BFGS", "Nelder-Mead")`.
`boot.method`	bootstrap method; must be chosen from `c("residual", "parametric")`.
`init.from.prev`	logical value indicating whether or not optimization runs should be initialized from the final weights of the previous run.
`max.fails`	maximum number of repeated exceptions allowed during optimization
`probs`	vector of cumulative probabilities for which quantile confidence intervals are desired.
`...`	additional arguments passed to the `control` list of `optim` function

Note: the boot package provides a more comprehensive suit of methods for estimating bootstrap-based confidence intervals.

a list consisting of

`weights.bootstrap`	a list of length `n.bootstrap` consisting of weights following the format returned by `gevcdn.fit`
`parms.bootstrap`	a list of length `n.bootstrap` consisting of GEV parameters following the format returned by `gevcdn.evaluate`
`location.bootstrap`	a matrix of GEV location parameters with number of rows equal to that of `x` and number of columns equal to `n.bootstrap`
`scale.bootstrap`	a matrix of GEV scale parameters with number of rows equal to that of `x` and number of columns equal to `n.bootstrap`
`shape.bootstrap`	a matrix of GEV shape parameters with number of rows equal to that of `x` and number of columns equal to `n.bootstrap`
`quantiles.bootstrap`	a list of length `n.bootstrap` with each consisting of a matrix with number of rows equal to that of `x` and columns corresponding to `probs`

Cannon, A.J., 2010. A flexible nonlinear modelling framework for nonstationary generalized extreme value analysis in hydroclimatology. Hydrological Processes, 24: 673-685. DOI: 10.1002/hyp.7506

gevcdn.cost, gevcdn.evaluate, gevcdn.fit, gevcdn.bag, dgev, optim

## Generate synthetic data

x <- as.matrix(seq(0.1, 1, length = 50))

loc <- x^2
scl <- x/2
shp <- seq(-0.1, 0.3, length = length(x))

set.seed(100)
y <- as.matrix(rgev(length(x), location = loc, scale = scl,
               shape = shp))

## Not run: 
## Fit 30 bootstrapped models

CI <- gevcdn.bootstrap(n.bootstrap = 30, x = x, y = y,
                       iter.max = 100, n.hidden = 2,
                       Th = gevcdn.logistic, n.trials = 1,
                       boot.method = "residual",
                       probs = c(0.1, 0.5, 0.9))

## Plot data and percentile confidence intervals for GEV parameters

par(mfrow = c(2, 2))
matplot(x, y, type = "b", pch = 19, col = "red", xlab = "x",
        ylab = "y", main = "gevcdn.bootstrap")
matplot(x, cbind(loc, t(apply(CI$location.bootstrap, 1, quantile,
        p = c(0.025, 0.975)))), type = c("l", "b", "b"), pch = 20,
        lwd = 3, col = c("black", rep("green", 2)), xlab = "x",
        ylab = "location", main = "location CI")
matplot(x, cbind(scl, t(apply(CI$scale.bootstrap, 1, quantile,
        p = c(0.025, 0.975)))), type = c("l", "b", "b"), pch = 20,
        lwd = 3, col = c("black", rep("orange", 2)), xlab = "x",
        ylab = "scale", main = "scale CI")
matplot(x, cbind(shp, t(apply(CI$shape.bootstrap, 1, quantile,
        p = c(0.025, 0.975)))), type = c("l", "b", "b"), pch = 20,
        lwd = 3, col = c("black", rep("brown", 2)), xlab = "x",
        ylab = "shape", main = "shape CI")

## End(Not run)