Predictive Model Assessment with a Probability Integral Transform Histogram

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Description

The function allows a probabilistic calibration check with a Probability Integral Transform (PIT) histogram.

Usage

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## S3 method for class 'tsglm'
pit(object, bins=10, ...)
## Default S3 method:
pit(response, pred, distr=c("poisson", "nbinom"), distrcoefs, bins=10, ...)

Arguments

object

an object of class "tsglm".

bins

number of bins in the histogram. Default value is 10.

response

integer vector. Vector of observed values.

pred

numeric vector. Vector of predicted values.

distr

character giving the conditional distribution. Currently implemented are the Poisson ("poisson")and the Negative Binomial ("nbinom") distribution.

distrcoefs

numeric vector of additional coefficients specifying the conditional distribution. For distr="poisson" no additional parameters need to be provided. For distr="nbinom" the additional parameter size needs to be specified (e.g. by distrcoefs=2), see tsglm for details.

...

additional arguments passed to plot.

Details

A PIT histogram is a tool for evaluating the statistical consistency between the probabilistic forecast and the observation. The predictive distributions of the observations are compared with the actual observations. If the predictive distribution is ideal the result should be a flat PIT histogram with no bin having an extraordinary high or low level. For more information about PIT histograms see the references listed below.

Author(s)

Philipp Probst and Tobias Liboschik

References

Christou, V. and Fokianos, K. (2013) On count time series prediction. Journal of Statistical Computation and Simulation (published online), http://dx.doi.org/10.1080/00949655.2013.823612.

Czado, C., Gneiting, T. and Held, L. (2009) Predictive model assessment for count data. Biometrics 65, 1254–1261, http://dx.doi.org/10.1111/j.1541-0420.2009.01191.x.

Gneiting, T., Balabdaoui, F. and Raftery, A.E. (2007) Probabilistic forecasts, calibration and sharpness. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 69, 243–268, http://dx.doi.org/10.1111/j.1467-9868.2007.00587.x.

See Also

tsglm for fitting a GLM for time series of counts.

marcal and scoring for other predictive model assessment tools.

Examples

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###Campylobacter infections in Canada (see help("campy"))
campyfit <- tsglm(ts=campy, model=list(past_obs=1, past_mean=c(7,13)))
pit(campyfit)

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