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Bayesian Basis Expansion Models

In: Bayesian Claims Reserving Methods in Non-life Insurance with Stan

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  • Guangyuan Gao

    (Renmin University of China, School of Statistics)

Abstract

In this chapter, Bayesian basis expansion models are used to fit various development patterns and accommodate the tail factor. A parametric model is typically characterized by a parametric mean function and an error distribution. The shape of the mean function is restricted by the space of parameters. Non-parametric models such as basis expansion models are able to automatically adjust to fit any shape of data. In Sect. 5.1, the aspects of splines are reviewed, including spline basis functions, smoothing splines, low rank smoothing splines and Bayesian shrinkage splines. In Sect. 5.2, we study two simulated examples. The first simulated example is based on a trigonometric mean function, while the second simulated example is based on the claims payments process. Both examples illustrate the usefulness of natural cubic spline basis in the extrapolation beyond the range of data. Section 5.3 is the application of above methodology to the doctor benefit in WorkSafe Victoria. The basis expansion model used to fit the PPCI triangle induces a tail development.

Suggested Citation

  • Guangyuan Gao, 2018. "Bayesian Basis Expansion Models," Springer Books, in: Bayesian Claims Reserving Methods in Non-life Insurance with Stan, chapter 0, pages 117-152, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-3609-6_5
    DOI: 10.1007/978-981-13-3609-6_5
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