On Neyman–Pearson minimax detection of Poisson process intensity

The problem of the minimax testing of the Poisson process intensity \({\mathbf{s}}\) is considered. For a given intensity \({\mathbf{p}}\) and a set \(\mathcal{Q}\), the minimax testing of the simple hypothesis \(H_{0}: {\mathbf{s}} = {\mathbf{p}}\) against the composite alternative \(H_{1}: {\mathbf{s}} = {\mathbf{q}},\,{\mathbf{q}} \in \mathcal{Q}\) is investigated. The case, when the 1-st kind error probability \(\alpha \) is fixed and we are interested in the minimal possible 2-nd kind error probability \(\beta ({\mathbf{p}},\mathcal{Q})\), is considered. What is the maximal set \(\mathcal{Q}\), which can be replaced by an intensity \({\mathbf{q}} \in \mathcal{Q}\) without any loss of testing performance? In the asymptotic case (\(T\rightarrow \infty \)) that maximal set \(\mathcal{Q}\) is described.

     

Detonation waves in polydisperse gas suspensions of monofuel in tubes with an abrupt expansion

The distinctive features of detonation wave propagation in polydisperse (double-fraction) gas suspensions of a monofuel in tubes with an abrupt expansion are numerically investigated. Numerical calculations are performed for different sizes and relative mass contents of the particles of both fractions. A comparative analysis of the effect of mono- and polydisperse monofuel particles on the detonation wave mitigation is made. The dependences of the critical tube-diameter ratio of a sectional pipeline on the relative mass content and polydispersity of monofuel particles with different sizes are presented.     

On minimax robust testing of composite hypotheses on Poisson process intensity

Statistical Inference for Stochastic Processes - The problem on the minimax testing of a Poisson process intensity is considered. For a given disjoint sets $${{\mathcal {S}}}_T$$ and $${{\mathcal...