One of the most remarkable examples of fast technology transfer from new developments in mathematical probability theory to applied statistical methodology is the use of counting processes, martingales in continuous time, and stochastic integration in event history analysis. By this (or generalized survival analysis), we understand the study of a collection of individuals, each moving among a finite (usually small) number of states. A basic example is moving from alive to dead, which forms the basis of survival analysis. Compared to other branches of statistics, this area is characterized by the dynamic temporal aspect, making modelling via the intensities useful, and by the special patterns of incompleteness of observation, of which right-censoring in survival analysis is the most important and best known example.
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