CRPS               package:ensembleBMA               R Documentation

_C_a_l_c_u_l_a_t_e _t_h_e _C_o_n_t_i_n_u_o_u_s _R_a_n_k_e_d _P_r_o_b_a_b_i_l_i_t_y _S_c_o_r_e _f_o_r _a_n _e_n_s_e_m_b_l_e _f_o_r_e_c_a_s_t.

_D_e_s_c_r_i_p_t_i_o_n:

     Calculate the Continuous Ranked Probability Score for an ensemble
     forecast.

_U_s_a_g_e:

     CRPS(a,b,sigma,w,X,Y)

_A_r_g_u_m_e_n_t_s:

       a: vector of K intercepts in the regression bias correction.  If
          no regression is desired, 'a' should be a vector of zeros. 

       b: vector of K slopes in the regression bias correction.  If no
          regression is desired, 'b' should be a vector of ones. 

   sigma: vector of K standard deviations from the BMA fit (a,b,sigma
          are all outputs of EM.normals or EM.for.date).  If there is
          only one variance parameter (constant variance), then this
          can be a single number. 

       w: vector of K weights from the BMA fit 

       X: matrix of ensemble forecasts. This is an n by K matrix, where
          there are n observations to be used in the fitting, and K
          ensemble members 

       Y: n-vector of observations. 

_D_e_t_a_i_l_s:

     This function calculates the Continuous Ranked Probability Score
     (CRPS) for an ensemble BMA forecast with the specified forecasts,
     observations, and BMA parameters

_V_a_l_u_e:

     value of the CRPS

_A_u_t_h_o_r(_s):

     Adrian E. Raftery, J. McLean Sloughter, Michael Polakowski

_R_e_f_e_r_e_n_c_e_s:

     Raftery, A. E., T. Gneiting, F. Balabdaoui, & M. Polakowski,
     "Using Bayesian Model Averaging to calibrate forecast ensembles."
     Monthly Weather Review, to appear, 2005. earlier version available
     at:
     http://www.stat.washington.edu/www/research/reports/2003/tr440.pdf

     Gneiting, T, and A. E. Raftery, "Strictly proper scoring rules,
     prediction, and estimation." University of Washington Technical
     Report 463. available at:
     http://www.stat.washington.edu/www/research/reports/2004/tr463.pdf

     Gneiting, T., A. Westveld, A. E. Raftery, and T. Goldman, "
     Calibrated Probabilistic Forecasting Using Ensemble Model Output
     Statistics and Minimum CRPS Estimation." Monthly Weather Review,
     to appear, 2005. earlier version available at:
     http://www.stat.washington.edu/www/research/reports/2004/tr449.pdf

_S_e_e _A_l_s_o:

     ' EM.normals ', ' EM.for.date ', ' bmaquant ', ' bmacdf '

_E_x_a_m_p_l_e_s:

     #read in the sea-level pressure data and calculate BMA estimates
     #for forecasting on the 35th day in the data set
     data(slp)
     unique.dates <- unique(slp$date)
     date.list <- NULL

     for(i in 1:length(unique.dates))
     {
       date.list[slp$date==unique.dates[i]] <- i
     }

     X <- cbind(slp$F1,slp$F2,slp$F3,slp$F4,slp$F5)
     Y <- slp$Y

     EMresult <- EM.for.date(date = 35,date.list = date.list,X = X,Y = Y )

     #now calculate the CRPS over the training period (observations 43 through 161)
     CRPS(a = EMresult$a,b = EMresult$b, sigma = EMresult$sigma, w =  EMresult$w, X=X[43:161,], Y=Y[43:161])

     #calculate the BMA estimates without CRPS minimization, and compare the new CRPS score
     EMresult.without <- EM.for.date(date = 35,date.list = date.list,X = X,Y = Y, min.CRPS=FALSE )
     CRPS(a = EMresult.without$a,b = EMresult.without$b, sigma = EMresult.without$sigma, w =  EMresult.without$w, X=X[43:161,], Y=Y[43:161])

