## A Bayesian Approach to Detection of Small Low Emission Sources, preprint 2010

Citations: | 1 - 1 self |

### BibTeX

@MISC{Xun_abayesian,

author = {Xiaolei Xun and Bani Mallick and Raymond J. Carroll},

title = {A Bayesian Approach to Detection of Small Low Emission Sources, preprint 2010},

year = {}

}

### OpenURL

### Abstract

Abstract. The article addresses the problem of detecting presence and location of a small low emission source inside of an object, when the background noise dominates. This problem arises, for instance, in some homeland security applications. The goal is to reach the signal-to-noise ratio (SNR) levels on the order of 10−3. A Bayesian approach to this problem is implemented in 2D. The method allows inference not only about the existence of the source, but also about its location. We derive Bayes factors for model selection and estimation of location based on Markov Chain Monte Carlo simulation. A simulation study shows that with sufficiently high total emission level, our method can effectively locate the source or indicate its absence. 1.

### Citations

988 | Bayes factors
- Kass, Raftery
- 1995
(Show Context)
Citation Context ...orted by the data. Otherwise, ... |

354 | Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (disc: P53-102 - Smith, Roberts - 1993 |

137 | The intrinsic Bayes factor for model selection and prediction - J, Pericchi - 1996 |

116 | Bayesian statistical inference for psychological research - Edwards, Lindman, et al. - 1963 |

105 |
Linograms in image reconstruction from projections
- Edholm
- 1987
(Show Context)
Citation Context ... KUCHMENT background). In other words, only about 1% of detected hits are by the ballistic particles coming from the source. Although medical emission tomographic imaging faces similar problems (e.g. =-=[9]-=-), the overwhelming level of noise that has just been mentioned would be considered impossible to handle there. So, how can one possibly attack this problem? In the applications we have in mind, the r... |

45 | Theory of Probability (3rd edition - Jeffreys - 1960 |

33 | Methods for approximating integrals in statistics with special emphasis on Bayesian integration - Evans, Swartz - 1995 |

26 |
Weight of Evidence: A Brief Survey
- Good, J
- 1985
(Show Context)
Citation Context ...tery [11], when the Bayes factor exceeds 3, 20 and 150, one can say that, correspondingly, a positive, strong, and overwhelming evidence exists that a source is present. See [10, Appendix B], [6] and =-=[7]-=- for further interpretation of Bayes factors. We thus need the marginal distributions pr( ˜ ... |

20 | Likelihood ratio tests in linear mixed models with one variance component
- Crainiceanu, Ruppert
- 2004
(Show Context)
Citation Context ...inference as to whether a non-negative parameter ... |

14 |
AE: Hypothesis testing and model selection. Markov Chain Monte Carlo in Practice
- Raftery
- 1996
(Show Context)
Citation Context ...alculated as ˆBF = ˆpr( ˜ ... |

8 |
Implementing Bayesian methods in forensic science. Paper presented at the Fourth Valencia International Meeting on Bayesian Statistics
- Evett
- 1991
(Show Context)
Citation Context ... and Raftery [11], when the Bayes factor exceeds 3, 20 and 150, one can say that, correspondingly, a positive, strong, and overwhelming evidence exists that a source is present. See [10, Appendix B], =-=[6]-=- and [7] for further interpretation of Bayes factors. We thus need the marginal distributions pr( ˜ ... |

6 |
On learning strategies for evolutionary Monte Carlo. Statistics and Computing
- Goswami, Liu
- 2007
(Show Context)
Citation Context ...ts of the implementation, can skip the following sub-sections and move directly to Section 4. 3.1.1. Implementing the Parallel Tempering Algorithm. One can find discussions of tempering algorithms in =-=[8]-=- and [13]. We run ... |

5 |
C-SPRINT: a prototype Compton camera system for low energy gammaray imaging
- LeBlanc, Clinthorne, et al.
- 1998
(Show Context)
Citation Context ...The idea is that if a source is present, this might lead to a statistically significant increase in the number of trajectories satisfying (1), and thus to detection. Under Compton type cameras (e.g., =-=[1, 12]-=-), which determine a hollow cone of possible directions, can be used instead.4XIAOLEI XUN, BANI MALLICK, RAYMOND J. CARROLL AND PETER KUCHMENT appropriate conditions (geometrically sufficiently small... |

2 |
Advanced Markov chain Monte Carlo: Learning from Past Samples
- Liang, Liu, et al.
- 2010
(Show Context)
Citation Context ...e implementation, can skip the following sub-sections and move directly to Section 4. 3.1.1. Implementing the Parallel Tempering Algorithm. One can find discussions of tempering algorithms in [8] and =-=[13]-=-. We run ... |

1 | Detecting small low emission radiating sources, preprint 2010
- Allmaras, Darrow, et al.
(Show Context)
Citation Context ... problem? In the applications we have in mind, the radiating source, if present, would be significantly (on the order of hundred times) geometrically smaller than the whole object. As is explained in =-=[1]-=-, this, and the availability of detectors determining direction of an incoming particle, make detection conceivable under appropriate conditions. In this text, we consider the 2... |