882 research outputs found
'Looking back, looking forward': An interview with Emeritus Professor Ted Glynn on his involvement in special education
In interview with Dr Peter Stanley, Professor Glynn reflects on how he became involved in special education, and on his work with the Pause Prompt Praise reading strategy, the Mangere Guidance and Learning Unit (which gave rise to Guidance and Learning Units nationally), and Glenburn Residential Centre, which was an innovative study of child behaviour management across multiple settings. Professor Glynn also talks about his time training psychologists on both the Auckland and Otago Diploma in Educational Psychology programmes and about his involvement in training Resource Teachers of Learning and Behaviour. Glynn advocates for inclusion, and for regular class teachers to be principally responsible for working with students with special needs. He also contends that much greater attention should be given to the cultural experiences of children in special and mainstream education
Conditional limit theorems for regulated fractional Brownian motion
We consider a stationary fluid queue with fractional Brownian motion input.
Conditional on the workload at time zero being greater than a large value ,
we provide the limiting distribution for the amount of time that the workload
process spends above level over the busy cycle straddling the origin, as
. Our results can be interpreted as showing that long delays occur
in large clumps of size of order . The conditional limit result
involves a finer scaling of the queueing process than fluid analysis, thereby
departing from previous related literature.Comment: Published in at http://dx.doi.org/10.1214/09-AAP605 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Efficient rare-event simulation for the maximum of heavy-tailed random walks
Let be a sequence of i.i.d. r.v.'s with negative mean. Set
and define . We propose an importance sampling
algorithm to estimate the tail of that is strongly
efficient for both light and heavy-tailed increment distributions. Moreover, in
the case of heavy-tailed increments and under additional technical assumptions,
our estimator can be shown to have asymptotically vanishing relative variance
in the sense that its coefficient of variation vanishes as the tail parameter
increases. A key feature of our algorithm is that it is state-dependent. In the
presence of light tails, our procedure leads to Siegmund's (1979) algorithm.
The rigorous analysis of efficiency requires new Lyapunov-type inequalities
that can be useful in the study of more general importance sampling algorithms.Comment: Published in at http://dx.doi.org/10.1214/07-AAP485 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Exact Simulation of Non-stationary Reflected Brownian Motion
This paper develops the first method for the exact simulation of reflected
Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The
running time of generating exact samples of non-stationary RBM at any time
is uniformly bounded by where is the
average drift of the process. The method can be used as a guide for planning
simulations of complex queueing systems with non-stationary arrival rates
and/or service time
Shape-constrained Estimation of Value Functions
We present a fully nonparametric method to estimate the value function, via
simulation, in the context of expected infinite-horizon discounted rewards for
Markov chains. Estimating such value functions plays an important role in
approximate dynamic programming and applied probability in general. We
incorporate "soft information" into the estimation algorithm, such as knowledge
of convexity, monotonicity, or Lipchitz constants. In the presence of such
information, a nonparametric estimator for the value function can be computed
that is provably consistent as the simulated time horizon tends to infinity. As
an application, we implement our method on price tolling agreement contracts in
energy markets
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