### Abstract

Original language | English |
---|---|

Title of host publication | Maximum Entropy and Bayesian Methods |

Editors | Kenneth M. Hanson, Richard N. Silver |

Publisher | Springer Netherlands |

Pages | 229-236 |

Number of pages | 8 |

ISBN (Print) | 978-94-010-6284-8 978-94-011-5430-7 |

Publication status | Published - 1996 |

### Publication series

Name | Fundamental Theories of Physics |
---|---|

Publisher | Springer Netherlands |

### Fingerprint

### Keywords

- Electrical Engineering, Entropic Prior, Image Processing, Inverse Problem, Physics, general, Probability Theory and Stochastic Processes, Regularization, Statistical Physics, Dynamical Systems and Complexity, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Statistics, general

### Cite this

*Maximum Entropy and Bayesian Methods*(pp. 229-236). (Fundamental Theories of Physics). Springer Netherlands.

**On the Importance of α Marginalization in Maximum Entropy.** / Fischer, R.; Linden, W. Von Der; Dose, V.

Research output: Chapter in Book/Report/Conference proceeding › Other chapter contribution › Research

*Maximum Entropy and Bayesian Methods.*Fundamental Theories of Physics, Springer Netherlands, pp. 229-236.

}

TY - CHAP

T1 - On the Importance of α Marginalization in Maximum Entropy

AU - Fischer, R.

AU - Linden, W. Von Der

AU - Dose, V.

N1 - DOI: 10.1007/978-94-011-5430-727

PY - 1996

Y1 - 1996

N2 - The correct entropic prior, computed by marginalization over the reg- ularization parameter a, is used to invert photoemission data and to restore the famous “Susie” image. Comparison with the conventional maximum entropy procedure shows less overfitting of noise and demonstrates the residual ringing which is intrinsic to ill-posed inversion problems. An improvement to the steepest descent approximation reveals the reason for the overfitting. On top of that, the correct treatment of the regularization parameter is vital for the existence of the continuum-limit of MaxEnt.

AB - The correct entropic prior, computed by marginalization over the reg- ularization parameter a, is used to invert photoemission data and to restore the famous “Susie” image. Comparison with the conventional maximum entropy procedure shows less overfitting of noise and demonstrates the residual ringing which is intrinsic to ill-posed inversion problems. An improvement to the steepest descent approximation reveals the reason for the overfitting. On top of that, the correct treatment of the regularization parameter is vital for the existence of the continuum-limit of MaxEnt.

KW - Electrical Engineering, Entropic Prior, Image Processing, Inverse Problem, Physics, general, Probability Theory and Stochastic Processes, Regularization, Statistical Physics, Dynamical Systems and Complexity, Statistics for Engineering, Physics, Computer

M3 - Other chapter contribution

SN - 978-94-010-6284-8 978-94-011-5430-7

T3 - Fundamental Theories of Physics

SP - 229

EP - 236

BT - Maximum Entropy and Bayesian Methods

A2 - Hanson, Kenneth M.

A2 - Silver, Richard N.

PB - Springer Netherlands

ER -