Sains Ma1aysiana 25(4) 1996: 11-18                                                     Pengajian Kuantitatif/

Quantitative Studies

On the Choice of the Prior Distribution in the

Bayesian Analysis for the Evaluation of

Kamarulzaman bin Ibrahim

Jabatan Statistik

Fakulti Sains Matematik

Universiti Kebangsaan Malaysia

43600 UKM Bangi Selangor D.E. Malaysia

ABSTRACT

An integral art of the Bayesian approach which is not present in the classical approach is the prior distribution. Different researchers may have different level of prior knowledge regarding the parameter of interest before seeing the data. Sometimes different prior distributions can result in different decisions, as such investigations have to be careful in making the choice of the prior distribution. In this paper, we compare results from the Bayesian analyses based on three possible choices of the prior distributions, which are uniform prior, lognormal prior and an improper prior, in the evaluation of the effectiveness of mini-roundabouts. Data from five before and after studies into the effect of mini-roundabouts when replacing priority junctions are used. The effects of the different prior distributions are distinguishable from the analysis of an anamolous 'desk-drawer' study. The uniform and improper prior pull the estimated treatment effect away from one more than the lognormal prior. The results based on lognormal prior depict a less worst scenario of the ineffectiveness of mini-roundabouts and this may correspond to the deficiency in engineering design at only a few sites. Consequently, it is more appropriate to use the lognormal prior in the analysis of mini-roundabouts as a road safety measure.

ABSTRAK

Satu ciri yang penting dalam kaedah Bayesian yang tidak ada dalam kaedah klasik ialah taburan prior. Sebelum melihat data, mungkin setiap penyelidik mempunyai tahap pengetahuan prior yang berbeza berkenaan sesuatu parameter yang ingin dikaji. Kadang-kala taburan prior yang berlainan boleh menghasilkan keputusan yang berlainan. Oleh itu, pengkaji perlu berhati-hati dalam memilih taburan prior. Dalam kertas-kerja ini, kami bandingkan keputusan dari analisis Bayesian berdasarkan tiga pilihan taburan prior yang menasabah iaitu prior seragam, prior lognormal dan prior tak wajar untuk menilai keberkesanan bulatan mini. Data dari kajian-kajian sebelum dan selepas terhadap kesan mengantikan persimpangan dengan bulatan mini digunakan. Kesan taburan prior yang berlainan dapat dibezakan berasaskan keputusan analisis terhadap satu kajian 'laci-meja' yang ganjil. Prior seragam dan prior fak wajar felah menyebabkan anggaran nilai kesan rawatan melebihi satu lebih dari prior lognormal. Keputusan berasaskan prior lognormal ini menunjukkan senario yang kurang teruk tentang kurang berkesannya bulatan mini dan mungkin ini boleh dikaitkan dengan rekabentuk kejuruteraan yang tidak baik di beberapa tempat sahaja. Dengan itu, prior lognormal adalah lebih sesuai digunakan untuk menilai bulatan mini sebagai langkah keselamatan jalanraya.

RUJUKAN/REFERENCES

Engineer and Surveyor. 1984. Safety of Pedestrians and Pedal Cyclists at small and mini-roundabouts. Avon County Council.

Green, H. 1977. Accidents at off-side priority roundabouts with mini or small islands. TRRL Laboratory Report 774, Transport and Road Research Laboratory, Crowthorne.

Hanson, S.J. and Wilson, C.D.L. 1979. The safety of small roundabouts in Newcastle upon Tyne. Internal report by Transport Operations Research Group, University of Newcastle upon Tyne in collaboration with the Tyne and Wear County Council (unpublished).

Ibrahim, K. and Metcalfe, A.V. 1993. Bayesian overview for evaluation of mini­ roundabouts as a road safety measure. The Statistician 42(4): 525-540.

Lalani, N. 1975. Introduction of mini, small and large roundabouts at major/minor

priority junctions - impact on accidents. Greater London Safety Unit. Road Accidents in Great Britain. 1970-1979. Department of the Environment Scottish Development Department and Welsh Office, London.

Wright, C.C., Abbess, C.R. & Jarrett, D.F. 1988. Estimating the regression-to-mean effect associated with road accident blackspot treatment: towards a more realistic approach, Accident Analysis and Prevention, 20(3): 199-214.

 content