'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 $b$, we provide the limiting distribution for the amount of time that the workload process spends above level $b$ over the busy cycle straddling the origin, as $b\to\infty$. Our results can be interpreted as showing that long delays occur in large clumps of size of order $b^{2-1/H}$. 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 $(X_n:n\geq 0)$ be a sequence of i.i.d. r.v.'s with negative mean. Set $S_0=0$ and define $S_n=X_1+... +X_n$. We propose an importance sampling algorithm to estimate the tail of $M=\max \{S_n:n\geq 0\}$ 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 $t$ is uniformly bounded by $\mathcal{O}(1/\bar\gamma^2)$ where $\bar\gamma$ 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