pit function

Probability Integral Transform for ensemble forcasting models

Computes the probabilty integral transform (PIT) of a BMA ensemble forecasting model at observation locations.

pit( fit, ensembleData, dates = NULL, randomizeATzero=FALSE, ...)

Arguments

• fit: A model fit to ensemble forecasting data.
• ensembleData: An ensembleData object that includes ensemble forecasts, verification observations and possibly dates. Missing values (indicated by NA) are allowed. \ This need not be the data used for the model fit, although it must include the same ensemble members.
• dates: The dates for which the CDF will be computed. These dates must be consistent with fit and ensembleData. The default is to use all of the dates in fit. The dates are ignored if fit originates from fitBMA, which also ignores date information.
• randomizeATzero: For the gamma0 model for precipitation, observations should be randomized at 0 for assessing the calibration. Has no effect for the other models.
• ...: Included for generic function compatibility.

Returns

The value of the BMA cumulative distribution function CDF corresponding to the fit at the observed values in ensembleData.

Details

Most often used for computing PIT histograms to assess calibration of forecasts, in which case the observations in ensembleData would be those used in modeling fit.

Instances in ensembleData without verifying observations are ignored.

Note the model may have been applied to a power transformation of the data, but that information is included in the input fit, and the output is transformed appropriately.

The PIT is a continuous analog of the verification rank.

See Also

pitHist, verifRankHist, ensembleBMA, fitBMA, quantileForecast

References

A. E. Raftery, T. Gneiting, F. Balabdaoui and M. Polakowski, Using Bayesian model averaging to calibrate forecast ensembles, Monthly Weather Review 133:1155--1174, 2005.

T. Gneiting, F. Balabdaoui and A. Raftery, Probabilistic forecasts, calibration and sharpness. Journal of the Royal Statistical Society, Series B 69:243--268, 2007.

J. M. Sloughter, A. E. Raftery, T Gneiting and C. Fraley, Probabilistic quantitative precipitation forecasting using Bayesian model averaging, Monthly Weather Review 135:3209--3220, 2007.

C. Fraley, A. E. Raftery, T. Gneiting and J. M. Sloughter, ensembleBMA: An R Package for Probabilistic Forecasting using Ensemble and Bayesian Model Averaging, Technical Report No. 516R, Department of Statistics, University of Washington, 2007 (revised 2010).

C. Fraley, A. E. Raftery, T. Gneiting, Calibrating Multi-Model Forecast Ensembles with Exchangeable and Missing Members using Bayesian Model Averaging, Monthly Weather Review 138:190--202, 2010.

J. M. Sloughter, T. Gneiting and A. E. Raftery, Probabilistic wind speed forecasting using ensembles and Bayesian model averaging, Journal of the American Statistical Association, 105:25--35, 2010.

Examples

data(ensBMAtest)

  ensMemNames <- c("gfs","cmcg","eta","gasp","jma","ngps","tcwb","ukmo")

  obs <- paste("T2","obs", sep = ".")
  ens <- paste("T2", ensMemNames, sep = ".")

  tempTestData <- ensembleData( forecasts = ensBMAtest[,ens],
                                dates = ensBMAtest[,"vdate"],
                                observations = ensBMAtest[,obs],
                                station = ensBMAtest[,"station"],
                                forecastHour = 48,
                                initializationTime = "00")

## Not run:
 # R check
  tempTestFit <- ensembleBMAnormal( tempTestData, trainingDays = 30)
## End(Not run)

  tempTestForc <- quantileForecast( tempTestFit, tempTestData)
  range(tempTestForc)

  tempTestPIT <- pit( tempTestFit, tempTestData)