Automatic Bayesian curve fitting

被引：277

作者：

Denison, DGT ^{[1
]}

Mallick, BK ^{[1
]}

Smith, AFM ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2BZ, England

来源：

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY | 1998年 / 60卷

关键词：

additive models; back-fitting algorithm; least squares regression; piecewise polynomials; reversible jump Markov chain Monte Carlo method; splines;

D O I：

10.1111/1467-9868.00128

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A method of estimating a variety of curves by a sequence of piecewise polynomials is proposed, motivated by a Bayesian model and an appropriate summary of the resulting posterior distribution. A joint distribution is set up over both the number and the position of the knots defining the piecewise polynomials. Throughout we use reversible jump Markov chain Monte Carlo methods to compute the posteriors. The methodology has been successful in giving good estimates for 'smooth' functions (i.e. continuous and differentiable) as well as functions which are not differentiable, and perhaps not even continuous, at a finite number of points. The methodology is extended to deal with generalized additive models.

引用

页码：333 / 350

页数：18

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