S. Sibisi (1990). Bayesian interpolation, in [4], 349--355. Home/Search Document Not in Database Summary Related Articles Check |
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Bayesian Interpolation - MacKay (1991) (227 citations) (Correct)
....analysis been developed and applied to real world problems. This paper will review Bayesian model comparison, regularisation, and noise estimation, by studying the problem of interpolating noisy data. The Bayesian framework I will describe for these tasks is due to Gull and Skilling [5, 6, 8, 17, 18], who have used Bayesian methods to achieve the state of the art in image reconstruction. The same approach to regularisation has also been developed in part by Szeliski [22] Bayesian model comparison is also discussed by Bretthorst [2] who has used Bayesian methods to push back the limits of ....
....approximations in evaluating the length of the ideal shortest message. I can see no advantage in MDL, and recommend that the evidence should be approximated directly. 3 The noisy interpolation problem Bayesian interpolation through noise free data has been studied by Skilling and Sibisi [17]. In this paper I study the case where the dependent variables are assumed to be noisy. I am not however examining the case where the independent variables are noisy too. This different and more difficult problem has been studied for the case of straight line fitting by Gull [7] Let us assume ....
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S. Sibisi (1990). Bayesian interpolation, in [4], 349--355.
Figure 7: - The Evidence For (Correct)
....penalise this free parameter an Occam factor is included, p 21rP (r) where 1r = posterior uncertainty in r, and P (r) is the prior on r, which is usually subjective to a small degree. This radial basis function model is identical to the intrinsic correlation model of Gull, Skilling and Sibisi [6, 17]. Figure 7b shows the evidence as a function of the number of basis functions, k. Note that for these models there is not an Occam penalty for large numbers of parameters. The reason for this is that these extra parameters do not make the model any more powerful (for fixed ff and r) The ....
S. Sibisi (1990). Bayesian interpolation, in [4], 349-- 355.
Bayesian Interpolation - MacKay (1992) (227 citations) (Correct)
....not addressed in this paper. Once the probabilities described above have been inferred, optimal actions can be chosen using standard decision theory with a suitable utility function. 3 The noisy interpolation problem Bayesian interpolation through noise free data has been studied by Skilling and Sibisi (1991). In this paper I study the problem of interpolating through data where the dependent variables are assumed to be noisy (a task also known as regression, curve fitting, signal estimation, or, in the neural networks community, learning ) I am not examining the case where the independent ....
....assign a value to P (ff; fi) I assume that it is a flat prior (flat over log ff and log fi, since ff and fi are scale parameters) which cancels out when we compare alternative interpolation models. 6 Demonstration These demonstrations will use two one dimensional data sets, in imitation of (Sibisi, 1991). The first data set, X, has discontinuities in derivative (figure 4) and the second is a smoother data set, Y (figure 8) In all the demonstrations, fi was not left as a free parameter, but was fixed to its known true value. The Bayesian method of setting ff, assuming a single model is ....
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S. Sibisi (1991). `Bayesian interpolation', in Grandy and Schick, eds. (1991), 349--355.
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