Model Selection in Statistical Inference and Geometric Fitting Kenichi
نویسنده
چکیده
Taking line tting to points in two dimensions as a typical example, we point out the inherent di erence between statistical inference and geometric tting. We describe their duality in the sense that the asymptotic properties of statistical inference in the limit of an in nite number of observations hold for geometric tting in the limit of in nitesimal perturbations. We contrast stochastic model selection with geometric model selection and describe the di erence between Akaike's AIC and the geometric AIC in their derivations.
منابع مشابه
Uncertainty Modeling and Geometric Inference
We investigate the meaning of “statistical methods” for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to “geometric fitting” and “geometric model selection”. We point out that a correspondence exists between the standard statistical analysis and the...
متن کاملModel Selection for Geometric Inference
Contrasting “geometric fitting”, for which the noise level is taken as the asymptotic variable, with “statistical inference”, for which the number of observations is taken as the asymptotic variable, we give a new definition of the “geometric AIC” and the “geometric MDL” as the counterparts of Akaike’s AIC and Rissanen’s MDL. We discuss various theoretical and practical problems that emerge fro...
متن کاملHow Are Statistical Methods for Geometric Inference Justified?
This paper investigates the meaning of “statistical methods” for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations for computer vision in general, we discuss implications of asymptotic analysis in reference to “geometric fitting” and “geometric model selection”. For the latter, we point out the prominent characterist...
متن کاملFor geometric inference from images, what kind of statistical model is necessary?
In order to facilitate smooth communications with researchers in other fields including statistics, this paper investigates the meaning of “statistical methods” for geometric inference based on image feature points. We point out that statistical analysis does not make sense unless the underlying “statistical ensemble” is clearly defined. We trace back the origin of feature uncertainty to image ...
متن کاملGeometric BIC
The author introduced the “geometric AIC” and the “geometric MDL” as model selection criteria for geometric fitting problems. These correspond to Akaike’s “AIC” and Rissanen’s “BIC”, respectively, well known in the statistical estimation framework. Another criterion well known is Schwarz’ “BIC”, but its counterpart for geometric fitting has been unknown. This paper introduces the corresponding ...
متن کامل