mri: Multivariate Reliability Index

In jobstdavid/eppverification: Verification Tools for the Statistical Postprocessing of Ensemble Forecasts

Multivariate Reliability Index

Description

This function calculates the Multivariate Reliability Index (RI) given observations of a multivariate variable and samples of a predictive distribution.

Usage

mri(y, x, method = "mv", bins = NULL, na.rm = FALSE)

Arguments

y	matrix of observations (see details)
x	3-dimensional array of samples of a predictive distribution (depending on y; see details)
method	character; "mv", "avg", "mst", "bd"; default: "mv" (see details)
bins	numeric; if NULL the number of bins is equal to nrow(x[, , 1])+1; otherwise bins must be chosen so that (nrow(x[, , 1])+1)/bins is an integer; default: NULL (see details)
na.rm	logical; if TRUE NA are stripped before the rank computation proceeds; if FALSE NA are used in the rank computation; default: FALSE

Details

The observations are given in the matrix y with n rows, where each column belongs to an univariate observation variable. The i-th row of matrix y belongs to the i-th third dimension entry of the array x. The i-th third dimension entry must be a matrix with n rows, having the same structure as y, filled with the samples of a multivariate predictive distribution. Only finite values of y and x are used.

The parameter bins specifies the number of columns for the MVRH. For "large" ncol(x[, , 1]) it is often reasonable to reduce the resolution of the MVRH by using bins so that (ncol(x[, , 1])+1)/bins is an integer.

For the calculation of the ranks, different methods are available, where "mv" stands for "multivariate ranks", "avg" stands for "average ranks", "mst" stands for "minimum-spanning-tree ranks" and "bd" stands for "band-depth ranks". These methods are implemented as described in e.g. Thorarinsdottir et al. (2016).

The deviation from uniformity of the MVRH can be quantified by the multivariate reliability index (RI). The smaller the RI, the more calibrated the forecast is. The optimal value of the RI is 0.

Value

Vector of the score value.

Author(s)

David Jobst

References

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.

Gneiting, T., Stanberry, L., Grimit, E., Held, L. and Johnson, N. (2008). Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds. Test, 17, 211-264.

Smith, L. and Hansen, J. (2004). Extending the limits of ensemble forecast verification with the minimum spanning tree. Monthly Weather Review, 132, 1522-1528.

Thorarinsdottir, T., Scheurer, M. and Heinz, C. (2016). Assessing the calibration of high-dimensional ensemble forecasts using rank histograms. Journal of Computational and Graphical Statistics, 25, 105-122.

Wilks, D. (2004). The minimum spanning tree histogram as verification tool for multidimensional ensemble forecasts. Monthly Weather Review, 132, 1329-1340.

Examples

# simulated data
n <- 30
m <- 50
y <- cbind(rnorm(n), rgamma(n, shape = 1))
x <- array(NA, dim = c(m, 2, n))
x[, 1, ] <- rnorm(n*m)
x[, 2, ] <- rgamma(n*m, shape = 1)

# multivariate entropy calculation
ment(y = y, x = x)
ment(y = y, x = x, bins = 17, method = "bd")

jobstdavid/eppverification documentation built on May 13, 2024, 5:20 p.m.