| O'Hagan, A. (1978). Curve fitting and optimal design for prediction (with discussion) , J. Roy. Statist. Soc. Ser. B , 40: 1--42. |
....9 techniques for regression problems; her work dates back to Kimeldorf and Wahba (1970) although Wahba (1990) provides a useful overview. Essentially splines correspond to Gaussian processes with a particular choice of covariance function 3 . Gaussian process prediction was also suggested by O Hagan (1978), and is widely used in the analysis of computer experiments (e.g Sacks et al., 1989) although in this application it is assumed that the observations are noise free. A connection to neural networks was made by Poggio and Girosi (1990) and Girosi, Jones and Poggio (1995) with their work on ....
O'Hagan, A. (1978). Curve Fitting and Optimal Design for Prediction (with discussion). Journal of the Royal Statistical Society B 40(1), 1--42.
....modifying variable R j is taken to be X j , and for simplicity suppose that the model is a normal linear model with only one term. Thus we have Y = Xfi(X) ffl (5) This is a common model for smoothing or nonparametric regression of Y versus X, and is discussed in various forms by Stone(1977) O Hagan (1978), and Cleveland (1979) vii) Each R j can be scalar or vector valued. For most of the paper we will assume the R j are scalar; extensions to the vector valued case are mentioned in sections 3.4.1 and 7. viii) In all the above cases, there are many ways to model the so far unspecified functions ....
O'Hagan, A. (1978) Curve fitting and optimal design for prediction (with discussion), J. R. Statist. Soc. B 40, 1--42.
....predicting the response. 1 Introduction A nonparametric Bayesian regression model must be based on a prior distribution over the infinite dimensional space of possible regression functions. It has been known for many years that such priors over functions can be defined using Gaussian processes (O Hagan 1978), and essentially the same model has long been used in spatial statistics under the name of kriging . Gaussian processes seem to have been largely ignored as general purpose regression models, however, apart from the special case of smoothing splines (Wahba 1978) and some applications to ....
O'Hagan, A. (1978) "Curve fitting and optimal design for prediction" (with discussion), Journal of the Royal Statistical Society B, vol. 40, pp. 1-42.
....should give a good idea about the value of j( in the vicinity of x: A means of describing our uncertainty about a function j( is needed, and we model j( as a Gaussian process. This is an idea that has been used in several applications. Examples of Gaussian processes in regression include O Hagan (1978) and Neal (1999) Neal (1999) also considers the use of Gaussian processes in classification problems. O Hagan (1991) models a computationally expensive function as a Gaussian process in order to make inferences about its integral. For any set of points x 1 , x n ; we represent our ....
O'Hagan, A. (1978). Curve fitting and optimal design for prediction (with discussion) , J. Roy. Statist. Soc. Ser. B , 40: 1--42.
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, 390--399. O'Hagan, A. (1978) Curve fitting and optimal design for prediction. J. R. Statist. Soc. B
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O'HAGAN, A. (1978). Curve fitting and optimal design for prediction. J. R. Statist. Soc.
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O'Hagan, A. (1978). Curve Fitting and Optimal Design for Prediction. Journal of the Royal Statistical Society, Ser. B, 40, 1--42 (with discussion).
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O'Hagan, A. (1978). "Curve fitting and optimal design for prediction," Journal of the Royal Statistical Society, Ser. B, 40, 1-41 (with discussion).
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