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Approximate distributions for Maximum Likelihood and maximum a posteriori estimates under a Gaussian noise model

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1230)

Abstract

The performance of Maximum Likelihood (ML) and Maximum a posteriori (MAP) estimates in nonlinear problems at low data SNR is not well predicted by the Cramér-Rao or other lower bounds on variance. In order to better characterize the distribution of ML and MAP estimates under these conditions, we derive an approximate density for the conditional distribution of such estimates. In one example, this approximate distribution captures the essential features of the distribution of ML and MAP estimates in the presence of Gaussian-distributed noise.

Keywords

  • Approximate Density
  • Pixel Variance
  • Gaussian Noise Model
  • True Parameter Vector
  • Observe Fisher Information Matrix

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1997 Springer-Verlag Berlin Heidelberg

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Abbey, C.K., Clarkson, E., Barrett, H.H., Müller, S.P., Rybicki, F.J. (1997). Approximate distributions for Maximum Likelihood and maximum a posteriori estimates under a Gaussian noise model. In: Duncan, J., Gindi, G. (eds) Information Processing in Medical Imaging. IPMI 1997. Lecture Notes in Computer Science, vol 1230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63046-5_13

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  • DOI: https://doi.org/10.1007/3-540-63046-5_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63046-3

  • Online ISBN: 978-3-540-69070-2

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