The Neyman type-A and Thomas counting distributions provide a useful description for a broad variety of phenomena from the distribution of larvas on small plots of land to the distribution of galaxies in space. They turn out to provide a good description for the counting of photons generated by multiplied Poisson processes, as long as the time course of the multiplication is short compared with...

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i), its probability of type I error is below a pre-specifi...

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with high probability: (i) its probability of type I error is below a pre-specifie...

The Neyman-Scott cluster point process, originally developed in 1958 to describe the distribution of galaxies in space [l], has become an important representation for a broad range of phenomena in the physical, biological, and social sciences [2], [3]. Bartlett [4] has shown that the shot-noise driven doubly stochastic Poisson point process (SNDP) is a special but important example of a Neyman-...

We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach as in Witting (1985). Results of Aubin & Ekeland (1984) from non-smooth convex analysis are employed, along with a theorem of Komlós (1967), in order to establish the existence of a max-min optimal test in considerable generality, and to investigate its p...