Bayesian Interpolation

Neural Computation - Tập 4 Số 3 - Trang 415-447 - 1992
David Mackay1
1Computation and Neural Systems, California Institute of Technology 139-74, Pasadena, CA 91125 USA

Tóm tắt

Although Bayesian analysis has been in use since Laplace, the Bayesian method of model-comparison has only recently been developed in depth. In this paper, the Bayesian approach to regularization and model-comparison is demonstrated by studying the inference problem of interpolating noisy data. The concepts and methods described are quite general and can be applied to many other data modeling problems. Regularizing constants are set by examining their posterior probability distribution. Alternative regularizers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them. “Occam's razor” is automatically embodied by this process. The way in which Bayes infers the values of regularizing constants and noise levels has an elegant interpretation in terms of the effective number of parameters determined by the data set. This framework is due to Gull and Skilling.

Từ khóa


Tài liệu tham khảo

10.1007/BF02506337

Bretthorst G. L., 1990, J. Mag. Reson., 88, 533

Charter M. K., 1991, Laramie, 2990, W. T. Grandy and L. H. Schick, eds., 245

10.1119/1.1990764

10.1017/S0334270000005221

Gull S. F., 1989, Cambridge, 2988, J. Skilling, ed., 511

10.1162/neco.1992.4.3.448

10.1016/0005-1098(78)90005-5

10.1214/aos/1176344136

10.1214/ss/1177013620

10.2307/1402932

Walker A. M., 1967, J. R. Stat. SOC. B, 31, 80

10.1093/comjnl/11.2.185

Wallace C. S., 1987, J. R. Statist. SOC. B, 49, 240

Thông tin
Thông tin xuất bản

Neural Computation

Tập 4 Số 3

415-447

Thông tin tác giả