During the last ten years my research in statistics and applied
probability has been focused on four areas:
- Prediction Theory for Finite Populations
- Reliability Theory
- Adaptive Procedures and Optimal Designs
- Distributions of stopping Times Defined on Compound Poisson
Each one of these areas is very wide and rich with problems. The
type of problems I have concentrated on are:
- Optimal predictors of population quantities, like the
population total or the population variance. These include
Bayesian predictors, minimax admissible, etc.
- Sequential methods for software testing (detection of errors).
In addition I study the operating characteristics of sequential
stopping rules for reliability testing and estimation.
- Adaptive decision procedures are connected with various
procedures which converge to the optimal ones, when essential
parameters are unknown. These contain "Bandits Problems", the
sequential search of optimal dosages in Phase I Clinical Trials,
- In this area of research I develop the distributions of
stopping times, or first-exit times of compound Poisson
processes. The results have wide applications in queuing theory
(distribution of the length of the busy period), in inventory
theory, dam theory and risk theory for insurance.