# pit: Probability Integral Transform for ensemble forcasting models In ensembleBMA: Probabilistic Forecasting using Ensembles and Bayesian Model Averaging

 pit R Documentation

## Probability Integral Transform for ensemble forcasting models

### Description

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

### Usage

```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.

### 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.

### Value

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

### 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.

`pitHist`, `verifRankHist`, `ensembleBMA`, `fitBMA`, `quantileForecast`

### 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)

```

ensembleBMA documentation built on Sept. 2, 2022, 9:05 a.m.