# ensembleBMA {ensembleBMA}

### Description

Fits a BMA mixture model to ensemble forecasts. Allows specification of a model, training rule, and forecasting dates.

### Usage

ensembleBMA( ensembleData, trainingDays, dates = NULL, control = NULL, model = NULL, exchangeable = NULL, minCRPS = NULL)

### Arguments

- ensembleData
- An
`ensembleData`

object including ensemble forecasts with the corresponding verifying observations and their dates. Missing values (indicated by`NA`

) are allowed. - dates
- The dates for which BMA forecasting models are desired. By default, this will be all dates in
`ensembleData`

for which modeling is allowed given training rule. - trainingDays
- An integer giving the number of time steps (e.g. days) in the training period. There is no default.
- control
- A list of control values for the fitting functions. The default is
`controlBMAnormal()`

for normal models and`controlBMAgamma0()`

for gamma models with a point mass at 0. - model
- A character string describing the BMA model to be fit. Current choices are
`"normal"`

, typically used for temperature or pressure data, and`"gamma0"`

, typically used for precipitation data. - exchangeable
- A numeric or character vector or factor indicating groups of ensemble members that are exchangeable (indistinguishable). The model fit will have equal weights and parameters within each group. The default determines exchangeability from
`ensembleData`

. - minCRPS
- A logical variable indicating whether or not to add a postprocessing step after a normal BMA fit to choose the standard deviation so as to minimize the CRPS for the training data. This argument is used only for normal models, and the default is to not do the CRPS minimization for those models because it may require consderably more computation time, expecially when there are many ensemble members.

### Details

If dates are specified in `dates`

that cannot be forecast with the training rule, the corresponding BMA model parameter outputs will be missing (`NA`

) but not `NULL`

.

The training rule uses the number of days corresponding to its `length`

regardless of whether or not the dates are consecutive.

The following methods are available for the output of `ensembleBMA`

: `cdf`

, `quantileForecast`

, `modelParameters`

, `brierScore`

, `crps`

, `CRPS`

and `MAE`

.

### Values

A list with the following output components:

- dateTable
- The table of observations corresponding to the dates in
`x`

in chronological order. - trainingDays
- The number of days in the training period as specified in input.
- ...
- One or more components corresponding to fitted coefficients for the model.
- weights
- The fitted BMA weights for the mixture components for each ensemble member at each date.
- power
- A scalar value giving the power (if any) by which the data was transformed for modeling. The untransformed forecast is used to fit the variance model. This is input as part of
`control`

, and applies only to certain models.

### 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*.

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 Ensembles 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*.

### See Also

`ensembleData`

, `ensembleBMAnormal`

, `ensembleBMAgamma0`

, `ensembleBMAgamma`

, `cdf`

, `quantileForecast`

, `modelParameters`

, `brierScore`

, `crps`

, `MAE`

, `controlBMAnormal`

, `controlBMAgamma0`

, `controlBMAgamma`

### 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 checl tempTestFit <- ensembleBMA( tempTestData, trainingDays = 30, model = "normal") ## equivalent to ## tempTestFit <- ensembleBMAnormal( tempTestData, trainingDays = 30) ## End(Not run) # for quick run only; use more training days for forecasting tempTestFit <- ensembleBMA( tempTestData[1:20,], trainingDays = 8, model = "normal")

Documentation reproduced from package ensembleBMA, version 5.1.2. License: GPL (>= 2)