ProbReco (version 0.1.2)

total_score: Total score (and gradient) for reconciled forecast

Description

Function to find an estimate of the total energy score for a linearly reconciled probabilistic forecast. Also finds the gradient by automatic differentiation.

Usage

total_score(data, prob, S, Gvec, scorecode = 1, alpha = 1, matches = FALSE)

Value

Total score and gradient w.r.t (d,G).

grad

The estimate of the gradient.

value

The estimated total score.

Arguments

data

Past data realisations as vectors in a list. Each list element corresponds to a period of training data.

prob

List of functions to simulate from probabilistic forecasts. Each list element corresponds to a period of training data. The output of each function should be a matrix.

S

Matrix encoding linear constraints.

Gvec

Reconciliation parameters \(d\) and \(G\) where \(\tilde{y}=S(d+G\hat{y})\). The first \(m\) elements correspond to translation vector \(d\), while the remaining elements correspond to the matrix \(G\) where the elements are filled in column-major order.

scorecode

Code that indicates score to be used. This is set to 1 for the energy score and 2 for the variogram score. Default is 1 (energy score)

alpha

An additional parameter used for scoring rule. Default is 1 (power used in energy score).

matches

A flag that indicates whether to check for exact matches between samples from reconciled distribution. This causes NaNs in the automatic differentiation. For approaches that rely on bootstrapping set to T. Otherwise set to F (the default) to speed up code.

See Also

Other ProbReco functions: inscoreopt(), scoreopt.control(), scoreopt()

Examples

#Use purr library to setup
library(purrr)
#Define S matrix
S<-matrix(c(1,1,1,0,0,1),3,2, byrow = TRUE)
#Randomly set a value of reconciliation parameters
Gvec<-as.matrix(runif(8))
#Set data (only 10 training observations used for speed)
data<-map(1:10,function(i){S%*%(c(1,1)+rnorm(2))})
#Set list of functions generating from probabilistic forecast
prob<-map(1:10,function(i){f<-function(){matrix(rnorm(3*50),3,50)}})
#Compute total score
out<-total_score(data,prob,S,Gvec)