Conditional Γ-minimax prediction with a precautionary loss function in a marked point process model

Statistics ◽  
2016 ◽  
Vol 50 (6) ◽  
pp. 1411-1420
Author(s):  
Daniel Lazar
Keyword(s):  
Point Process ◽  
Loss Function ◽  
Process Model ◽  
Marked Point ◽  
Marked Point Process ◽  
Point Process Model

Bayesian object recognition with baddeley's delta loss

1998 ◽  
Vol 30 (1) ◽  
pp. 64-84 ◽  
Author(s):  
Håvard Rue ◽  
Anne Randi Syversveen
Keyword(s):  
Object Recognition ◽  
Point Process ◽  
Loss Function ◽  
Process Model ◽  
Marked Point ◽  
Process Models ◽  
Bayesian Estimator ◽  
Marked Point Process ◽  
Point Estimate ◽  
Step Algorithm

A common problem in Bayesian object recognition using marked point process models is to produce a point estimate of the true underlying object configuration: the number of objects and the size, location and shape of each object. We use decision theory and the concept of loss functions to design a more reasonable estimator for this purpose, rather than using the common zero-one loss corresponding to the maximum a posteriori estimator. We propose to use the squared Δ-metric of Baddeley (1992) as our loss function and demonstrate that the corresponding optimal Bayesian estimator can be well approximated by combining Markov chain Monte Carlo methods with simulated annealing into a two-step algorithm. The proposed loss function is tested using a marked point process model developed for locating cells in confocal microscopy images.

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