Analysis of probability distribution of inverse problem of nonlinear model | |
Tong, Xiaolin; Wang, Zhenzhan; Li, Qingxia | |
Department | 微波遥感部 |
Source Publication | Progress in Electromagnetics Research Symposium |
2014 | |
Pages | 1785-1787 |
Language | 英语 |
ISSN | 1559-9450 |
ISBN | 9781934142288 |
Abstract | In the remote sensing field, the SNR is very low and the model is nonlinearity usually. Thus, it is important to analyze the impact of model nonlinearity. Probability distribution can be used to analyze the parameter distribution directly. Some issues involving priors and posteriors were proposed for models with significant nonlinearity and low signal to noise ratio (SNR). Two important issues are as follows: (1) The unimodal probability density function (PDF) of the observation quantity can give rise to a multi-modal PDF of the parameter (parameter). This property could lead to an incorrect maximum a posteriori estimate or a biased mean central estimate. It means that the biased evaluation results could be derived from statistical methods; (2) The rules for assigning non-informative priors in the measurement approach are different from the principle of maximum entropy. The authors point out the distinctions between PDF and probability distribution of non-linear models in the parameter space based on the resolution relationship between the observation space and the parameter space. For models with significant nonlinearity, if the unit grid interval of the observation space is considered regular, then the unit grid interval of the parameter space is considered irregular. The distribution obtained from regular grid is an approximation to the PDF. The probability should be calculated by integrating the PDF in the corresponding irregular grid. The difference between PDF and probability distribution gives rise to the difficulty in reverse problems. Analyzing the properties of the parameter by using the probability distribution instead of the PDF in the parameter space is necessary. The corresponding relationship between the observation and the parameter is researched based on resolution limit analysis. The non-uniform prior PDF was derived from uniform prior probability distribution in accordance with the principle of maximum entropy. Nonlinear analysis of the nature of the probability density distribution is necessary to eliminate bias caused by statistical methods. |
Conference Name | Progress in Electromagnetics Research Symposium, PIERS 2014 |
Conference Date | August 25, 2014 - August 28, 2014 |
Conference Place | Guangzhou, China |
Indexed By | EI |
Document Type | 会议论文 |
Identifier | http://ir.nssc.ac.cn/handle/122/4357 |
Collection | 微波遥感部 |
Recommended Citation GB/T 7714 | Tong, Xiaolin,Wang, Zhenzhan,Li, Qingxia. Analysis of probability distribution of inverse problem of nonlinear model[C]:Electromagnetics Academy,2014:1785-1787. |
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20143A141785.pdf（281KB） | 开放获取 | CC BY-NC-SA | Application Full Text |
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