Empty confidence sets for epidemics, branching processes and Brownian motion

This paper treats some examples where likelihood-based inference for certain model parameters may produce empty confidence sets. The first example concerns epidemics, and the parameter of interest is the basic reproduction number R-sub-0, which is to be estimated from the final size of an epidemic in a finite population. The second example treats estimation of the mean of the offspring distribution in a branching process, based on observing the total progeny, i.e. the total number of individuals ever born in the branching process. The final example considers estimation of the linear drift in a Brownian motion, based on observing the first hitting time of some horizontal barrier. Copyright Biometrika Trust 2002, Oxford University Press.

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