EnsRpsDiff: Calculate average score differences for competing ensemble forecasts.

Description

Calculate the average ranked probability score (RPS) difference between two competing ensemble forecasts for the same observation. Approximate sampling quantiles of the average score difference and p-value of the paired one-sided t-test are provided. The difference between the score of 'ens.ref' and 'ens' is calculated. The higher the score difference, the higher the improvement of 'ens' over 'ens.ref'.

Usage

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EnsRpsDiff(ens, ens.ref, obs, probs)

Arguments

ens

N*K matrix. ens[i,j] is the number of ensemble members that predict category j at time i.

ens.ref

N*K matrix, similar to ens

obs

N*K matrix. obs[i,j] = 1 if category j is observed at time i, 0 otherwise.

probs

vector of probabilities. The probabilities of estimated sampling quantiles of the average score difference. Can be used to construct confidence intervals.

Value

A list with the following elements:

"rps.diff": The value of the average score difference.

"sampling.quantiles": The quantiles of the sampling distribution of the average score difference corresponding to the 'probs' argument. The sampling quantiles are approximated by a t-distribution as follows:

qt(probs, df=N-1) * sd(score.diff) / sqrt(N) + mean.score.diff

"p.value": p value of the one-sided paired t-test.

Examples

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  # Example:
  ens <- matrix(c(1,2,3, 1,3,2), byrow=TRUE, nrow=2)
  ens.ref <- matrix(c(2,2,2, 2,2,2), byrow=TRUE, nrow=2)
  obs <- matrix(c(0,0,1, 0,1,0), byrow=TRUE, nrow=2)
  EnsRpsDiff(ens, ens.ref, obs, probs=c(0.025, 0.975))

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

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