Statistics seminars
Liverpool University Statistics Division
Time: 2pm, Wednesday October 13th
Speaker: Anthony Ledford, University of Surrey
Title: Diagnostics for dependence within time-series extremes
Time: 2pm, Wednesday October 20th
Speaker: Gesine Reinert, University of Cambridge
Title: Stein's method for epidemic processes
Venue for both talks: Room 2.11, Maths & Oceanography Building, University of
Liverpool
Abstracts given below.
Full seminar programme available via http://www.liv.ac.uk/maths/SOR/
Damian Clancy
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October 13th
"Diagnostics for dependence within time-series extremes" (Anthony Ledford)
The analysis of extreme values within a stationary time series requires
various assumptions to be made concerning the long and short range
dependence features of the underlying process. We present a range of
diagnostic tools for assessing whether these dependence assumptions are
appropriate and for identifying structure within extreme events. These
tools are all based on tail characteristics of joint survivor functions,
but can be implemented using existing estimation methods for extremes of
univariate independent and identically distributed variables. We identify
a class of processes where these methods produce biased results and
present a new approach that addresses this difficulty. Our diagnostic aids
are illustrated through theoretical examples, simulation studies and by
application to rainfall and exchange rate data.
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October 20th
"Stein's method for epidemic processes" (Gesine Reinert)
A General Stochastic Epidemic with non-Markovian transition
behaviour is considered. At time $t = 0$, the population of total size $K$
consists of $aK$ individuals that are infected by a certain disease (and
infectious); the remaining $bK$ individuals are susceptible with respect
to that disease. We assume the durations of the infectious periods to be
i.i.d., but not necessarily exponentially distributed. An initially
susceptible individual gets infected as soon as the overall accumulated
infectiousness in the population exceeds the individual's level of
resistance. Thus the infection time may depend on the time course of
the epidemic. This generalizes the classical Markovian epidemic model.
A bound to the distance of the empirical measure
describing the average path behaviour, to its mean-field limit is
established, using Stein's method. The bound, being in fact the first
bound available for this mean-filed approximation for epidemics, gives
explicit constants depending on the time length that the epidemic is
observed, and on the total population size. Thus it is possible to assess
whether the (often used) mean-field approximation is reasonable.
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