Asymptotic behavior of the likelihood function. Asymptotically sufficient statistics

1974 ◽  
pp. 40-50
Author(s):  
Lionel Weiss ◽  
Jacob Wolfowitz
Keyword(s):  
Asymptotic Behavior ◽  
Likelihood Function ◽  
Sufficient Statistics

scholarly journals Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Ralf Zimmermann
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Gaussian Processes ◽  
Likelihood Function ◽  
Covariance Structure ◽  
Kriging Model ◽  
Correlation Matrices ◽  
Covariance Functions ◽  
Method Of Maximum Likelihood ◽  
Model Training

The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood of spatial Gaussian predictor models as a function of its hyperparameters is investigated theoretically. Asymptotic sandwich bounds for the maximum likelihood function in terms of the condition number of the associated covariance matrix are established. As a consequence, the main result is obtained:optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood-based Kriging model training is necessarily bound to fail.

A mutual information‐based likelihood function for particle filter flood extent assimilation

2021 ◽  
Author(s):  
Antara Dasgupta ◽  
Renaud Hostache ◽  
RAAJ Ramasankaran ◽  
Guy J.‐P Schumann ◽  
Stefania Grimaldi ◽  
...  
Keyword(s):  
Mutual Information ◽  
Particle Filter ◽  
Likelihood Function
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