bias_sample: Determines bias of forecasts

In scoringutils: Utilities for Scoring and Assessing Predictions

Determines bias of forecasts

Description

Determines bias from predictive Monte-Carlo samples. The function automatically recognises, whether forecasts are continuous or integer valued and adapts the Bias function accordingly.

Usage

bias_sample(true_values, predictions)

Arguments

true_values	A vector with the true observed values of size n
predictions	nxN matrix of predictive samples, n (number of rows) being the number of data points and N (number of columns) the number of Monte Carlo samples. Alternatively, predictions can just be a vector of size n.

Details

For continuous forecasts, Bias is measured as

B_t (P_t, x_t) = 1 - 2 * (P_t (x_t))

where P_t is the empirical cumulative distribution function of the prediction for the true value x_t. Computationally, P_t (x_t) is just calculated as the fraction of predictive samples for x_t that are smaller than x_t.

For integer valued forecasts, Bias is measured as

B_t (P_t, x_t) = 1 - (P_t (x_t) + P_t (x_t + 1))

to adjust for the integer nature of the forecasts.

In both cases, Bias can assume values between -1 and 1 and is 0 ideally.

Value

vector of length n with the biases of the predictive samples with respect to the true values.

Author(s)

Nikos Bosse [e-mail]

References

The integer valued Bias function is discussed in Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15 Funk S, Camacho A, Kucharski AJ, Lowe R, Eggo RM, et al. (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 Computational Biology 15(2): e1006785. doi: 10.1371/journal.pcbi.1006785

Examples

## integer valued forecasts
true_values <- rpois(30, lambda = 1:30)
predictions <- replicate(200, rpois(n = 30, lambda = 1:30))
bias_sample(true_values, predictions)

## continuous forecasts
true_values <- rnorm(30, mean = 1:30)
predictions <- replicate(200, rnorm(30, mean = 1:30))
bias_sample(true_values, predictions)

scoringutils documentation built on Feb. 16, 2023, 7:30 p.m.