scores: Proper Scoring Rules for Poisson or Negative Binomial... In surveillance: Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic Phenomena

Description

Proper scoring rules for Poisson or negative binomial predictions of count data are described in Czado et al. (2009). The following scores are implemented: logarithmic score (`logs`), ranked probability score (`rps`), Dawid-Sebastiani score (`dss`), squared error score (`ses`).

Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```scores(x, ...) ## Default S3 method: scores(x, mu, size = NULL, which = c("logs", "rps", "dss", "ses"), sign = FALSE, ...) logs(x, mu, size = NULL) rps(x, mu, size = NULL, k = 40, tolerance = sqrt(.Machine\$double.eps)) dss(x, mu, size = NULL) ses(x, mu, size = NULL) ```

Arguments

 `x` the observed counts. All functions are vectorized and also accept matrices or arrays. Dimensions are preserved. `mu` the means of the predictive distributions for the observations `x`. `size` either `NULL` (default), indicating Poisson predictions with mean `mu`, or dispersion parameters of negative binomial forecasts for the observations `x`, parametrized as in `dnbinom` with variance `mu*(1+mu/size)`. `which` a character vector specifying which scoring rules to apply. By default, all four proper scores are calculated. The normalized squared error score (`"nses"`) is also available but it is improper and hence not computed by default. `sign` a logical indicating if the function should also return `sign(x-mu)`, i.e., the sign of the difference between the observed counts and corresponding predictions. `...` unused (argument of the generic). `k` scalar argument controlling the finite sum approximation for the `rps` with truncation at `ceiling(mu + k*sd)`. `tolerance` absolute tolerance for the finite sum approximation employed in the `rps` calculation. A warning is produced if the approximation with `k` summands is insufficient for the specified `tolerance`. In this case, increase `k` for higher precision (or use a larger tolerance).

Value

The scoring functions return the individual scores for the predictions of the observations in `x` (maintaining their dimension attributes).

The default `scores`-method applies the selected (`which`) scoring functions (and calculates `sign(x-mu)`) and returns the results in an array (via `simplify2array`), where the last dimension corresponds to the different scores.

Author(s)

Sebastian Meyer and Michaela Paul

References

Czado, C., Gneiting, T. and Held, L. (2009): Predictive model assessment for count data. Biometrics, 65 (4), 1254-1261. doi: 10.1111/j.1541-0420.2009.01191.x

The R package scoringRules implements the logarithmic score and the (continuous) ranked probability score for many distributions.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```mu <- c(0.1, 1, 3, 6, pi, 100) size <- 0.1 set.seed(1) y <- rnbinom(length(mu), mu = mu, size = size) scores(y, mu = mu, size = size) scores(y, mu = mu, size = 1) # ses ignores the variance scores(y, mu = 1, size = size) ## apply a specific scoring rule scores(y, mu = mu, size = size, which = "rps") rps(y, mu = mu, size = size) ```

Example output

```Loading required package: sp
This is surveillance 1.14.0. For overview type 'help(surveillance)'.
logs          rps       dss          ses
[1,] 0.06931472  0.004964256 -1.559438     0.010000
[2,] 5.33286895  7.531930222  8.216077    64.000000
[3,] 0.34339872  0.327742345  4.629374     9.000000
[4,] 4.90597889  6.601820669  5.946349    16.000000
[5,] 0.34786499  0.344097506  4.720295     9.869604
[6,] 0.69087548 11.651369846 11.613825 10000.000000
logs          rps       dss          ses
[1,] 0.09531018  0.008333333 -2.116366     0.010000
[2,] 6.93147181  7.337239583 32.693147    64.000000
[3,] 1.38629436  1.285714286  3.234907     9.000000
[4,] 3.48741695  3.337930556  4.118622    16.000000
[5,] 1.42108041  1.355121967  3.324357     9.869604
[6,] 4.61512052 49.751243781 10.210390 10000.000000
logs        rps      dss ses
[1,] 0.2397895 0.09897212 2.488804   1
[2,] 5.3328690 7.53193022 8.216077  64
[3,] 0.2397895 0.09897212 2.488804   1
[4,] 5.5224898 8.47616310 9.761532  81
[5,] 0.2397895 0.09897212 2.488804   1
[6,] 0.2397895 0.09897212 2.488804   1
rps
[1,]  0.004964256
[2,]  7.531930222
[3,]  0.327742345
[4,]  6.601820669
[5,]  0.344097506
[6,] 11.651369846
[1]  0.004964256  7.531930222  0.327742345  6.601820669  0.344097506
[6] 11.651369846
```

surveillance documentation built on July 25, 2018, 1:01 a.m.