Forecasting in CPT Simon J Mason simoniri columbia
Forecasting in CPT Simon J. Mason simon@iri. columbia. edu International Research Institute for Climate and Society The Earth Institute of Columbia University CIMH Workshop on the Climate Predictability Tool Bridgetown, Barbados, July / August 2013
Prediction If we construct a regression model, we can get a best guess estimate of Y given new X:
Prediction … and can calculate the expected error: … assuming the model is correct!
Prediction There are 3 ways in which the model may be incorrect: 1. Sampling errors in the intercept
Prediction There are 3 ways in which the model may be incorrect: 2. Sampling errors in the slope
Prediction There are 3 ways in which the model may be incorrect: 3. Errors in the predictors
Prediction error variance • CPT takes the cross-validated error variance, and the standard errors of the regression constant and coefficient(s) to calculate the prediction error variance. • We then have the best guess value, plus or minus one standard error in prediction, giving a prediction interval in which we can state there is about a 68% probability.
Prediction error variance Using the cross-validated error variance, and the standard errors of the regression parameters: … assuming the model may or may not be correct!
Prediction error variance Given one standard prediction error we know there is a 16% probability of getting more than the upper limit:
Prediction error variance But we could use two standard errors …:
Prediction error variance Or we could use just the right numbers of standard errors to give the probabilities of exceeding the terciles:
Prediction error variance If the best guess value is right on the upper tercile, the above-normal category will have 50% probability.
Low probability of normal This problem often occurs if there are “outliers” in the data – the assumption of normally distributed data is invalid.
Low probability of normal The problem can often be solved by switching on Options ~ Data ~ Transform Y Data.
Exercises • Using the gridded Caribbean data, construct a prediction model using CCA and a predictor of your choice. • Produce a probabilistic forecast map using predictors for 2013, and then select a location of your choice. • Now try to tailor this forecast to answer questions such as: – Will it be exceptionally wet? – Will there be less than 100 mm? – Will there be less than 80% of average? – Will it be drier than last year; will it be wetter than 2010?
- Slides: 15