This function allows automatic scoring of forecasts using a range of metrics. For most users it will be the workhorse for scoring forecasts as it wraps the lower level functions package functions. However, these functions are also available if you wish to make use of them independently.

A range of forecasts formats are supported, including quantile-based,
sample-based, binary forecasts. Prior to scoring, users may wish to make use
of `check_forecasts()`

to ensure that the input data is in a supported
format though this will also be run internally by `score()`

. Examples for
each format are also provided (see the documentation for `data`

below or in
`check_forecasts()`

).

Each format has a set of required columns (see below). Additional columns may
be present to indicate a grouping of forecasts. For example, we could have
forecasts made by different models in various locations at different time
points, each for several weeks into the future. It is important, that there
are only columns present which are relevant in order to group forecasts.
A combination of different columns should uniquely define the
*unit of a single forecast*, meaning that a single forecast is defined by the
values in the other columns. Adding additional unrelated columns may alter
results.

To obtain a quick overview of the currently supported evaluation metrics,
have a look at the metrics data included in the package. The column
`metrics$Name`

gives an overview of all available metric names that can be
computed. If interested in an unsupported metric please open a feature request or consider
contributing a pull request.

For additional help and examples, check out the Getting Started Vignette as well as the paper Evaluating Forecasts with scoringutils in R.

## Arguments

- data
A data.frame or data.table with the predictions and observations. For scoring using

`score()`

, the following columns need to be present:`true_value`

- the true observed values`prediction`

- predictions or predictive samples for one true value. (You only don't need to provide a prediction column if you want to score quantile forecasts in a wide range format.)

For scoring integer and continuous forecasts a

`sample`

column is needed:`sample`

- an index to identify the predictive samples in the prediction column generated by one model for one true value. Only necessary for continuous and integer forecasts, not for binary predictions.

For scoring predictions in a quantile-format forecast you should provide a column called

`quantile`

:`quantile`

: quantile to which the prediction corresponds

In addition a

`model`

column is suggested and if not present this will be flagged and added to the input data with all forecasts assigned as an "unspecified model").You can check the format of your data using

`check_forecasts()`

and there are examples for each format (example_quantile, example_continuous, example_integer, and example_binary).- metrics
the metrics you want to have in the output. If

`NULL`

(the default), all available metrics will be computed. For a list of available metrics see`available_metrics()`

, or check the metrics data set.- ...
additional parameters passed down to

`score_quantile()`

(internal function used for scoring forecasts in a quantile-based format).

## Value

A data.table with unsummarised scores. There will be one score per
quantile or sample, which is usually not desired, so you should almost
always run `summarise_scores()`

on the unsummarised scores.

## References

Funk S, Camacho A, Kucharski AJ, Lowe R, Eggo RM, Edmunds WJ (2019) Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15. PLoS Comput Biol 15(2): e1006785. doi:10.1371/journal.pcbi.1006785

## Author

Nikos Bosse nikosbosse@gmail.com

## Examples

```
library(magrittr) # pipe operator
# \dontshow{
data.table::setDTthreads(2) # restricts number of cores used on CRAN
# }
check_forecasts(example_quantile)
#> The following messages were produced when checking inputs:
#> 1. 144 values for `prediction` are NA in the data provided and the corresponding rows were removed. This may indicate a problem if unexpected.
#> Your forecasts seem to be for a target of the following type:
#> $target_type
#> [1] "integer"
#>
#> and in the following format:
#> $prediction_type
#> [1] "quantile"
#>
#> The unit of a single forecast is defined by:
#> $forecast_unit
#> [1] "location" "target_end_date" "target_type" "location_name"
#> [5] "forecast_date" "model" "horizon"
#>
#> Cleaned data, rows with NA values in prediction or true_value removed:
#> $cleaned_data
#> location target_end_date target_type true_value location_name
#> 1: DE 2021-05-08 Cases 106987 Germany
#> 2: DE 2021-05-08 Cases 106987 Germany
#> 3: DE 2021-05-08 Cases 106987 Germany
#> 4: DE 2021-05-08 Cases 106987 Germany
#> 5: DE 2021-05-08 Cases 106987 Germany
#> ---
#> 20397: IT 2021-07-24 Deaths 78 Italy
#> 20398: IT 2021-07-24 Deaths 78 Italy
#> 20399: IT 2021-07-24 Deaths 78 Italy
#> 20400: IT 2021-07-24 Deaths 78 Italy
#> 20401: IT 2021-07-24 Deaths 78 Italy
#> forecast_date quantile prediction model horizon
#> 1: 2021-05-03 0.010 82466 EuroCOVIDhub-ensemble 1
#> 2: 2021-05-03 0.025 86669 EuroCOVIDhub-ensemble 1
#> 3: 2021-05-03 0.050 90285 EuroCOVIDhub-ensemble 1
#> 4: 2021-05-03 0.100 95341 EuroCOVIDhub-ensemble 1
#> 5: 2021-05-03 0.150 99171 EuroCOVIDhub-ensemble 1
#> ---
#> 20397: 2021-07-12 0.850 352 epiforecasts-EpiNow2 2
#> 20398: 2021-07-12 0.900 397 epiforecasts-EpiNow2 2
#> 20399: 2021-07-12 0.950 499 epiforecasts-EpiNow2 2
#> 20400: 2021-07-12 0.975 611 epiforecasts-EpiNow2 2
#> 20401: 2021-07-12 0.990 719 epiforecasts-EpiNow2 2
#>
#> Number of unique values per column per model:
#> $unique_values
#> model location target_end_date target_type true_value
#> 1: EuroCOVIDhub-ensemble 4 12 2 96
#> 2: EuroCOVIDhub-baseline 4 12 2 96
#> 3: epiforecasts-EpiNow2 4 12 2 95
#> 4: UMass-MechBayes 4 12 1 48
#> location_name forecast_date quantile prediction horizon
#> 1: 4 11 23 3969 3
#> 2: 4 11 23 3733 3
#> 3: 4 11 23 3903 3
#> 4: 4 11 23 1058 3
#>
#> $messages
#> [1] "144 values for `prediction` are NA in the data provided and the corresponding rows were removed. This may indicate a problem if unexpected."
#>
score(example_quantile) %>%
add_coverage(by = c("model", "target_type")) %>%
summarise_scores(by = c("model", "target_type"))
#> The following messages were produced when checking inputs:
#> 1. 144 values for `prediction` are NA in the data provided and the corresponding rows were removed. This may indicate a problem if unexpected.
#> model target_type interval_score dispersion underprediction
#> 1: EuroCOVIDhub-baseline Cases 28483.57465 4102.50094 10284.972826
#> 2: EuroCOVIDhub-baseline Deaths 159.40387 91.40625 2.098505
#> 3: EuroCOVIDhub-ensemble Cases 17943.82383 3663.52458 4237.177310
#> 4: EuroCOVIDhub-ensemble Deaths 41.42249 30.18099 4.103261
#> 5: UMass-MechBayes Deaths 52.65195 26.87239 16.800951
#> 6: epiforecasts-EpiNow2 Cases 20831.55662 5664.37795 3260.355639
#> 7: epiforecasts-EpiNow2 Deaths 66.64282 31.85692 15.893314
#> overprediction coverage_deviation bias ae_median coverage_50
#> 1: 14096.100883 -0.11211957 0.09796875 38473.60156 0.3281250
#> 2: 65.899117 0.11614130 0.33906250 233.25781 0.6640625
#> 3: 10043.121943 -0.09785326 -0.05640625 24101.07031 0.3906250
#> 4: 7.138247 0.19528533 0.07265625 53.13281 0.8750000
#> 5: 8.978601 -0.02312500 -0.02234375 78.47656 0.4609375
#> 6: 11906.823030 -0.06660326 -0.07890625 27923.81250 0.4687500
#> 7: 18.892583 -0.04287176 -0.00512605 104.74790 0.4201681
#> coverage_90
#> 1: 0.8203125
#> 2: 1.0000000
#> 3: 0.8046875
#> 4: 1.0000000
#> 5: 0.8750000
#> 6: 0.7890625
#> 7: 0.9075630
# set forecast unit manually (to avoid issues with scoringutils trying to
# determine the forecast unit automatically), check forecasts before scoring
example_quantile %>%
set_forecast_unit(
c("location", "target_end_date", "target_type", "horizon", "model")
) %>%
check_forecasts() %>%
score()
#> The following messages were produced when checking inputs:
#> 1. 144 values for `prediction` are NA in the data provided and the corresponding rows were removed. This may indicate a problem if unexpected.
#> location target_end_date target_type horizon model range
#> 1: DE 2021-05-08 Cases 1 EuroCOVIDhub-baseline 0
#> 2: DE 2021-05-08 Cases 1 EuroCOVIDhub-baseline 10
#> 3: DE 2021-05-08 Cases 1 EuroCOVIDhub-baseline 10
#> 4: DE 2021-05-08 Cases 1 EuroCOVIDhub-baseline 20
#> 5: DE 2021-05-08 Cases 1 EuroCOVIDhub-baseline 20
#> ---
#> 20397: IT 2021-07-24 Deaths 3 epiforecasts-EpiNow2 90
#> 20398: IT 2021-07-24 Deaths 3 epiforecasts-EpiNow2 95
#> 20399: IT 2021-07-24 Deaths 3 epiforecasts-EpiNow2 95
#> 20400: IT 2021-07-24 Deaths 3 epiforecasts-EpiNow2 98
#> 20401: IT 2021-07-24 Deaths 3 epiforecasts-EpiNow2 98
#> interval_score dispersion underprediction overprediction coverage
#> 1: 25620.00 0.00 0 25620 0
#> 2: 25599.50 184.50 0 25415 0
#> 3: 25599.50 184.50 0 25415 0
#> 4: 25481.00 556.00 0 24925 0
#> 5: 25481.00 556.00 0 24925 0
#> ---
#> 20397: 15.85 15.85 0 0 1
#> 20398: 11.75 11.75 0 0 1
#> 20399: 11.75 11.75 0 0 1
#> 20400: 6.52 6.52 0 0 1
#> 20401: 6.52 6.52 0 0 1
#> coverage_deviation bias quantile ae_median quantile_coverage
#> 1: 0.00 0.95 0.500 25620 TRUE
#> 2: -0.10 0.95 0.450 25620 TRUE
#> 3: -0.10 0.95 0.550 25620 TRUE
#> 4: -0.20 0.95 0.400 25620 TRUE
#> 5: -0.20 0.95 0.600 25620 TRUE
#> ---
#> 20397: 0.10 0.50 0.950 26 TRUE
#> 20398: 0.05 0.50 0.025 26 FALSE
#> 20399: 0.05 0.50 0.975 26 TRUE
#> 20400: 0.02 0.50 0.010 26 FALSE
#> 20401: 0.02 0.50 0.990 26 TRUE
# forecast formats with different metrics
if (FALSE) {
score(example_binary)
score(example_quantile)
score(example_integer)
score(example_continuous)
}
# score point forecasts (marked by 'NA' in the quantile column)
score(example_point) %>%
summarise_scores(by = "model", na.rm = TRUE)
#> The following messages were produced when checking inputs:
#> 1. 144 values for `prediction` are NA in the data provided and the corresponding rows were removed. This may indicate a problem if unexpected.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
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#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> Median not available, computing as mean of two innermost quantiles in order to compute bias.
#> model interval_score dispersion underprediction
#> 1: EuroCOVIDhub-baseline 14092.7647 2192.26967 4996.92898
#> 2: EuroCOVIDhub-ensemble 8852.4196 1930.80064 2005.56357
#> 3: epiforecasts-EpiNow2 10659.5125 3084.85850 1604.96135
#> 4: UMass-MechBayes 51.4781 28.09387 15.32315
#> overprediction coverage_deviation bias ae_point se_point
#> 1: 6903.56605 0.002102273 0.21851562 19353.42969 2.883446e+09
#> 2: 4916.05540 0.050752841 0.00812500 12077.10156 1.945118e+09
#> 3: 5969.69268 -0.057861612 -0.04376518 14521.10526 2.680928e+09
#> 4: 8.06108 -0.024886364 -0.02312500 78.47656 1.170976e+04
#> ae_median
#> 1: NaN
#> 2: NaN
#> 3: NaN
#> 4: NaN
```