Statistical models for analysing criminal careers
The estimation of probabilistic deformable template models in computer vision or of probabilistic atlases in Computational Anatomy are core issues in both fields. A first coherent statistical framework where the geometrical variability is modelled as a hidden random variable has been given by [S. Allassonnière et al., J. Roy. Stat. Soc.69 (2007) 3–29]. They introduce a Bayesian approach and mixture of them to estimate deformable template models. A consistent stochastic algorithm has been introduced...
This paper deals with the problem of estimation in the parametric case for discrete random variables. Their study is facilitated by the powerful method of probability generating function.
Let be a biased estimate of the parameter based on all observations , , and let () be the same estimate of the parameter obtained after deletion of the -th observation. If the expectation of the estimators and are expressed as where is a known sequence of real numbers and is a function of , then this system of equations can be regarded as a linear model. The least squares method gives the generalized jackknife estimator. Using this method, it is possible to obtain the unbiased...
The present paper deals with the extension of the likelihood estimation to the situation where the experimentation does not provide exact information but rather vague information.The extension process tries to achieve three fundamental objectives: the new method must be an extension of the maximum likelihood method, it has to be very simple to apply and it must allow for an interesting interpretation.These objectives are achieved herein by using the following concepts: the fuzzy information (introduced...