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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bent, F.: Design by Deception: The Politics of Megaproject Approval. Harvard Design Magazine. no. 22, Spring/Summer, pp. 50–59 (2005)
Bent, F., Bruzelius, N., Rothengatter, W.: Megaprojects and Risk: An Anatomy of Ambition, Cambridge University Press, Cambridge (2003)
Bent, F., Cowi.: Procedures for Dealing with Optimism Bias in Transport Planning: Guidance Document, London, UK Department for Transport (2004)
Bent, F., Skamris Holm, M.K., Buhl, S.L.: Underestimating costs in public works projects, error or lie? J. Am. Plan. Assoc. 68(3), Summer, pp. 279–295 (2002)
Bent, F., Skamris Holm, M.K., Buhl, S.L.: What causes cost overrun in transport infrastructure projects? Transp. Rev. 24(1), 3–18 (2004)
Bent, F., Skamris Holm, M.K., Buhl, S.L.: How (In)accurate are demand forecasts in public works projects? The case of transportation. J. Am. Plan. Assoc. 71(2), 131–146 (2005)
Bent, F., Lovallo, D.: Delusion and Deception: Two Models for Explaining Executive Disaster (in progress)
Bent, F.: Curbing optimism bias and strategic misrepresentation in planning, reference class forecasting in practice. Eur. Plan. Stud. 16, 3–21 (2008)
Gilovich, T., Griffin, D., Kahneman, D. (eds.) Heuristics and Biases: The Psychology of Intuitive Judgment. 19/32 Cambridge University Press (2002)
Gordon, P., Wilson, R.: The determinants of light-rail transit demand: an international cross-sectional comparison. Transp. Res. A 18A(2), 135–140 (1984)
Kahneman, D.: New challenges to the rationality assumption. J. Inst. Theor. Econ. 150, 18–36 (1994)
Kahneman, D., Lovallo, D.: Timid choices and bold forecasts, a cognitive perspective on risk taking. Manag. Sci. 39, 17–31 (1993)
Kahneman, D., Tversky, A.: Prospect theory, an analysis of decisions under risk. Econometrica 47, 313–327 (1979)
Kahneman, D., Tversky, A.: Intuitive prediction, biases and corrective procedures. In: Makridakis, S., Wheelwright, S.C. (ed.), Studies in the Management Sciences, Forecasting, vol. 12. Amsterdam, North Holland (1979)
Lovallo, D., Kahneman, D.: Delusions of success. how optimism undermines executives’ decisions. Harv. Bus. Rev. pp. 56–63 (2003)
Ellerton, R.R.W., Kitsos, C.P., Rinco, S.: Choosing the optimal order of a response polynomical-structural approach with minimax criterion. Commun. Stat. Theory Methodol. 15, 129–136 (1986)
Kitsos, C.P.: An algorithm for construct the best predictive model. In: Faulbaum, F. (ed.) Softstat 93, Advances in Statistical Software, pp. 535–539, Stuttgart, New York (1994)
Muller, C.H., Kitsos C.P.: Optimal design criteria based on tolerance regions. In: Bucchianico, A., Lauter, H., Wynn. H.P. (Eds.) mODa 7-Advances in Model-Oriented Design and Analysis, pp: 107–115, Physica-Verlag, Heidelberg (2004)
Maddala, G.: Introduction to Econometrics, 2nd edn. p. 663, Macmillan, New York (1992)
Stigler, S.M.: Gauss and the invention of least squares. Ann. Stat. 9(3), 465–474 (1981)
Anderson, T.W.: The choice of the degree of a polynomial regression as a multiple decision problem. Ann. Math. Stat. 33, 255–265 (1962)
Martins, J.P., Mendonca, S., Pestana, D.: Optimal and quasi-optimal designs. Revstat 6, 279–307 (2008). Available via http://www.ine.pt/revstat/pdf/rs080304.pdf
Hocking, R.R.: The analysis of selection of variables in linear regression. Biometrics 32, 1–49 (1976)
Wilks, S.S.: Mathematical Statistics. Wiley, New York (1962)
Guttman, I.: Construction of -content tolerance regions at confidence level for large samples for k-Variate normal distribution. Ann. Math. Stat. 41, 376–400 (1970)
Boente, G., Farall, A.: Robust multivariate tolerance regions, influence function and Monte Carlo study. Technometrics 50, 487–500 (2008)
Kendall, M.G., Stuart A.: The Advanced Theory of Statistics, vols. II, III. C. Griffin Ltd., London (1976)
Zarikas, V., Gikas, V., Kitsos, C.P.: Evaluation of the optimal design “Cosinor model” for enhancing the potential of robotic theodolite kinematic observation. Measurement 43(10), 1416–1424 (2010)
Kitsos, C.P., Zarikas, V.: On the best predictive general linear model for data analysis, a tolerance region algorithm for prediction. J. Appl. Sci. 13(4), 513–524 (2013)
Kaiser, M.J., Snyder, B.: Offshore wind capital cost estimation in the US outer continental shelf, a reference class approach. Marian. Policy 36, 1112–1122 (2012)
Valente, V., Oliveira T. A.: Hierarchical linear models: review and applications. In: Proceedings of the 9th International Conference of Numerical Analysis and Applied Mathematics, September 19–25, Halkidiki, Greece, pp. 1549–1552 (2011)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
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 *)
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-18029-8_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18028-1
Online ISBN: 978-3-319-18029-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)