| bmaquant {ensembleBMA} | R Documentation |
Returns the quantile of a mixture of weighted normals pdf. This can be used to find the bounds of a confidence interval for such a pdf. The bisection method is used to find the desired quantile.
bmaquant(a, b, sigma, w, alpha, X, niter = 14)
a |
vector of K intercepts in the regression bias correction. If no regression is desired, 'a' should be a vector of zeros. |
b |
vector of K slopes in the regression bias correction. If no regression is desired, 'b' should be a vector of ones. |
sigma |
vector of K standard deviations from the BMA fit (a,b,sigma are all outputs of EM.normals or EM.for.date). If there is only one variance parameter (constant variance), then this can be a single number. |
w |
vector of K weights from the BMA fit |
alpha |
quantile desired (.05, .95, etc.). Can be a vector of quantiles. |
X |
vector of ensemble predictions. |
niter |
number of iterations for the bisection method. Default is 14. |
the desired quantile.
Adrian E. Raftery, J. McLean Sloughter, Michael Polakowski
Raftery, A. E., T. Gneiting, F. Balabdaoui, & M. Polakowski, "Using Bayesian Model Averaging to calibrate forecast ensembles." Monthlly Weather Review, to appear, 2005. earlier version available at: http://www.stat.washington.edu/www/research/reports/2003/tr440.pdf
EM.normals
,
EM.for.date
,
CRPS
,
bmacdf
#create a simulated dataset with equal weights, no bias,
#and standard deviation of 1 in each component
x <- matrix(rnorm(1000,0,2),nrow = 200, ncol = 5)
y.latent <- floor(runif(200,1,6))
y.means <- NULL
for(i in 1:200)
{
y.means[i] <- x[i,y.latent[i]]
}
y <- rnorm(200,y.means, sd = 1)
#calculate the BMA estimates of the parameters
EMresult <- EM.normals(x, y, reg.adjust=FALSE, min.CRPS=FALSE)
# 95th percentile
bmaquant(a = EMresult$a,b = EMresult$b, sigma = EMresult$sigma,
w = EMresult$w, alpha = .95, x[1,])
# 5th percentile
bmaquant(a = EMresult$a,b = EMresult$b, sigma = EMresult$sigma,
w = EMresult$w, alpha = .05 ,x[1,])
#read in the sea-level pressure data and calculate BMA estimates
#for forecasting on the 35th day in the data set
data(slp)
unique.dates <- unique(slp$date)
date.list <- NULL
for(i in 1:length(unique.dates))
{
date.list[slp$date==unique.dates[i]] <- i
}
X <- cbind(slp$F1,slp$F2,slp$F3,slp$F4,slp$F5)
Y <- slp$Y
EMresult <- EM.for.date(date = 35,date.list = date.list,X = X,Y = Y )
# 5th and 95th percentiles
bmaquant(a = EMresult$a,b = EMresult$b, sigma = EMresult$sigma,
w = EMresult$w, alpha = c(.05,.95) ,X[1,])