Archivio 2005
54
seminari
Sequential experiments are widely used in pharmaceutical and clinical
practice. These procedures are very flexible since the experimenter can
modify the trial as it goes along. A large number of them have been
suggested in the literature: they correspond to different purposes
of the experimenters': accurate inference, cost saving, ethical
preoccupations, etc. Sequential procedures, however, pose problems as
regards the correct inferential paradigm.
In this presentation I give some results on the asymptotic optimality
of a large class of sequential designs when the responses belong to the
exponential family. In particular, for designs based on the step-by-step
updating of the parameter estimates by maximum likelihood, the MLE's
retain the strong consistency and asymptotic normality properties.
Other results concern stopping rules and inverse sampling.
A mention will be made of a special type of sequential experiments, i.e.
Markovian ones:
they include Biased coin Designs, Urn models, and Up-and-Down Designs.
Abstract:
<br />
Almost all work on empirical processes, so far,
<br />
concerned i.i.d.
<br />
data. To my knowledge, the non independent case is almost neglected and
<br />
essentially
<br />
restricted to ergodic sequences. In this talk, convergence in distribution
<br />
(under uniform distance) of empirical processes, based on non ergodic data,
<br />
is investigated. I focus on
<br />
conditionally identically distributed sequences of
<br />
random variables. This type of dependence, more general than
<br />
exchangeability, plays a role in
<br />
Bayesian predictive inference. Some foundational problems, connected to
<br />
convergence in distribution of non measurable random elements, are also
<br />
discussed. Among other things, necessary and sufficient conditions for
<br />
convergence in distribution of empirical processes for exchangeable data
<br />
are given.