vr.hist | R Documentation |
This function plots the Verification Rank Histogram (VRH) given observations of an univariate variable and samples of a predictive distribution.
vr.hist(
y,
x,
bins = NULL,
type = "relative",
title = "Verification Rank Histogram",
reliability = FALSE,
entropy = FALSE,
na.rm = TRUE
)
y |
vector of observations |
x |
matrix of samples of a predictive distribution (depending on |
bins |
numeric; if |
type |
character; " |
title |
character; title of the plot; default: " |
reliability |
logical; if |
entropy |
logical; if |
na.rm |
logical; if |
For a vector y
of length n, x
should be given as matrix
with n rows, where the i-th entry of y
belongs to the i-th row
of x
. The columns of x
represent the samples of a predictive distribution.
Only finite values of y
and x
are used.
The parameter bins
specifies the number of columns for the VRH. For "large"
ncol(x)
it is often reasonable to reduce the resolution of the VRH by
using bins
so that (ncol(x)+1)/bins
is an integer.
If type
is "relative
" the relative frequencies of the bins are plotted.
If type
is "absolute
" the absolute frequencies of the bins are plotted.
If type
is "density
" the relative densities of the bins are plotted.
An uniform VRH indicates a calibrated predictive distribution. A ∩-shape in the VRH indicates overdispersion and a ∪-shape indicates underdispersion of the predictive distribution. A systematic bias of the predictive distribution results in a triangular shaped VRH histogram.
The deviation from uniformity of the VRH can be quantified by the reliability index (RI). The smaller the RI, the better is the calibration of the forecast. The optimal value of the RI is 0.
The entropy is a tool to assess the calibration of a forecast. The optimal value of the entropy is 1, representing a calibrated forecast.
ggplot object with a plot of the Verification Rank Histogram.
David Jobst
Anderson, J. (1996). A method for producing and evaluating probabilistic forecasts from ensemble model integrations. Journal of Climate, 9, 1518-1530.
Candille, G. and Talagrand, O. (2005). Evaluation of probabilistic prediction systems for a scalar variable. Quarterly Journal of the Royal Meteorological Society, 131(609), 2131-2150.
Delle Monache, L., Hacker, J., Zhou, Y., Deng, X. and Stull, R., (2006). Probabilistic aspects of meteorological and ozone regional ensemble forecasts. Journal of Geophysical Research: Atmospheres, 111, D24307.
Hamill, T. and Colucci, S. (1997). Verification of Eta-RSM short-range ensemble forecasts. Monthly Weather Review, 125, 1312-1327.
Hamill, T. (2001). Interpretation of rank histograms for verifying ensemble forecasts. Monthly Weather Review, 129, 550-560.
Taillardat, M., Mestre, O., Zamo, M. and Naveau, P., (2016). Calibrated Ensemble Forecasts Using Quantile Regression Forests and Ensemble Model Output Statistics. American Meteorological Society, 144, 2375-2393.
Tribus, M. (1969). Rational Descriptions, Descisions and Designs. Pergamon Press.
Talagrand, O., Vautard, R. and Strauss, B. (1997). Evaluation of probabilistic prediction systems. Workshop on Predictability (ECMWF), 1-25.
# simulated data
n <- 30
m <- 50
y <- rnorm(n)
x <- matrix(rnorm(n*m), ncol = m)
# vr.hist plot
vr.hist(y = y, x = x)
vr.hist(y = y, x = x, bins = 17, title = "VRH", reliability = TRUE, entropy = FALSE)
vr.hist(y = y, x = x, bins = 3, type = "absolute", reliability = FALSE, entropy = TRUE)
vr.hist(y = y, x = x, bins = 3, type = "density", reliability = TRUE, entropy = TRUE)
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