# bride: Brier Score Decomposition In bride: Brier score decomposition of probabilistic forecasts for binary events

## Description

Decomposes the empirical Brier score into reliability, resolution and uncertainty. The components are computed in two different ways: Using the original (biased) estimators by Murphy (1974), and using bias-corrected estimators proposed by Ferro and Fricker (2012). Variance estimators are calculated. Can deal with probabilistic predictions of binary events.

## Usage

 `1` ``` bride(p, y, n.bins=10, ...) ```

## Arguments

 `p` a vector of forecast probabilities. No default. `y` a vector of binary event indicators. No default. `n.bins` number of bins used for calculating the calibration function. Default `n.bins = 10`. `...` possible additional arguments. Not used at the moment.

## Details

The values of the forecast probabilities in `p` are binned into `n.bins` equidistant bins on the unit interval. Based on this binning, the calibration function

P(y=1|p)

is estimated, which is required to calculate the reliability and resolution term.

## Value

An object of class `bride`, essentially a list containing:

 `p,y` the objects of the original request. `n.bins` number of equidistant, exhaustive bins used to calculate cross table. `p.binavgs` in-bin-average forecast probabilities. `p.binned` a vector of length(p), where each original p was replaced by its in-bin-average. `c.table` the cross-table, aka consistency table; c.table[i,j] indicates number of times that y was in the i-th class and at the same time p was in the j-th bin. `rel,res,unc` reliability, resolution, uncertainty estimates derived by Murphy (1970). `rel2,res2,unc2` bias-corrected reliability, resolution, uncertainty estimates derived by Ferro (2012). `relv,resv,uncv,rel2v,res2v,unc2v` variance estimators derived by Siegert (2012).

Stefan Siegert

## References

Murphy, AH (1974) A new vector partition of the probability score, Journal of Applied Meteorology, 12:595-600

Ferro CAT, Fricker TE (2012) A bias-corrected decomposition of the Brier Score, Quarterly Journal of the Royal Meteorological Society, 138(668): 1954-1960

Siegert, S. (2013) Variance estimators for Brier Score decomposition, document in preparation

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## number of forecasts and verifications N <- 100 ## produce some p-values p <- runif(n=N) ## produce events with corresponding probabilities y <- rbinom(n=N, size=1, prob=p) ## perform brier score decomposition b <- bride(p=p,y=y) ## print print(b) ```

### Example output

```Call:
bride.default(p = p, y = y)

REL = 0.0032 +/- 0.0094
RES = 0.1029 +/- 0.0232
UNC = 0.2500 +/- 0.0030

REL - RES + UNC = 0.1503
Br = 0.1493
```

bride documentation built on May 2, 2019, 5:15 p.m.