Abstract
The target of this paper is to demonstrate the benefits of using tolerance regions statistics in risk analysis. In particular, adopting the expected beta content tolerance regions as an alternative approach for choosing the optimal order of a response polynomial it is possible to improve results in reference class forecasting methodology. Reference class forecasting tries to predict the result of a planned action based on actual outcomes in a reference class of similar actions to that being forecast. Scientists/analysts do not usually work with a best fitting polynomial according to a prediction criterion. The present paper proposes an algorithm, which selects the best response polynomial, as far as a future prediction is concerned for reference class forecasting. The computational approach adopted is discussed with the help of an example of a relevant application.
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Acknowledgments
We would like to thank the referees for the improvement of the English as well for their valuable comments which help us to improve the paper. V. Zarikas acknowledges the support of research funding from ATEI of Central Greece.
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Appendix
(* in this list we set data for matrix X. Here the user of the code has to insert data either for Normalised Capacity, Capacity, Distance to Shore, Water depth or European Steel price index *)
(* here the function tst(n) gives the t student distribution probability density
function for the relevant tolerance region *)
(* here the code normalises data concerning matrix X in the interval [-1,1]*)
(* the coefficients of the six polynomials which will be tested with both ctiteria are structured below *)
(* the variable structure of the six polynomials which will be tested with both
ctiteria are structured below *)
(* This expression should be maximised *)
(* the function below finds the value of t inside the region [-1,1] that maximises EXPR *)
(* LP is the prediction criterion of the proposed method. It is the length of the
tolerance region and it is evaluated for the t found before that maximises EXPR *)
(*This mathematica function is the one that the user of the programme only needs to use. He has to set as argument of this function the largest order of the polynomial to be tested. i.e. 6. This function evaluates and returns for each order of the polynomial the prediction criterion LP and the conventional criterion RMS. It also returns for each order of the polynomial the plot of the data together with the best fitting polynomial for prediction. Finally it plots also the Expression that is maximized for a certain t *)
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Zarikas, V., Kitsos, C.P. (2015). Risk Analysis with Reference Class Forecasting Adopting Tolerance Regions. In: Kitsos, C., Oliveira, T., Rigas, A., Gulati, S. (eds) Theory and Practice of Risk Assessment. Springer Proceedings in Mathematics & Statistics, vol 136. Springer, Cham. https://doi.org/10.1007/978-3-319-18029-8_18
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