| bmacdf {ensembleBMA} | R Documentation |
Find the BMA cdf at a given value Y.
bmacdf(a, b, sigma, w, X, Y)
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 |
X |
vector of K forecasts |
Y |
Observation value at which cdf is required. |
The BMA pdf is a mixture of weighted normals. This function returns the cdf at a given quantile x.
value of the BMA cdf evaluated at x
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
,
bmaquant
#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)
#evaluate and plot the BMA cdf for the first observation
index <- seq(-5,5,by=.1)
cdf.at.index=NULL
for(i in 1:length(index))
{
cdf.at.index[i]=bmacdf(a = EMresult$a,b = EMresult$b, sigma = EMresult$sigma,
w = EMresult$w, x[1,],index[i])
}
plot(index, cdf.at.index, type="l")
#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 )
#evaluate and plot the BMA cdf for the first observation
index <- seq(1000,1025,by=.1)
cdf.at.index=NULL
for(i in 1:length(index))
{
cdf.at.index[i]=bmacdf(a = EMresult$a,b = EMresult$b, sigma = EMresult$sigma,
w = EMresult$w, X[1,],index[i])
}
plot(index, cdf.at.index, type="l")