Computes the probability integral transform of the obervations relative to the BMA forecast, and plots its histogram.
A model fit to ensemble forecasting data.
The dates for which the CDF will be computed.
These dates must be consistent with
PIT histograms are used to assess calibration of
forecasts, in which case the observations in
be those used in modeling
ensembleData without verifying observations
In the case of the
gamma0 model for precipitation,
observations of zero precipitation are randomized within their
probabilistics range to avoid a false
impression of bias.
Note the model may have been applied to a power transformation of the data, but that information is included in the input
the output is transformed appropriately.
The PIT is a continuous analog of the verification rank.
The value of the BMA cumulative distribution function CDF
corresponding to the fit at the observed values in
The corresponding histogram is also plotted.
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,
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.
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data(srft) labels <- c("CMCG","ETA","GASP","GFS","JMA","NGPS","TCWB","UKMO") srftData <- ensembleData( forecasts = srft[ ,labels], dates = srft$date, observations = srft$obs, latitude = srft$lat, longitude = srft$lon, forecastHour = 48, initializationTime = "00") ## Not run: # this takes time # the PIT should be evaluated over relatively long periods srftFITall <- ensembleBMA( srftData, model = "normal", trainingDays = 25) srftPIT <- pitHist( srftFITall, srftData) ## End(Not run)
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